Rolf Niedermeier | TU Berlin (original) (raw)

Papers by Rolf Niedermeier

Let M be a class of 0/1-matrices. A 0/1/-matrix A where the s induce a submatrix is a probe matri... more Let M be a class of 0/1-matrices. A 0/1/-matrix A where the s induce a submatrix is a probe matrix of M if the s in A can be replaced by 0s and 1s such that A becomes a member of M. We show that for M being the class of totally balanced matrices, it can be decided in polynomial time whether A is a probe totally balanced matrix. On our route toward proving this main result, we also prove that so-called partitioned probe strongly chordal graphs and partitioned probe chordal bipartite graphs can be recognized in polynomial time.

A matrix M is said to be k-anonymous if for each row r in M there are at least k − 1 other rows i... more A matrix M is said to be k-anonymous if for each row r in M there are at least k − 1 other rows in M which are identical to r. The NP-hard k-Anonymity problem asks, given an n × m-matrix M over a fixed alphabet and an integer s > 0, whether M can be made k-anonymous by suppressing (blanking out) at most s entries. Complementing previous work, we introduce two new "data-driven" parameterizations for k-Anonymity-the number t in of different input rows and the number t out of different output rowsboth modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter t in , and that it is NP-hard even for t out = 2 and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when t in is a constant. Our computational hardness results also extend to the related privacy problems p-Sensitivity and-Diversity, while our fixed-parameter tractability results extend to p-Sensitivity and the usage of domain generalization hierarchies, where the entries are replaced by more general data instead of being completely suppressed. Keywords k-Anonymity • p-Sensitivity •-Diversity • Domain generalization hierarchies • Matrix modification problems • Parameterized algorithmics • Fixed-parameter tractability • NP-hardness An extended abstract entitled "The Effect of Homogeneity on the Complexity of k-Anonymity" appeared in Proceedings of the 18th International Symposium on Fundamentals of Computation Theory (FCT '11), volume 6914 of LNCS, pages 53-64, Springer 2011. Apart from the full proofs omitted in that version, the current article also contains new results on-Diversity, p-Sensitivity, and on the usage of domain generalization hierarchies.

Computational Social Choice is an interdisciplinary research area involving Economics, Political ... more Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problemspecific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. The general topic is addressed by a biennial International Workshop on Computational Social Choice (COMSOC), whose 2012 and 2014 editions have been held in Kraków/Poland and in Pittsburgh/Pennsylvania/USA, respectively. Furthermore, the topic is covered by a number of leading conferences in Artificial Intelligence (including AAAI, ECAI, IJCAI) and by several specialized conferences (including AAMAS, ADT, EC, SAGT, WINE). There are numerous research journals that address many aspects of computational social choice, including Artifi

Algorithmica, 2014

For directed and undirected graphs, we study the problem to make a distinguished vertex the uniqu... more For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

National Conference on Artificial Intelligence, 2010

We perform new theoretical as well as first-time experimental studies for the NP-hard problem to ... more We perform new theoretical as well as first-time experimental studies for the NP-hard problem to find a closest ultrametric for given dissimilarity data on pairs. This is a central problem in the area of hierarchical clustering, where so far only polynomial-time approximation algorithms were known. In contrast, we develop efficient preprocessing algorithms (known as kernelization in parameterized algorithmics) with provable performance guarantees and a simple search tree algorithm. These are used to find optimal solutions. Our experiments with synthetic and biological data show the effectiveness of our algorithms and demonstrate that an approximation algorithm due to Ailon and Charikar [FOCS 2005] often gives (almost) optimal solutions.

Lecture Notes in Computer Science, 2011

For directed and undirected graphs, we study the problem to make a distinguished vertex the uniqu... more For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

Lecture Notes in Computer Science, 1998

... However, only elementary combinatorial considerations have been used for this result and mayb... more ... However, only elementary combinatorial considerations have been used for this result and maybe with the help of machine support one could still ... to Jin Wiedermann for inviting me to a talk on the presented topic, which together with the lecture notes served ... The MIT Press, 1990 ...

