Hirotaka Ono - Academia.edu (original) (raw)
Papers by Hirotaka Ono
Research Square (Research Square), Apr 18, 2024
Proceedings of the ... AAAI Conference on Artificial Intelligence, Mar 24, 2024
The uniqueness of an optimal solution to a combinatorial optimization problem attracts many field... more The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and an instance with only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a "pre-assignment" approach for the vertex cover problem as a typical combinatorial optimization problem and discusses its computational complexity. First, we show that the problem is Σ P 2-complete in general, while the problem becomes NP-complete when an input graph is bipartite. We then present an O(2.1996 n)-time algorithm for general graphs and an O(1.9181 n)-time algorithm for bipartite graphs, where n is the number of vertices. The latter is based on an FPT algorithm with O * (3.6791 τ) time for vertex cover number τ. Furthermore, we show that the problem for trees can be solved in O(1.4143 n) time.
arXiv (Cornell University), May 1, 2019
Independent Set Reconfiguration is one of the most well-studied problems in the setting of combin... more Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016].
arXiv (Cornell University), Jul 7, 2021
The cost-sharing connection game is a variant of routing games on a network. In this model, given... more The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge costs and edge capacities, each agent wants to construct a path from a source to a sink with low cost. The users share the cost of each edge based on a cost-sharing function. One of the simple cost-sharing functions is defined as the cost divided by the number of users. Most of the previous papers about cost-sharing connection games addressed this cost-sharing function. It models an ideal setting where no overhead arises when people share things, though it might be quite rare in real life; it is more realistic to consider the setting that the cost paid by an agent is the original cost per the number of agents using the edge plus the overhead. In this paper, we model the more realistic scenario of cost-sharing connection games by generalizing cost-sharing functions. The arguments on the model are based on not concrete cost-sharing functions but cost-sharing functions under a reasonable scheme; they are applicable for a broad class of cost-sharing functions satisfying the following natural properties: they are (1) non-increasing, (2) lower bounded by the original cost per the number of the agents, and (3) upper bounded by the original cost, which enables to represent various scenarios of cost-sharing. We investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) under sum-cost and max-cost criteria with the generalized cost-sharing function. Despite the generalization, we obtain the same tight bounds of PoA and PoS as the cost-sharing with no overhead except PoS under sum-cost. Moreover, for the sum-cost case, the lower bound on PoS increases from log n to n + 1/n − 1 by the generalization, which is also almost tight because the upper bound is n. We further investigate the bounds from the viewpoints of graph classes, such as parallel-link graphs, series-parallel graphs, and directed acyclic graphs, which show critical differences in PoS/PoA values.
Consider the longest path problem for directed acyclic graphs (DAGs), where a mutually independen... more Consider the longest path problem for directed acyclic graphs (DAGs), where a mutually independent random variable is associated with each of the edges as its edge length. Given
Springer eBooks, 2023
We study the following variant of the 15 puzzle. Given a graph and two token placements on the ve... more We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.
arXiv (Cornell University), Jul 7, 2021
The cost-sharing connection game is a variant of routing games on a network. In this model, given... more The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge-costs and edge-capacities, each agent wants to construct a path from a source to a sink with low cost. The cost of each edge is shared by the users based on a cost-sharing function. One of simple cost-sharing functions is defined as the cost divided by the number of users. In fact, most of the previous papers about cost-sharing connection games addressed this cost-sharing function. It models an ideal setting, where no overhead arises when people share things, though it might be quite rare in real life; it is more realistic to consider the setting that the cost paid by an agent is the original cost per the number of the agents plus the overhead. In this paper, we model the more realistic scenario of cost-sharing connection games by generalizing cost-sharing functions. The arguments on the model do not depend on specific cost-sharing functions, and are applicable for a wide class of cost-sharing functions satisfying the following natural properties: they are (1) non-increasing, (2) lower bounded by the original cost per the number of the agents, and (3) upper bounded by the original cost, which enables to represent various scenarios of cost-sharing. We investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) under sum-cost and max-cost criteria with the generalized cost-sharing function. In spite of the generalization, we obtain the same bounds of PoA and PoS as the cost-sharing with no overhead except PoS under sum-cost. Note that these bounds are tight. In the case of sum-cost, the lower bound on PoS increases from log n to n + 1/n − 1 by the generalization, which is also almost tight because the upper bound is n. We further investigate the bounds from the viewpoints of graph classes, such as parallel-link graphs, series-parallel graphs, and directed acyclic graphs, which show critical differences of PoS/PoA values.
