Mikael Hammar - Academia.edu (original) (raw)

Papers by Mikael Hammar

Research paper thumbnail of A note on submodular set cover on matroids

Discrete Mathematics, 2009

ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the grou... more ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.

Research paper thumbnail of F-Chord: Improved uniform routing on Chord

Networks, 2008

We propose a family of novel Chord-based P2P schemes retaining all positive aspects that made Cho... more We propose a family of novel Chord-based P2P schemes retaining all positive aspects that made Chord a popular topology for routing in P2P networks. The schemes, based on the Fibonacci number system, allow to simultaneously improve on the maximum/average number of hops for lookups and the routing table size per node.

Research paper thumbnail of There Are Spanning Spiders in Dense Graphs (and We Know How to Find Them)

Lecture Notes in Computer Science, 2003

ABSTRACT A spanning spider for a graph G is a spanning tree T of G with at most one vertex having... more ABSTRACT A spanning spider for a graph G is a spanning tree T of G with at most one vertex having degree three or more in T. In this paper we give densitycriteria for the existence of spanning spiders in graphs. We constructivelypro ve the following result: Given a graph G with n vertices, if the degree sum of anyindep endent triple of vertices is at least n − 1, then there exists a spanning spider in G. We also studythe case of bipartite graphs and give densityconditions for the existence of a spanning spider in a bipartite graph. All our proofs are constructive and implythe existence of polynomial time algorithms to construct the spanning spiders. The interest in the existence of spanning spiders originallyarises in the realm of multicasting in optical networks. However, the graph theoretical problems discussed here are interesting in their own right.

Research paper thumbnail of A note on submodular set cover on matroids

Discrete Mathematics, 2009

ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the grou... more ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.

Research paper thumbnail of Approximation Results for Kinetic Variants for TSP

Research paper thumbnail of Parallel Searching on

In this paper we investigate parallel searching on m concurrent rays. We assume that a target t i... more In this paper we investigate parallel searching on m concurrent rays. We assume that a target t is located somewhere on one of the rays and that a group of m point robots has to reach t. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy S we are interested in the competitive ratio which is defined as the ratio of the time needed by the robots using S and the time needed if the location of t is known in advance. If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of 9 --- independent of m. We show that even in the case m = 2 there is a lower bound of 9 on the competitive ratio for two large classes of strategies. Moreover, we show that a lower bound of 9 for m = 2 implies a lower bound of 9 for m ? 2 --- as is to be expected. If the minimum distance to the target is not known in advance, then we show a lower bound on the competitive ratio of 1 + 2(k + 1) k+1 =k k ...

Research paper thumbnail of Using maximum coverage to optimize recommendation systems in e-commerce

Proceedings of the 7th ACM conference on Recommender systems - RecSys '13, 2013

We study the problem of optimizing recommendation systems for e-commerce sites. We consider in pa... more We study the problem of optimizing recommendation systems for e-commerce sites. We consider in particular a combinatorial solution to this optimization based on the well known Maximum Coverage problem that asks for the k sets (products) that cover the most elements from a ground set (consumers). This formulation provides an abstract model for what k products should be recommended to maximize the probability of consumer purchase. Unfortunately, Maximum Coverage is NP-complete but an efficient approximation algorithm exists based on the Greedy methodology.

Research paper thumbnail of Improved Exploration of Rectilinear Polygons

Exploring a polygon is the problem of a robot that does not have a map of its surroundings to see... more Exploring a polygon is the problem of a robot that does not have a map of its surroundings to see the complete polygon. In other words, for the robot to construct a map of the polygon. Exploration can be viewed as an online problem. Typical for online problems is that the solution method must make decisions based on past events but without knowledge about the future. In our case the robot does not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive factor of such a method is the ratio between the method's performance and the performance of the best method having full knowledge about the future. We prove a 5/3-competitive strategy for exploring a simple rectilinear polygon in the L1 metric. This improves the previous factor two bound of Deng, Kameda and Papadimitriou.

