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

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*...

##
###
Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem

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. ...

##
###
Clustering with partial information

2010
*
Theoretical Computer Science
*

Furthermore we also show that

doi:10.1016/j.tcs.2009.12.016
fatcat:zzgj6sohgrhlxmgimfkxk7noxe
*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. ...##
###
Fixed-Parameter Algorithms for Graph-Modeled Date Clustering
[chapter]

2009
*
Lecture Notes in Computer Science
*

After that, we shortly review

doi:10.1007/978-3-642-02017-9_7
fatcat:rxuht23lafhslaaj7hg26pyj7q
*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). ...##
###
Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

2012
*
Journal of Discrete Algorithms
*

A simple Ramsey argument implies

doi:10.1016/j.jda.2011.12.012
fatcat:uya2nsnpmzbwbpsxmzmlm3g35m
*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. ...##
###
Editing Graphs into Disjoint Unions of Dense Clusters

2011
*
Algorithmica
*

Then, we study

doi:10.1007/s00453-011-9487-4
fatcat:t5fz5sqbn5dzrlpjbiktfcrlfm
*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 ...##
###
Editing Graphs into Disjoint Unions of Dense Clusters
[chapter]

2009
*
Lecture Notes in Computer Science
*

Then, we study

doi:10.1007/978-3-642-10631-6_60
fatcat:m6cnfehrszdl7cmneduq7qstxu
*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 ...##
###
Parameterized Complexity of Team Formation in Social Networks
[chapter]

2016
*
Lecture Notes in Computer Science
*

In contrast, when using

doi:10.1007/978-3-319-41168-2_12
fatcat:mq25koy6yvglnnafaio25tephq
*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. ...##
###
Not So Easy Problems for Tree Decomposable Graphs
[article]

2011
*
arXiv
*
pre-print

Second we establish a new hardness result for

arXiv:1107.1177v1
fatcat:zkithfng4ncjhjdfee2isqvifm
*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. ...##
###
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming

2011
*
Algorithmica
*

We show that this subproblem is

doi:10.1007/s00453-011-9548-8
fatcat:cqdvcn5cc5cf3izao7zdqoezjq
*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. ...##
###
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

This technique has proven very useful for achieving a number

doi:10.1007/978-3-642-02094-0_4
fatcat:ley2ifkrxbcw7bhzrktb5ijawq
*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. ...##
###
Parameterized Dynamic Cluster Editing

2018
*
Foundations of Software Technology and Theoretical Computer Science
*

We obtain both

doi:10.4230/lipics.fsttcs.2018.46
dblp:conf/fsttcs/LuoMNN18
fatcat:orl6v37o3ngdjh5haidoklv5g4
*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*. ...##
###
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming
[chapter]

2010
*
Lecture Notes in Computer Science
*

We show that this subproblem is

doi:10.1007/978-3-642-17493-3_16
fatcat:6pop7th6hrebbkwgphlzhn2pau
*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. ...##
###
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming
[article]

2011
*
arXiv
*
pre-print

We show that this subproblem is

arXiv:1106.3527v1
fatcat:p72473piavavxkuxayqflhhbza
*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. ...##
###
Editing graphs to satisfy degree constraints: A parameterized approach

2012
*
Journal of computer and system sciences (Print)
*

We classify

doi:10.1016/j.jcss.2011.02.001
fatcat:fljdtrsj4jfpfidlwcekot7zuu
*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 ...
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