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Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem [article]

Andreas Emil Feldmann and Davis Issac and Ashutosh Rai
2020 arXiv   pre-print
The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques.  ...  We develop an FPT algorithm and a bi-kernel for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the aim  ...  In fact, our algorithm solves a more general problem that we call the Weighted Edge Clique Partition (WECP) problem defined as follows: WECP (Weighted Edge Clique Partition) Input: a graph G, a weight  ... 
arXiv:2002.07761v3 fatcat:k4qi2xhknrdprhzaw7hp4lhi3y

Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem

Andreas Emil Feldmann, Davis Issac, Ashutosh Rai, Yixin Cao, Marcin Pilipczuk
2020
The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques.  ...  We develop an FPT algorithm and a compression for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the  ...  I P E C 2 0 2 0 17:14 Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem Proof. First let us prove that |V (C)| ≤ N + 1.  ... 
doi:10.4230/lipics.ipec.2020.17 fatcat:pkskrcnuw5dbjpaddskla4bj6u

Clustering with partial information

Hans L. Bodlaender, Michael R. Fellows, Pinar Heggernes, Federico Mancini, Charis Papadopoulos, Frances Rosamond
2010 Theoretical Computer Science  
Furthermore we also show that parameterizing only by the number of cliques k, is not enough to obtain fixed-parameter tractability. The problem remains, in fact, NP-hard for each fixed k > 2.  ...  We provide an analogous result for the Edge Clique Partitioning problem on fuzzy graphs.  ...  Acknowledgement The authors would like to thank Daniel Lokshtanov for drawing our attention to the bound given in Theorem 3.6.  ... 
doi:10.1016/j.tcs.2009.12.016 fatcat:zzgj6sohgrhlxmgimfkxk7noxe

Fixed-Parameter Algorithms for Graph-Modeled Date Clustering [chapter]

Jiong Guo
2009 Lecture Notes in Computer Science  
After that, we shortly review the use of two further algorithmic techniques, iterative compression and average parameterization, applied to graph-modeled data clustering.  ...  Such clustering problems ask to modify a given graph into a union of dense subgraphs.  ...  Theorem 5 ( 5 [16] ). s-Defective Clique Editing is fixed-parameter tractable with respect to the combined parameter (s, k).  ... 
doi:10.1007/978-3-642-02017-9_7 fatcat:rxuht23lafhslaaj7hg26pyj7q

Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

Konrad Dabrowski, Vadim Lozin, Haiko Müller, Dieter Rautenbach
2012 Journal of Discrete Algorithms  
A simple Ramsey argument implies the fixed-parameter tractability of the maximum independent set problem in classes of graphs of bounded clique number.  ...  It is also known that the problem is generally intractable from a parameterized point of view.  ...  If the Weighted Independent Set problem is fixed-parameter tractable in X 0 , then it is fixed-parameter tractable in X . Proof.  ... 
doi:10.1016/j.jda.2011.12.012 fatcat:uya2nsnpmzbwbpsxmzmlm3g35m

Editing Graphs into Disjoint Unions of Dense Clusters

Jiong Guo, Iyad A. Kanj, Christian Komusiewicz, Johannes Uhlmann
2011 Algorithmica  
Then, we study the fixed-parameter tractability of the three clustering problems, showing that the first two problems are fixed-parameter tractable with respect to the parameter (s, k) and that the third  ...  The well-studied Cluster Editing problem is a special case of this problem with Π :="being a clique".  ...  A parameterized problem is fixed-parameter tractable (FPT) with respect to a parameter k, if there exists an algorithm solving the problem in time f (k) · n O(1) , where n denotes the overall input size  ... 
doi:10.1007/s00453-011-9487-4 fatcat:t5fz5sqbn5dzrlpjbiktfcrlfm

Editing Graphs into Disjoint Unions of Dense Clusters [chapter]

Jiong Guo, Iyad A. Kanj, Christian Komusiewicz, Johannes Uhlmann
2009 Lecture Notes in Computer Science  
Then, we study the fixed-parameter tractability of the three clustering problems, showing that the first two problems are fixed-parameter tractable with respect to the parameter (s, k) and that the third  ...  The well-studied Cluster Editing problem is a special case of this problem with Π :="being a clique".  ...  A parameterized problem is fixed-parameter tractable (FPT) with respect to a parameter k, if there exists an algorithm solving the problem in time f (k) · n O(1) , where n denotes the overall input size  ... 
doi:10.1007/978-3-642-10631-6_60 fatcat:m6cnfehrszdl7cmneduq7qstxu

Parameterized Complexity of Team Formation in Social Networks [chapter]

Robert Bredereck, Jiehua Chen, Falk Hüffner, Stefan Kratsch
2016 Lecture Notes in Computer Science  
In contrast, when using the diameter as measure, the problem is intractable with respect to any single parameter; however, combining ∆ with either b or l yields fixed-parameter tractability.  ...  We show that the computational complexity strongly depends on the communication cost measure: when using the weight of a minimum spanning tree of the subgraph formed by the selected team, we obtain fixed-parameter  ...  This work was started at the research retreat of the TU Berlin Algorithms and Computational Complexity group held in April 2014.  ... 
doi:10.1007/978-3-319-41168-2_12 fatcat:mq25koy6yvglnnafaio25tephq