Research paper thumbnail of Brief announcement

Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing - PODC '04, 2004

Research paper thumbnail of Approximation Results for Kinetic Variants of TSP

Lecture Notes in Computer Science, 1999

We study the approximation complexity of certain kinetic variants of the Traveling Salesman Probl... more We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem (TSP) where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results:

Research paper thumbnail of Concerning the time bounds of existing shortest watchman route algorithms

Lecture Notes in Computer Science, 1997

A watchman route in a polygon P is a route inside P such that each point in the interior of P is ... more A watchman route in a polygon P is a route inside P such that each point in the interior of P is visible from at least one point along the route. The objective of the shortest watchman route problem is to minimize the length of the watchman route for a given polygon. In 1991 Chin and Ntafos claimed an O(n 4 ) algorithm, solving the shortest watchman route problem for simple polygons, given a starting point of the route. Later, improvements of this result were presented by Tan, Hirata and Inagaki, decreasing the timebound to O(n 2 ). We prove that the time bound analyses of these algorithms are erroneous and that their true time bound is (2 n ). Furthermore, a modi cation to the latest algorithm is given, restoring its time bound to O(n 2 ).

Research paper thumbnail of The Online Freeze-Tag Problem

Lecture Notes in Computer Science, 2006

We consider the following problem from swarm robotics: given one or more "awake" robots in some m... more We consider the following problem from swarm robotics: given one or more "awake" robots in some metric space M , wake up a set of "asleep" robots. A robot awakens a sleeping robot by moving to the sleeping robot's position. When a robot awakens, it is available to assist in awakening other slumbering robots. We investigate offline and online versions of this problem and give a 2-competitive strategy and a lower bound of 2 in the case when M is discrete and the objective is to minimize the total movement cost. We also study the case when M is continuous and show a lower bound of 7/3 when the objective is to minimize the time when the last robot awakens.

Research paper thumbnail of On R-Trees with Low Stabbing Number

Lecture Notes in Computer Science, 2000

. The R-tree is a well-known bounding-volume hierarchy thatis suitable for storing geometric data... more . The R-tree is a well-known bounding-volume hierarchy thatis suitable for storing geometric data on secondary memory. Unfortunately,no good analysis of its query time exists. We describe a new algorithmto construct an R-tree for a set of planar objects that has provablygood query complexity for point location queries and range queries withranges of small width. For certain important special cases,

Research paper thumbnail of Degree-Optimal Deterministic Routing for P2P Systems

10th IEEE Symposium on Computers and Communications (ISCC'05), 2005

We propose routing schemes that optimize the average number of hops for lookup requests in Peer-t... more We propose routing schemes that optimize the average number of hops for lookup requests in Peer-to-Peer (P2P) systems without adding any overhead to the system. Our work is inspired by the recently introduced variation of greedy routing, called neighbor-of-neighbor (NoN), which allows to get optimal average path length with respect to the degree. Our proposal has the advantage of first "limiting" and then "eliminating" the use of randomization. As a consequence, the NoN technique can be implemented with our schemes without adding any overhead. Analyzed networks include several popular topologies: Chord, Hypercube based networks, Symphony, SkipGraphs. Theoretical results and extensive simulations show that the proposed simplifications (while maintaining the original node degree) do not increase the average path length of the networks, which is often improved in practice. The improvement is obtained with no harm to the operational efficiency (e.g stability, easy of programming, scalability, fault-tolerance) of the considered systems.

Research paper thumbnail of Limiting flooding expenses in on-demand source-initiated protocols for mobile wireless networks

18th International Parallel and Distributed Processing Symposium, 2004. Proceedings., 2004

In this paper we study on-demand source initiated protocols for mobile wireless networks. In part... more In this paper we study on-demand source initiated protocols for mobile wireless networks. In particular, we study the flooding procedure commonly used by these protocols to set up temporary communication paths. The benefit of the flooding technique is its generosity regarding changes in network structure. On the other hand, each time a message is sent, the entire network will be involved to set up the communication path from the source node to the target node. We propose a new approach, which we call limited broadcasting. It is aimed to reduce the overhead by localizing the search for the target node both in terms of the time the process needs to globally stop after the target has been reached and/or in terms of the region which is affected by the search. It works in unknown networks and does not need any kind of additional information.

Research paper thumbnail of Parallel Searching on m Rays

In this paper we investigate parallel searching on m concurrent rays. We assume that atarget t is... more In this paper we investigate parallel searching on m concurrent rays. We assume that atarget t is located somewhere on one of the rays and that a group of m point robots has toreach t. Furthermore, we assume that the robots have no way of communicating over distance.Given a strategy S we are interested in the competitive ratio which is defined as the ratio ofthe time needed by the robots using S and the time needed if the location of t is known inadvance.If a lower bound on the distance...