Lecture Notes in Computer Science, 2010

Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated... more Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated Vertex Cover, and Maximum Partial Vertex Cover) have been intensively studied in terms of polynomial-time approximability. By way of contrast, their parameterized complexity,has so far been completely,open. We close this gap here by showing that, with the size of the desired vertex cover as parameter, Connected

Lecture Notes in Computer Science, 2009

The NP-hard Interval Constrained Coloring problem appears in the interpretation of experimental d... more The NP-hard Interval Constrained Coloring problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments. Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to be used for its elements), one asks whether there is a "consistent" coloring for all integer points from {1, . . . , n} that complies with the constraints specified by the color multisets. We initiate a study of Interval Constrained Coloring from the viewpoint of combinatorial algorithmics, trying to avoid polyhedral and randomized rounding methods as used in previous work. To this end, we employ the method of systematically deconstructing intractability. It is based on a thorough analysis of the known NP-hardness proof for Interval Constrained Coloring. In particular, we identify numerous parameters that naturally occur in the problem and strongly influence the problem's practical solvability. Thus, we present several positive (fixed-parameter) tractability results and, moreover, identify a large spectrum of combinatorial research challenges for Interval Constrained Coloring.

Lecture Notes in Computer Science, 2010

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a m... more Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect to the number k of extension edges (arcs). For an n-vertex multigraph, the corresponding running time amounts to O(4 k · n 3 ). This implies a fixed-parameter tractability result for the "equivalent" Rural Postman problem. In addition, we present several polynomial-time algorithms for natural Eulerian extension problems.

Lecture Notes in Computer Science, 1999

The problem instance of Vertex Cover consists of anundirected graph G = (V; E) and a positive int... more The problem instance of Vertex Cover consists of anundirected graph G = (V; E) and a positive integer k,the question is whether there exists a subset C ` V ofvertices such that each edge in E has at least one ofits endpoints in C with jCj k. We improve two recentworst case upper bounds for Vertex Cover. First,Balasubramanian et al.

Lecture Notes in Computer Science, 2001

Closest String is one of the core problems in the field of consensus word analysis with particula... more Closest String is one of the core problems in the field of consensus word analysis with particular importance for computational biology. Given k strings of same length and a positive integer d, find a "closest string" s such that none of the given strings has Hamming distance greater than d from s. Closest String is NP-complete. We show how to

Lecture Notes in Computer Science, 1999

Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignmen... more Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignment satisfying at least k clauses? This is the decision version of the Maximum Satisfiability (MaxSax) problem we study in this paper. We improve upper bounds on the worst case running time for MAXSAT. First, Cai and Chen showed that MAXSAT can be

Lecture Notes in Computer Science, 1994

... on naa a D a D an a a D nnaa aa DD a D aaanaan aa DD ana aa D ao DD a D aoo aa a DD aa D o aa... more ... on naa a D a D an a a D nnaa aa DD a D aaanaan aa DD ana aa D ao DD a D aoo aa a DD aa D o aa oa aaa nn DO an D aan D a D a aa DO a D a ao DD aoa oa oa D aa n D DO a D a a ODD aa D DDD a DD a ana ODD ODD aap aaa aoa ana DOD DDD DDD DDD D DO nap ...

Lecture Notes in Computer Science, 2000

We present an algorithm that constructively produces a solution to the k-dominating set problem f... more We present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c √ k n), where c = 3 6 √ 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O( γ(G)), and that such a tree decomposition can be found in O( γ(G)n) time. The same technique can be used to show that the k-face cover problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c √ k 1 n + n 2 ) time, where c 1 = 2 36 √ 34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of k-dominating set, e.g., k-independent dominating set and k-weighted dominating set.

Lecture Notes in Computer Science, 2006

Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity a... more Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity analysis in solving NP-hard problems. Its practical usefulness is confirmed by experimental work. Here, generalizing and extending previous work, we present a set of data reduction preprocessing rules on the way to compute optimal dominating sets in graphs. In this way, we arrive at the novel notion of "data reduction schemes." In addition, we obtain data reduction results for domination in directed graphs that allow to prove a linear-size problem kernel for Directed Dominating Set in planar graphs.