Algorithmica, 2020
Independent Set Reconfiguration is one of the most well-studied problems in the setting of combin... more Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016].
Discrete Applied Mathematics, 2018
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Algorithmica, 2017
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Discrete Applied Mathematics, 2019
In the economic activities, the central bank has an important role to cover payments of banks, wh... more In the economic activities, the central bank has an important role to cover payments of banks, when they are short of funds to clear their debts. For this purpose, the central bank timely puts funds so that the economic activities go smooth. Since payments in this mechanism are processed sequentially, the total amount of funds put by the central bank critically depends on the order of the payments. Then an interest goes to the amount to prepare if the order of the payments can be controlled by the central bank, or if it is determined under the worst case scenario. This motivates us to introduce a brand-new problem, which we call the settlement fund circulation problem. The problems are formulated as follows: Let G = (V, A) be a directed multigraph with a vertex set V and an arc set A. Each arc a ∈ A is endowed debt d(a) ≥ 0, and the debts are settled sequentially under a sequence π of arcs. Each vertex v ∈ V is put fund in the amount of p π (v) ≥ 0 under the sequence. The minimum/maximum settlement fund circulation problem (Min-SFC/Max-SFC) in a given graph G with debts d : A → R + ∪ {0} asks to find a bijection π : A → {1, 2,.. . , |A|} that minimizes/maximizes the total funds v∈V p π (v). In this paper, we show that both Min-SFC and Max-SFC are NP-hard; in particular, Min-SFC is (I) strongly NP-hard even if G is (i) a multigraph with |V | = 2 or (ii) a simple graph with treewidth at most two, and is (II) (not necessarily strongly) NP-hard for simple trees of diameter four, while it is solvable in polynomial time for stars. Also, we identify several polynomial time solvable cases for both problems.
Discrete Applied Mathematics, 2019
In this paper, we study covering and domination problems on directed graphs. Although undirected ... more In this paper, we study covering and domination problems on directed graphs. Although undirected Vertex Cover and Edge Dominating Set are well-studied classical graph problems, the directed versions have not been studied much due to the lack of clear definitions. We give natural definitions for Directed r-In (Out) Vertex Cover and Directed (p, q)-Edge Dominating Set as directed generations of Vertex Cover and Edge Dominating Set. For these problems, we show that (1) Directed r-In (Out) Vertex Cover and Directed (p, q)-Edge Dominating Set are NP-complete on planar directed acyclic graphs except when r = 1 or (p, q) = (0, 0), (2) if r ≥ 2, Directed r-In (Out) Vertex Cover is W [2]hard and c ln k-inapproximable on directed acyclic graphs, (3) if either p or q is greater than 1, Directed (p, q)-Edge Dominating Set is W [2]-hard and c ln k-inapproximable on directed acyclic graphs, (4) all problems can be solved in polynomial time on trees, and (5) Directed (0, 1), (1, 0), (1, 1)-Edge Dominating Set are fixed-parameter tractable in general graphs. The first result implies that (directed) r-Dominating Set on directed line graphs is NPcomplete even if r = 1.