Not So Easy Problems for Tree Decomposable Graphs [article]

Stefan Szeider
2011 arXiv   pre-print
Second we establish a new hardness result for the problem of minimizing the maximum weighted outdegree for orientations of edge-weighted graphs of bounded treewidth.  ...  We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the  ...  Acknowledgement Research partially supported by the European Research Council, grant reference 239962.  ... 
arXiv:1107.1177v1 fatcat:zkithfng4ncjhjdfee2isqvifm

Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming

Gregory Gutin, Eun Jung Kim, Arezou Soleimanfallah, Stefan Szeider, Anders Yeo
2011 Algorithmica  
We show that this subproblem is fixed-parameter tractable when parameterized by the size of the second partite set V .  ...  More generally, we show that the general factor problem for bipartite graphs, parameterized by |V |, is fixed-parameter tractable as long as all vertices in U are assigned lists of length 1, but becomes  ...  FPT is the class of all fixed-parameter tractable decision problems. A parameterized reduction is a many-one reduction where the parameter for one problem maps into the parameter for the other.  ... 
doi:10.1007/s00453-011-9548-8 fatcat:cqdvcn5cc5cf3izao7zdqoezjq

Iterative Compression for Exactly Solving NP-Hard Minimization Problems [chapter]

Jiong Guo, Hannes Moser, Rolf Niedermeier
2009 Lecture Notes in Computer Science  
This technique has proven very useful for achieving a number of recent breakthroughs in the development of fixed-parameter algorithms for NP-hard minimization problems.  ...  We survey the conceptual framework and several applications of the iterative compression technique introduced in 2004 by Reed, Smith, and Vetta.  ...  Acknowledgement: We are grateful to Christian Komusiewicz, Matthias Müller-Hannemann, and Siavash Vahdati Daneshmand for constructive comments improving the presentation of this paper.  ... 
doi:10.1007/978-3-642-02094-0_4 fatcat:ley2ifkrxbcw7bhzrktb5ijawq

Parameterized Dynamic Cluster Editing

Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
We obtain both fixed-parameter tractability as well as parameterized hardness results, thus (except for two open questions) providing a fairly complete picture of the parameterized computational complexity  ...  We introduce a dynamic version of the NP-hard Cluster Editing problem.  ...  problem variants we cannot hope for fixed-parameter tractability.  ... 
doi:10.4230/lipics.fsttcs.2018.46 dblp:conf/fsttcs/LuoMNN18 fatcat:orl6v37o3ngdjh5haidoklv5g4

Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming [chapter]

Gregory Gutin, Eun Jung Kim, Arezou Soleimanfallah, Stefan Szeider, Anders Yeo
2010 Lecture Notes in Computer Science  
We show that this subproblem is fixed-parameter tractable when parameterized by the size of the second partite set V .  ...  We establish fixed-parameter tractability by reducing the problem instance to a bounded number of acyclic instances, each of which can be solved in polynomial time by dynamic programming.  ...  FPT is the class of all fixed-parameter tractable decision problems. A parameterized reduction is a many-one reduction where the parameter for one problem maps into the parameter for the other.  ... 
doi:10.1007/978-3-642-17493-3_16 fatcat:6pop7th6hrebbkwgphlzhn2pau

Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming [article]

Gregory Gutin, Eun Jung Kim, Arezou Soleimanfallah, Stefan Szeider, Anders Yeo
2011 arXiv   pre-print
We show that this subproblem is fixed-parameter tractable when parameterized by the size of the second partite set V.  ...  More generally, we show that the general factor problem for bipartite graphs, parameterized by |V|, is fixed-parameter tractable as long as all vertices in U are assigned lists of length 1, but becomes  ...  FPT is the class of all fixed-parameter tractable decision problems. A parameterized reduction is a many-one reduction where the parameter for one problem maps into the parameter for the other.  ... 
arXiv:1106.3527v1 fatcat:p72473piavavxkuxayqflhhbza

Editing graphs to satisfy degree constraints: A parameterized approach

Luke Mathieson, Stefan Szeider
2012 Journal of computer and system sciences (Print)  
We classify the parameterized complexity of the considered problems taking upper bounds on the number of editing steps and the maximum degree of the resulting graph as parameters. • We consider several  ...  By allowing arbitrary lists we can express variants of the General Factor problem introduced and studied by Lovász [19, 20] . • Vertices and edges can have positive integer weights, giving each edit operation  ...  We have classified the parameterized complexity of a wide range of graph editing problems; our general finding is that all the problems are fixed-parameter tractable if parameterized by the combination  ... 
doi:10.1016/j.jcss.2011.02.001 fatcat:fljdtrsj4jfpfidlwcekot7zuu
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