Lecture Notes in Computer Science, 2002

We present an improved dynamic programming strategy for dominating set and related problems on gr... more We present an improved dynamic programming strategy for dominating set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4k n) algorithm for dominating set, where n is the number of nodes of the tree decomposition. This result improves the previously best known algorithm of Telle and Proskurowski running in

Let M be a class of 0/1-matrices. A 0/1/-matrix A where the s induce a submatrix is a probe matri... more Let M be a class of 0/1-matrices. A 0/1/-matrix A where the s induce a submatrix is a probe matrix of M if the s in A can be replaced by 0s and 1s such that A becomes a member of M. We show that for M being the class of totally balanced matrices, it can be decided in polynomial time whether A is a probe totally balanced matrix. On our route toward proving this main result, we also prove that so-called partitioned probe strongly chordal graphs and partitioned probe chordal bipartite graphs can be recognized in polynomial time.

A matrix M is said to be k-anonymous if for each row r in M there are at least k − 1 other rows i... more A matrix M is said to be k-anonymous if for each row r in M there are at least k − 1 other rows in M which are identical to r. The NP-hard k-Anonymity problem asks, given an n × m-matrix M over a fixed alphabet and an integer s > 0, whether M can be made k-anonymous by suppressing (blanking out) at most s entries. Complementing previous work, we introduce two new "data-driven" parameterizations for k-Anonymity-the number t in of different input rows and the number t out of different output rowsboth modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter t in , and that it is NP-hard even for t out = 2 and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when t in is a constant. Our computational hardness results also extend to the related privacy problems p-Sensitivity and-Diversity, while our fixed-parameter tractability results extend to p-Sensitivity and the usage of domain generalization hierarchies, where the entries are replaced by more general data instead of being completely suppressed. Keywords k-Anonymity • p-Sensitivity •-Diversity • Domain generalization hierarchies • Matrix modification problems • Parameterized algorithmics • Fixed-parameter tractability • NP-hardness An extended abstract entitled "The Effect of Homogeneity on the Complexity of k-Anonymity" appeared in Proceedings of the 18th International Symposium on Fundamentals of Computation Theory (FCT '11), volume 6914 of LNCS, pages 53-64, Springer 2011. Apart from the full proofs omitted in that version, the current article also contains new results on-Diversity, p-Sensitivity, and on the usage of domain generalization hierarchies.

Computational Social Choice is an interdisciplinary research area involving Economics, Political ... more Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problemspecific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. The general topic is addressed by a biennial International Workshop on Computational Social Choice (COMSOC), whose 2012 and 2014 editions have been held in Kraków/Poland and in Pittsburgh/Pennsylvania/USA, respectively. Furthermore, the topic is covered by a number of leading conferences in Artificial Intelligence (including AAAI, ECAI, IJCAI) and by several specialized conferences (including AAMAS, ADT, EC, SAGT, WINE). There are numerous research journals that address many aspects of computational social choice, including Artifi

Algorithmica, 2014

For directed and undirected graphs, we study the problem to make a distinguished vertex the uniqu... more For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

National Conference on Artificial Intelligence, 2010

We perform new theoretical as well as first-time experimental studies for the NP-hard problem to ... more We perform new theoretical as well as first-time experimental studies for the NP-hard problem to find a closest ultrametric for given dissimilarity data on pairs. This is a central problem in the area of hierarchical clustering, where so far only polynomial-time approximation algorithms were known. In contrast, we develop efficient preprocessing algorithms (known as kernelization in parameterized algorithmics) with provable performance guarantees and a simple search tree algorithm. These are used to find optimal solutions. Our experiments with synthetic and biological data show the effectiveness of our algorithms and demonstrate that an approximation algorithm due to Ailon and Charikar [FOCS 2005] often gives (almost) optimal solutions.

Lecture Notes in Computer Science, 2011

For directed and undirected graphs, we study the problem to make a distinguished vertex the uniqu... more For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

Lecture Notes in Computer Science, 1998

... However, only elementary combinatorial considerations have been used for this result and mayb... more ... However, only elementary combinatorial considerations have been used for this result and maybe with the help of machine support one could still ... to Jin Wiedermann for inviting me to a talk on the presented topic, which together with the lecture notes served ... The MIT Press, 1990 ...