Research paper thumbnail of Degree-Optimal Routing for P2P Systems

Theory of Computing Systems, 2009

We propose routing schemes that optimize the average number of hops for lookup requests in Peer-t... more We propose routing schemes that optimize the average number of hops for lookup requests in Peer-to-Peer (P2P) systems without adding any overhead to the system. Our work is inspired by the recently introduced variation of greedy routing, called neighbor-of-neighbor (NoN), which allows to get optimal average path length with respect to the degree. Our proposal has the advantage of first "limiting" and then "eliminating" the use of randomization. As a consequence, the NoN technique can be implemented with our schemes without adding any overhead. Analyzed networks include several popular topologies: Chord, Hypercube based networks, Symphony, Skip-Graphs. Theoretical results and extensive simulations show that the proposed simplifications (while maintaining the original node degree) do not increase the average path length of the networks, which is often improved in practice. The improvement is obtained with no harm to the operational efficiency (e.g. stability, ease of programming, scalability, fault-tolerance) of the considered systems.

Research paper thumbnail of Competitive exploration of rectilinear polygons

Theoretical Computer Science, 2006

Research paper thumbnail of A System for Virtual Directories Using Euler Diagrams

Electronic Notes in Theoretical Computer Science, 2005

In this paper, we describe how to use Euler Diagrams to represent virtual directories. i.e. colle... more In this paper, we describe how to use Euler Diagrams to represent virtual directories. i.e. collection of files that are computed on demand and satisfy a number of constraints. We, then, briefly describe the state of VennFS project that is currently modified to include this new capability. In particular, we show a data structure designed to answer queries about a given Euler Diagram and its sets. The data structure EulerTree described here is based on the R-Tree (see [1]), a data structure designed for answering range queries over a family of shapes in the 2-dimensional space.

Research paper thumbnail of Spanning spiders and light-splitting switches

Discrete Mathematics, 2004

Motivated by a problem in the design of optical networks, we ask when a graph has a spanning spid... more Motivated by a problem in the design of optical networks, we ask when a graph has a spanning spider (subdivision of a star), or, more generally, a spanning tree with a bounded number of branch vertices. We investigate the existence of these spanning subgraphs in analogy to classical studies of Hamiltonicity.

Research paper thumbnail of A note on submodular set cover on matroids

Discrete Mathematics, 2009

ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the grou... more ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.

Research paper thumbnail of F-Chord: Improved uniform routing on Chord

Networks, 2008

We propose a family of novel Chord-based P2P schemes retaining all positive aspects that made Cho... more We propose a family of novel Chord-based P2P schemes retaining all positive aspects that made Chord a popular topology for routing in P2P networks. The schemes, based on the Fibonacci number system, allow to simultaneously improve on the maximum/average number of hops for lookups and the routing table size per node.

Research paper thumbnail of There Are Spanning Spiders in Dense Graphs (and We Know How to Find Them)

Lecture Notes in Computer Science, 2003

ABSTRACT A spanning spider for a graph G is a spanning tree T of G with at most one vertex having... more ABSTRACT A spanning spider for a graph G is a spanning tree T of G with at most one vertex having degree three or more in T. In this paper we give densitycriteria for the existence of spanning spiders in graphs. We constructivelypro ve the following result: Given a graph G with n vertices, if the degree sum of anyindep endent triple of vertices is at least n − 1, then there exists a spanning spider in G. We also studythe case of bipartite graphs and give densityconditions for the existence of a spanning spider in a bipartite graph. All our proofs are constructive and implythe existence of polynomial time algorithms to construct the spanning spiders. The interest in the existence of spanning spiders originallyarises in the realm of multicasting in optical networks. However, the graph theoretical problems discussed here are interesting in their own right.

Research paper thumbnail of A note on submodular set cover on matroids

Discrete Mathematics, 2009

ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the grou... more ABSTRACT We consider a problem related to the submodular set cover on polymatroids, when the ground set is the family of independent sets of a matroid. The achievement here is getting a strongly polynomial running time with respect to the ground set of the matroid even though the family of independent sets has exponential size. We also address the optimization problem of the maximization of submodular set functions on the independent sets of a matroid.