2015 IEEE International Symposium on Information Theory (ISIT), 2015
A code design problem for memory devises with restricted state transitions is formulated as a com... more A code design problem for memory devises with restricted state transitions is formulated as a combinatorial optimization problem that is called a subgraph domatic partition (subDP) problem. If any neighbor set of a given state transition graph contains all the colors, then the coloring is said to be valid. The goal of a subDP problem is to find a valid coloring with the largest number of colors for a subgraph of a given directed graph. The number of colors in an optimal valid coloring gives the writing capacity of a given state transition graph. The subDP problems are computationally hard; it is proved to be NP-complete in this paper. One of our main contributions in this paper is to show the asymptotic behavior of the writing capacity C(G) for sequences of dense bidirectional graphs, that is given by C(G) = Ω(n/ ln n) where n is the number of nodes. A probabilistic method called Lovász local lemma (LLL) plays an essential role to derive the asymptotic expression.
Lecture Notes in Computer Science, 2000
In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to ... more In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to ÿnd relations among attributes are considered important. In this paper, given a data set (T; F) where T ⊆ {0; 1} n denotes a set of positive examples and F ⊆ {0; 1} n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We ÿrst study computational complexity of the problem of ÿnding decomposable Boolean extensions. Since the problem turns out to be intractable (i.e., NP-complete), we propose a heuristic algorithm in the second half of the paper. Our method searches a decomposable partition of the set of all attributes by using the error sizes of almost-ÿt decomposable extensions as a guiding measure, and then ÿnds structural relations among the attributes in the obtained partition. Some results of numerical experiment on randomly generated data sets are also reported.
Lecture Notes in Computer Science, 2014
Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and im... more Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between I0 and Ir with the minimum number of token movements.
Lecture Notes in Computer Science, 2010
A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e.,... more A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e., CORDA) robots is investigated in this paper. The conventional pattern formation problem assumes that the target pattern is given as a set of the positions by their coordinates in the global coordinate system, under the assumption that the robots are not aware of it. In the pattern formation problem we discuss in this paper, the points comprising the pattern are assumed to be "visible" to all robots, like landmarks. However, the robots still cannot obtain their positions in the global coordinate system. This paper shows that this pattern formation problem is solvable by oblivious asynchronous robots through the optimum matching between the robots and the pattern's points. Our study is partly motivated by the state-of-arts of the conventional pattern formation problem by oblivious asynchronous robots; description and correctness proof of a formation algorithm is usually complicated and ambiguous, because of the oblivious and asynchronous natures of the robots. A modular method is thus looked for to describe and prove algorithm in a clearer and more concrete way. Our pattern formation problem and the formation algorithm based on the optimum matching are used as a primitive building block in the modular method.
Theoretical Computer Science, 2010
Given a finite graph G = (V, E) and a probability distribution π = (π v) v∈V on V , Metropolis wa... more Given a finite graph G = (V, E) and a probability distribution π = (π v) v∈V on V , Metropolis walks, i.e., random walks on G building on the Metropolis-Hastings algorithm obey a transition probability matrix P = (p uv) u,v∈V defined by, for any u, v ∈ V , p uv = 1 du min{ d u π v dvπu , 1} if v ∈ N (u), 1 − w =u p uw if u = v, 0 otherwise, and guarantee to have π as the stationary distribution, where N (u) is the set of adjacent vertices of u ∈ V and d u = |N (u)| is the degree of u. This paper shows that the hitting and the cover times of Metropolis walks are O(f n 2) and O(f n 2 log n), respectively, for any graph G of order n and any probability distribution π such that f = max u,v∈V π u /π v < ∞. We also show that there are graph G and stationary distribution π such that any random walk on G realizing π attains Ω(f n 2) hitting and Ω(f n 2 log n) cover times. It follows that the hitting and the cover times of Metropolis walks are Θ(f n 2) and Θ(f n 2 log n), respectively.
Theory of Computing Systems, 2014
A degree-constrained graph orientation of an undirected graph G is an assignment of a direction t... more A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W , the problems Max W-Light, Min W-Light, Max W-Heavy, and Min W-Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems' computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.
Lecture Notes in Computer Science, 2015
We study reconfiguration problems for cliques in a graph, which determine whether there exists a ... more We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs.