Lecture Notes in Computer Science, 2010

Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated... more Important variants of the Vertex Cover problem (among others, Connected Vertex Cover, Capacitated Vertex Cover, and Maximum Partial Vertex Cover) have been intensively studied in terms of polynomial-time approximability. By way of contrast, their parameterized complexity,has so far been completely,open. We close this gap here by showing that, with the size of the desired vertex cover as parameter, Connected

Lecture Notes in Computer Science, 2009

The NP-hard Interval Constrained Coloring problem appears in the interpretation of experimental d... more The NP-hard Interval Constrained Coloring problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments. Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to be used for its elements), one asks whether there is a "consistent" coloring for all integer points from {1, . . . , n} that complies with the constraints specified by the color multisets. We initiate a study of Interval Constrained Coloring from the viewpoint of combinatorial algorithmics, trying to avoid polyhedral and randomized rounding methods as used in previous work. To this end, we employ the method of systematically deconstructing intractability. It is based on a thorough analysis of the known NP-hardness proof for Interval Constrained Coloring. In particular, we identify numerous parameters that naturally occur in the problem and strongly influence the problem's practical solvability. Thus, we present several positive (fixed-parameter) tractability results and, moreover, identify a large spectrum of combinatorial research challenges for Interval Constrained Coloring.

Lecture Notes in Computer Science, 2010

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a m... more Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect to the number k of extension edges (arcs). For an n-vertex multigraph, the corresponding running time amounts to O(4 k · n 3 ). This implies a fixed-parameter tractability result for the "equivalent" Rural Postman problem. In addition, we present several polynomial-time algorithms for natural Eulerian extension problems.

Lecture Notes in Computer Science, 1999

The problem instance of Vertex Cover consists of anundirected graph G = (V; E) and a positive int... more The problem instance of Vertex Cover consists of anundirected graph G = (V; E) and a positive integer k,the question is whether there exists a subset C ` V ofvertices such that each edge in E has at least one ofits endpoints in C with jCj k. We improve two recentworst case upper bounds for Vertex Cover. First,Balasubramanian et al.

Lecture Notes in Computer Science, 2001

Closest String is one of the core problems in the field of consensus word analysis with particula... more Closest String is one of the core problems in the field of consensus word analysis with particular importance for computational biology. Given k strings of same length and a positive integer d, find a "closest string" s such that none of the given strings has Hamming distance greater than d from s. Closest String is NP-complete. We show how to

Lecture Notes in Computer Science, 1999

Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignmen... more Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignment satisfying at least k clauses? This is the decision version of the Maximum Satisfiability (MaxSax) problem we study in this paper. We improve upper bounds on the worst case running time for MAXSAT. First, Cai and Chen showed that MAXSAT can be

Lecture Notes in Computer Science, 1994

... on naa a D a D an a a D nnaa aa DD a D aaanaan aa DD ana aa D ao DD a D aoo aa a DD aa D o aa... more ... on naa a D a D an a a D nnaa aa DD a D aaanaan aa DD ana aa D ao DD a D aoo aa a DD aa D o aa oa aaa nn DO an D aan D a D a aa DO a D a ao DD aoa oa oa D aa n D DO a D a a ODD aa D DDD a DD a ana ODD ODD aap aaa aoa ana DOD DDD DDD DDD D DO nap ...

Lecture Notes in Computer Science, 2000

We present an algorithm that constructively produces a solution to the k-dominating set problem f... more We present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c √ k n), where c = 3 6 √ 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O( γ(G)), and that such a tree decomposition can be found in O( γ(G)n) time. The same technique can be used to show that the k-face cover problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c √ k 1 n + n 2 ) time, where c 1 = 2 36 √ 34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of k-dominating set, e.g., k-independent dominating set and k-weighted dominating set.

Lecture Notes in Computer Science, 2006

Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity a... more Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity analysis in solving NP-hard problems. Its practical usefulness is confirmed by experimental work. Here, generalizing and extending previous work, we present a set of data reduction preprocessing rules on the way to compute optimal dominating sets in graphs. In this way, we arrive at the novel notion of "data reduction schemes." In addition, we obtain data reduction results for domination in directed graphs that allow to prove a linear-size problem kernel for Directed Dominating Set in planar graphs.

Lecture Notes in Computer Science, 2002

We present an improved dynamic programming strategy for dominating set and related problems on gr... more We present an improved dynamic programming strategy for dominating set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4k n) algorithm for dominating set, where n is the number of nodes of the tree decomposition. This result improves the previously best known algorithm of Telle and Proskurowski running in