Research paper thumbnail of Approximation Results for Kinetic Variants for TSP

Research paper thumbnail of Parallel Searching on

In this paper we investigate parallel searching on m concurrent rays. We assume that a target t i... more In this paper we investigate parallel searching on m concurrent rays. We assume that a target t is located somewhere on one of the rays and that a group of m point robots has to reach t. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy S we are interested in the competitive ratio which is defined as the ratio of the time needed by the robots using S and the time needed if the location of t is known in advance. If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of 9 --- independent of m. We show that even in the case m = 2 there is a lower bound of 9 on the competitive ratio for two large classes of strategies. Moreover, we show that a lower bound of 9 for m = 2 implies a lower bound of 9 for m ? 2 --- as is to be expected. If the minimum distance to the target is not known in advance, then we show a lower bound on the competitive ratio of 1 + 2(k + 1) k+1 =k k ...

Research paper thumbnail of Using maximum coverage to optimize recommendation systems in e-commerce

Proceedings of the 7th ACM conference on Recommender systems - RecSys '13, 2013

We study the problem of optimizing recommendation systems for e-commerce sites. We consider in pa... more We study the problem of optimizing recommendation systems for e-commerce sites. We consider in particular a combinatorial solution to this optimization based on the well known Maximum Coverage problem that asks for the k sets (products) that cover the most elements from a ground set (consumers). This formulation provides an abstract model for what k products should be recommended to maximize the probability of consumer purchase. Unfortunately, Maximum Coverage is NP-complete but an efficient approximation algorithm exists based on the Greedy methodology.

Research paper thumbnail of Improved Exploration of Rectilinear Polygons

Exploring a polygon is the problem of a robot that does not have a map of its surroundings to see... more Exploring a polygon is the problem of a robot that does not have a map of its surroundings to see the complete polygon. In other words, for the robot to construct a map of the polygon. Exploration can be viewed as an online problem. Typical for online problems is that the solution method must make decisions based on past events but without knowledge about the future. In our case the robot does not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive factor of such a method is the ratio between the method's performance and the performance of the best method having full knowledge about the future. We prove a 5/3-competitive strategy for exploring a simple rectilinear polygon in the L1 metric. This improves the previous factor two bound of Deng, Kameda and Papadimitriou.

Research paper thumbnail of Brief announcement

Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing - PODC '04, 2004

Research paper thumbnail of Approximation Results for Kinetic Variants of TSP

Lecture Notes in Computer Science, 1999

We study the approximation complexity of certain kinetic variants of the Traveling Salesman Probl... more We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem (TSP) where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results:

Research paper thumbnail of Concerning the time bounds of existing shortest watchman route algorithms

Lecture Notes in Computer Science, 1997

A watchman route in a polygon P is a route inside P such that each point in the interior of P is ... more A watchman route in a polygon P is a route inside P such that each point in the interior of P is visible from at least one point along the route. The objective of the shortest watchman route problem is to minimize the length of the watchman route for a given polygon. In 1991 Chin and Ntafos claimed an O(n 4 ) algorithm, solving the shortest watchman route problem for simple polygons, given a starting point of the route. Later, improvements of this result were presented by Tan, Hirata and Inagaki, decreasing the timebound to O(n 2 ). We prove that the time bound analyses of these algorithms are erroneous and that their true time bound is (2 n ). Furthermore, a modi cation to the latest algorithm is given, restoring its time bound to O(n 2 ).

Research paper thumbnail of The Online Freeze-Tag Problem

Lecture Notes in Computer Science, 2006

We consider the following problem from swarm robotics: given one or more "awake" robots in some m... more We consider the following problem from swarm robotics: given one or more "awake" robots in some metric space M , wake up a set of "asleep" robots. A robot awakens a sleeping robot by moving to the sleeping robot's position. When a robot awakens, it is available to assist in awakening other slumbering robots. We investigate offline and online versions of this problem and give a 2-competitive strategy and a lower bound of 2 in the case when M is discrete and the objective is to minimize the total movement cost. We also study the case when M is continuous and show a lower bound of 7/3 when the objective is to minimize the time when the last robot awakens.

Research paper thumbnail of On R-Trees with Low Stabbing Number

Lecture Notes in Computer Science, 2000

. The R-tree is a well-known bounding-volume hierarchy thatis suitable for storing geometric data... more . The R-tree is a well-known bounding-volume hierarchy thatis suitable for storing geometric data on secondary memory. Unfortunately,no good analysis of its query time exists. We describe a new algorithmto construct an R-tree for a set of planar objects that has provablygood query complexity for point location queries and range queries withranges of small width. For certain important special cases,