Research Square (Research Square), Apr 18, 2024
Proceedings of the ... AAAI Conference on Artificial Intelligence, Mar 24, 2024
The uniqueness of an optimal solution to a combinatorial optimization problem attracts many field... more The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and an instance with only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a "pre-assignment" approach for the vertex cover problem as a typical combinatorial optimization problem and discusses its computational complexity. First, we show that the problem is Σ P 2-complete in general, while the problem becomes NP-complete when an input graph is bipartite. We then present an O(2.1996 n)-time algorithm for general graphs and an O(1.9181 n)-time algorithm for bipartite graphs, where n is the number of vertices. The latter is based on an FPT algorithm with O * (3.6791 τ) time for vertex cover number τ. Furthermore, we show that the problem for trees can be solved in O(1.4143 n) time.
arXiv (Cornell University), May 1, 2019
Independent Set Reconfiguration is one of the most well-studied problems in the setting of combin... more Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016].
arXiv (Cornell University), Jul 7, 2021
The cost-sharing connection game is a variant of routing games on a network. In this model, given... more The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge costs and edge capacities, each agent wants to construct a path from a source to a sink with low cost. The users share the cost of each edge based on a cost-sharing function. One of the simple cost-sharing functions is defined as the cost divided by the number of users. Most of the previous papers about cost-sharing connection games addressed this cost-sharing function. It models an ideal setting where no overhead arises when people share things, though it might be quite rare in real life; it is more realistic to consider the setting that the cost paid by an agent is the original cost per the number of agents using the edge plus the overhead. In this paper, we model the more realistic scenario of cost-sharing connection games by generalizing cost-sharing functions. The arguments on the model are based on not concrete cost-sharing functions but cost-sharing functions under a reasonable scheme; they are applicable for a broad class of cost-sharing functions satisfying the following natural properties: they are (1) non-increasing, (2) lower bounded by the original cost per the number of the agents, and (3) upper bounded by the original cost, which enables to represent various scenarios of cost-sharing. We investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) under sum-cost and max-cost criteria with the generalized cost-sharing function. Despite the generalization, we obtain the same tight bounds of PoA and PoS as the cost-sharing with no overhead except PoS under sum-cost. Moreover, for the sum-cost case, the lower bound on PoS increases from log n to n + 1/n − 1 by the generalization, which is also almost tight because the upper bound is n. We further investigate the bounds from the viewpoints of graph classes, such as parallel-link graphs, series-parallel graphs, and directed acyclic graphs, which show critical differences in PoS/PoA values.
Consider the longest path problem for directed acyclic graphs (DAGs), where a mutually independen... more Consider the longest path problem for directed acyclic graphs (DAGs), where a mutually independent random variable is associated with each of the edges as its edge length. Given
Springer eBooks, 2023
We study the following variant of the 15 puzzle. Given a graph and two token placements on the ve... more We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of the given token placements from the other one. This problem was introduced as Sequential Token Swapping by Yamanaka et al. [JGAA 2019], who showed that the problem is intractable in general but polynomial-time solvable for trees, complete graphs, and cycles. In this paper, we present a polynomial-time algorithm for block-cactus graphs, which include all previously known cases. We also present general tools for showing the hardness of the problem on restricted graph classes such as chordal graphs and chordal bipartite graphs. We also show that the problem is hard on grids and king's graphs, which are the graphs corresponding to the 15 puzzle and its variant with relaxed moves.
arXiv (Cornell University), Jul 7, 2021
The cost-sharing connection game is a variant of routing games on a network. In this model, given... more The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge-costs and edge-capacities, each agent wants to construct a path from a source to a sink with low cost. The cost of each edge is shared by the users based on a cost-sharing function. One of simple cost-sharing functions is defined as the cost divided by the number of users. In fact, most of the previous papers about cost-sharing connection games addressed this cost-sharing function. It models an ideal setting, where no overhead arises when people share things, though it might be quite rare in real life; it is more realistic to consider the setting that the cost paid by an agent is the original cost per the number of the agents plus the overhead. In this paper, we model the more realistic scenario of cost-sharing connection games by generalizing cost-sharing functions. The arguments on the model do not depend on specific cost-sharing functions, and are applicable for a wide class of cost-sharing functions satisfying the following natural properties: they are (1) non-increasing, (2) lower bounded by the original cost per the number of the agents, and (3) upper bounded by the original cost, which enables to represent various scenarios of cost-sharing. We investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) under sum-cost and max-cost criteria with the generalized cost-sharing function. In spite of the generalization, we obtain the same bounds of PoA and PoS as the cost-sharing with no overhead except PoS under sum-cost. Note that these bounds are tight. In the case of sum-cost, the lower bound on PoS increases from log n to n + 1/n − 1 by the generalization, which is also almost tight because the upper bound is n. We further investigate the bounds from the viewpoints of graph classes, such as parallel-link graphs, series-parallel graphs, and directed acyclic graphs, which show critical differences of PoS/PoA values.