Research paper thumbnail of Degree-Optimal Deterministic Routing for P2P Systems

10th IEEE Symposium on Computers and Communications (ISCC'05), 2005

We propose routing schemes that optimize the average number of hops for lookup requests in Peer-t... more We propose routing schemes that optimize the average number of hops for lookup requests in Peer-to-Peer (P2P) systems without adding any overhead to the system. Our work is inspired by the recently introduced variation of greedy routing, called neighbor-of-neighbor (NoN), which allows to get optimal average path length with respect to the degree. Our proposal has the advantage of first "limiting" and then "eliminating" the use of randomization. As a consequence, the NoN technique can be implemented with our schemes without adding any overhead. Analyzed networks include several popular topologies: Chord, Hypercube based networks, Symphony, SkipGraphs. Theoretical results and extensive simulations show that the proposed simplifications (while maintaining the original node degree) do not increase the average path length of the networks, which is often improved in practice. The improvement is obtained with no harm to the operational efficiency (e.g stability, easy of programming, scalability, fault-tolerance) of the considered systems.

Research paper thumbnail of Limiting flooding expenses in on-demand source-initiated protocols for mobile wireless networks

18th International Parallel and Distributed Processing Symposium, 2004. Proceedings., 2004

In this paper we study on-demand source initiated protocols for mobile wireless networks. In part... more In this paper we study on-demand source initiated protocols for mobile wireless networks. In particular, we study the flooding procedure commonly used by these protocols to set up temporary communication paths. The benefit of the flooding technique is its generosity regarding changes in network structure. On the other hand, each time a message is sent, the entire network will be involved to set up the communication path from the source node to the target node. We propose a new approach, which we call limited broadcasting. It is aimed to reduce the overhead by localizing the search for the target node both in terms of the time the process needs to globally stop after the target has been reached and/or in terms of the region which is affected by the search. It works in unknown networks and does not need any kind of additional information.

Research paper thumbnail of Parallel Searching on m Rays

In this paper we investigate parallel searching on m concurrent rays. We assume that atarget t is... more In this paper we investigate parallel searching on m concurrent rays. We assume that atarget t is located somewhere on one of the rays and that a group of m point robots has toreach t. Furthermore, we assume that the robots have no way of communicating over distance.Given a strategy S we are interested in the competitive ratio which is defined as the ratio ofthe time needed by the robots using S and the time needed if the location of t is known inadvance.If a lower bound on the distance...

Research paper thumbnail of Degree-Optimal Routing for P2P Systems

Theory of Computing Systems, 2009

We propose routing schemes that optimize the average number of hops for lookup requests in Peer-t... more We propose routing schemes that optimize the average number of hops for lookup requests in Peer-to-Peer (P2P) systems without adding any overhead to the system. Our work is inspired by the recently introduced variation of greedy routing, called neighbor-of-neighbor (NoN), which allows to get optimal average path length with respect to the degree. Our proposal has the advantage of first "limiting" and then "eliminating" the use of randomization. As a consequence, the NoN technique can be implemented with our schemes without adding any overhead. Analyzed networks include several popular topologies: Chord, Hypercube based networks, Symphony, Skip-Graphs. Theoretical results and extensive simulations show that the proposed simplifications (while maintaining the original node degree) do not increase the average path length of the networks, which is often improved in practice. The improvement is obtained with no harm to the operational efficiency (e.g. stability, ease of programming, scalability, fault-tolerance) of the considered systems.

Research paper thumbnail of Competitive exploration of rectilinear polygons

Theoretical Computer Science, 2006

Research paper thumbnail of A System for Virtual Directories Using Euler Diagrams

Electronic Notes in Theoretical Computer Science, 2005

In this paper, we describe how to use Euler Diagrams to represent virtual directories. i.e. colle... more In this paper, we describe how to use Euler Diagrams to represent virtual directories. i.e. collection of files that are computed on demand and satisfy a number of constraints. We, then, briefly describe the state of VennFS project that is currently modified to include this new capability. In particular, we show a data structure designed to answer queries about a given Euler Diagram and its sets. The data structure EulerTree described here is based on the R-Tree (see [1]), a data structure designed for answering range queries over a family of shapes in the 2-dimensional space.

Research paper thumbnail of Spanning spiders and light-splitting switches

Discrete Mathematics, 2004

Motivated by a problem in the design of optical networks, we ask when a graph has a spanning spid... more Motivated by a problem in the design of optical networks, we ask when a graph has a spanning spider (subdivision of a star), or, more generally, a spanning tree with a bounded number of branch vertices. We investigate the existence of these spanning subgraphs in analogy to classical studies of Hamiltonicity.