Algorithmica, 2020
Independent Set Reconfiguration is one of the most well-studied problems in the setting of combin... more Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016].
Discrete Applied Mathematics, 2018
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Algorithmica, 2017
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Discrete Applied Mathematics, 2019
In the economic activities, the central bank has an important role to cover payments of banks, wh... more In the economic activities, the central bank has an important role to cover payments of banks, when they are short of funds to clear their debts. For this purpose, the central bank timely puts funds so that the economic activities go smooth. Since payments in this mechanism are processed sequentially, the total amount of funds put by the central bank critically depends on the order of the payments. Then an interest goes to the amount to prepare if the order of the payments can be controlled by the central bank, or if it is determined under the worst case scenario. This motivates us to introduce a brand-new problem, which we call the settlement fund circulation problem. The problems are formulated as follows: Let G = (V, A) be a directed multigraph with a vertex set V and an arc set A. Each arc a ∈ A is endowed debt d(a) ≥ 0, and the debts are settled sequentially under a sequence π of arcs. Each vertex v ∈ V is put fund in the amount of p π (v) ≥ 0 under the sequence. The minimum/maximum settlement fund circulation problem (Min-SFC/Max-SFC) in a given graph G with debts d : A → R + ∪ {0} asks to find a bijection π : A → {1, 2,.. . , |A|} that minimizes/maximizes the total funds v∈V p π (v). In this paper, we show that both Min-SFC and Max-SFC are NP-hard; in particular, Min-SFC is (I) strongly NP-hard even if G is (i) a multigraph with |V | = 2 or (ii) a simple graph with treewidth at most two, and is (II) (not necessarily strongly) NP-hard for simple trees of diameter four, while it is solvable in polynomial time for stars. Also, we identify several polynomial time solvable cases for both problems.
Discrete Applied Mathematics, 2019
In this paper, we study covering and domination problems on directed graphs. Although undirected ... more In this paper, we study covering and domination problems on directed graphs. Although undirected Vertex Cover and Edge Dominating Set are well-studied classical graph problems, the directed versions have not been studied much due to the lack of clear definitions. We give natural definitions for Directed r-In (Out) Vertex Cover and Directed (p, q)-Edge Dominating Set as directed generations of Vertex Cover and Edge Dominating Set. For these problems, we show that (1) Directed r-In (Out) Vertex Cover and Directed (p, q)-Edge Dominating Set are NP-complete on planar directed acyclic graphs except when r = 1 or (p, q) = (0, 0), (2) if r ≥ 2, Directed r-In (Out) Vertex Cover is W [2]hard and c ln k-inapproximable on directed acyclic graphs, (3) if either p or q is greater than 1, Directed (p, q)-Edge Dominating Set is W [2]-hard and c ln k-inapproximable on directed acyclic graphs, (4) all problems can be solved in polynomial time on trees, and (5) Directed (0, 1), (1, 0), (1, 1)-Edge Dominating Set are fixed-parameter tractable in general graphs. The first result implies that (directed) r-Dominating Set on directed line graphs is NPcomplete even if r = 1.
2015 IEEE International Symposium on Information Theory (ISIT), 2015
A code design problem for memory devises with restricted state transitions is formulated as a com... more A code design problem for memory devises with restricted state transitions is formulated as a combinatorial optimization problem that is called a subgraph domatic partition (subDP) problem. If any neighbor set of a given state transition graph contains all the colors, then the coloring is said to be valid. The goal of a subDP problem is to find a valid coloring with the largest number of colors for a subgraph of a given directed graph. The number of colors in an optimal valid coloring gives the writing capacity of a given state transition graph. The subDP problems are computationally hard; it is proved to be NP-complete in this paper. One of our main contributions in this paper is to show the asymptotic behavior of the writing capacity C(G) for sequences of dense bidirectional graphs, that is given by C(G) = Ω(n/ ln n) where n is the number of nodes. A probabilistic method called Lovász local lemma (LLL) plays an essential role to derive the asymptotic expression.
Lecture Notes in Computer Science, 2000
In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to ... more In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to ÿnd relations among attributes are considered important. In this paper, given a data set (T; F) where T ⊆ {0; 1} n denotes a set of positive examples and F ⊆ {0; 1} n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We ÿrst study computational complexity of the problem of ÿnding decomposable Boolean extensions. Since the problem turns out to be intractable (i.e., NP-complete), we propose a heuristic algorithm in the second half of the paper. Our method searches a decomposable partition of the set of all attributes by using the error sizes of almost-ÿt decomposable extensions as a guiding measure, and then ÿnds structural relations among the attributes in the obtained partition. Some results of numerical experiment on randomly generated data sets are also reported.
Lecture Notes in Computer Science, 2014
Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and im... more Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between I0 and Ir with the minimum number of token movements.
Lecture Notes in Computer Science, 2010
A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e.,... more A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e., CORDA) robots is investigated in this paper. The conventional pattern formation problem assumes that the target pattern is given as a set of the positions by their coordinates in the global coordinate system, under the assumption that the robots are not aware of it. In the pattern formation problem we discuss in this paper, the points comprising the pattern are assumed to be "visible" to all robots, like landmarks. However, the robots still cannot obtain their positions in the global coordinate system. This paper shows that this pattern formation problem is solvable by oblivious asynchronous robots through the optimum matching between the robots and the pattern's points. Our study is partly motivated by the state-of-arts of the conventional pattern formation problem by oblivious asynchronous robots; description and correctness proof of a formation algorithm is usually complicated and ambiguous, because of the oblivious and asynchronous natures of the robots. A modular method is thus looked for to describe and prove algorithm in a clearer and more concrete way. Our pattern formation problem and the formation algorithm based on the optimum matching are used as a primitive building block in the modular method.
Theoretical Computer Science, 2010
Given a finite graph G = (V, E) and a probability distribution π = (π v) v∈V on V , Metropolis wa... more Given a finite graph G = (V, E) and a probability distribution π = (π v) v∈V on V , Metropolis walks, i.e., random walks on G building on the Metropolis-Hastings algorithm obey a transition probability matrix P = (p uv) u,v∈V defined by, for any u, v ∈ V , p uv = 1 du min{ d u π v dvπu , 1} if v ∈ N (u), 1 − w =u p uw if u = v, 0 otherwise, and guarantee to have π as the stationary distribution, where N (u) is the set of adjacent vertices of u ∈ V and d u = |N (u)| is the degree of u. This paper shows that the hitting and the cover times of Metropolis walks are O(f n 2) and O(f n 2 log n), respectively, for any graph G of order n and any probability distribution π such that f = max u,v∈V π u /π v < ∞. We also show that there are graph G and stationary distribution π such that any random walk on G realizing π attains Ω(f n 2) hitting and Ω(f n 2 log n) cover times. It follows that the hitting and the cover times of Metropolis walks are Θ(f n 2) and Θ(f n 2 log n), respectively.
Theory of Computing Systems, 2014
A degree-constrained graph orientation of an undirected graph G is an assignment of a direction t... more A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W , the problems Max W-Light, Min W-Light, Max W-Heavy, and Min W-Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems' computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.
Lecture Notes in Computer Science, 2015
We study reconfiguration problems for cliques in a graph, which determine whether there exists a ... more We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs.