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Algorithms for vertex-partitioning problems on graphs with fixed clique-width

Michael U. Gerber, Daniel Kobler
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this paper, we consider a very similar framework, in relationship with more general classes of graphs: we propose a polynomial time algorithm on classes of graphs with bounded clique-width for all the  ...  Many vertex-partitioning problems can be expressed within a general framework introduced by Telle and Proskurowski.  ...  Acknowledgements The authors thank the anonymous referees for their comments that signiÿcantly improved the presentation of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(02)00725-9">doi:10.1016/s0304-3975(02)00725-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k6urgadmbfc47nc2w3f2y3lmb4">fatcat:k6urgadmbfc47nc2w3f2y3lmb4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304153310/https://core.ac.uk/download/pdf/82351644.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/1b/2a1bc6d0e82ff8ba578d5e589a08872c35f53540.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(02)00725-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Partitioning graphs into induced subgraphs [article]

Dušan Knop
<span title="2016-03-10">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the Induced H Partition problem from the parameterized complexity point of view. In the Induced H Partition problem the task is to partition vertices of a graph G into sets V_1,V_2,...  ...  Finally, for the parametrization by the modular-width we derive an FPT algorithm for every prime graph H.  ...  If the number r and the clique-width cw are fixed then the algorithm runs in polynomial time and hence the problem belongs to an XP class with parametrization by the clique-width.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1508.04725v2">arXiv:1508.04725v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/na4ckjdtt5fafjhs4wgh6mezl4">fatcat:na4ckjdtt5fafjhs4wgh6mezl4</a> </span>
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Speeding up Networks Mining via Neighborhood Diversity

Gennaro Cordasco, Luisa Gargano, Adele A. Rescigno, Ryuhei Uehara, Giuseppe Prencipe, Martin Farach-Colton
<span title="2020-09-16">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6w7vtzaje5byvkqy2g36uk74qq" style="color: black;">Fun with Algorithms</a> </i> &nbsp;
Parameterized complexity was classically used to efficiently solve NP-hard problems for small values of a fixed parameter.  ...  Then it has also been used as a tool to speed up algorithms for tractable problems.  ...  On the positive side, efforts have been made to improve algorithms for problems in P on some restricted classes of graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.fun.2021.21">doi:10.4230/lipics.fun.2021.21</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fun/CordascoGR21.html">dblp:conf/fun/CordascoGR21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/anksnea2hjezplia4w7ekqjocm">fatcat:anksnea2hjezplia4w7ekqjocm</a> </span>
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Page 1722 of Mathematical Reviews Vol. , Issue 2004c [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
edge.” 2004c:05142 05C69 05C15 05C85 68Q25 Kobler, Daniel (3-F_LDS2; Toronto, ON); Rotics, Udi (3-TRNT-C; Toronto, ON) Edge dominating set and colorings on graphs with fixed clique-width.  ...  For the two list-qg-coloring problems with costs, we even have linear algorithms.  ... 
<span class="external-identifiers"> </span>
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Faster algorithms for vertex partitioning problems parameterized by clique-width

Sang-il Oum, Sigve Hortemo Sæther, Martin Vatshelle
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width k given with a k-expression, Dominating Set can be solved in 4^k n^O(1) time.  ...  For a graph of clique-width k, if we rely on known algorithms to compute a (2^3k-1)-expression via rank-width and then solving Dominating Set using the (2^3k-1)-expression, the above algorithm will only  ...  This allows us to construct an algorithm that runs in time 2 O(k log k) n O(1) for graphs of clique-width at most k and solve every fixed LC-VSP problem, improving the previous runtime 2 O(k 2 ) n O(1)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2014.03.024">doi:10.1016/j.tcs.2014.03.024</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ndz66n6c7beutlmrdaqmumfhpe">fatcat:ndz66n6c7beutlmrdaqmumfhpe</a> </span>
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A comparison of two approaches for polynomial time algorithms computing basic graph parameters [article]

Frank Gurski
<span title="2008-06-25">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also present linear time algorithms for computing the latter four basic graph parameters on trees, i.e. graphs of tree-width 1, and on co-graphs, i.e. graphs of clique-width at most 2.  ...  For this purpose we give polynomial time algorithms for computing the four basic graph parameters independence number, clique number, chromatic number, and clique covering number on a given tree structure  ...  On the other hand, there are graph problems which remain NP-complete on graphs of bounded clique-width, but which are fixed-parameter tractable on graphs of bounded tree-width, such as the vertex disjoint  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0806.4073v1">arXiv:0806.4073v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ho5spatm6fb4pculjjptzegwhi">fatcat:ho5spatm6fb4pculjjptzegwhi</a> </span>
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Improving Vertex Cover as a Graph Parameter

Robert Ganian
<span title="2015-09-14">2015</span> <i title="Centre pour la Communication Scientifique Directe (CCSD)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/aagtqr2vajamvduhte7kigeygi" style="color: black;">Discrete Mathematics &amp; Theoretical Computer Science</a> </i> &nbsp;
In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that  ...  International audience Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs.  ...  fire in time O(|V |). 2 Other FPT and kernelization algorithms FPT algorithms for problems hard on clique-width Here we present two FPT algorithms for problems which are not in FPT when parameterized  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.46298/dmtcs.2136">doi:10.46298/dmtcs.2136</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z3viox6nwvaojc3iibyikwqywu">fatcat:z3viox6nwvaojc3iibyikwqywu</a> </span>
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Clique Cover on Sparse Networks [chapter]

Mathieu Blanchette, Ethan Kim, Adrian Vetta
<span title="2012-01-16">2012</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ka7ha6qhmfhmtbnfcmmmjao4ia" style="color: black;">2012 Proceedings of the Fourteenth Workshop on Algorithm Engineering and Experiments (ALENEX)</a> </i> &nbsp;
We then provide an algorithm for planar graphs with bounded branchwidth upon which we build a PTAS for planar graphs.  ...  We consider the problem of edge clique cover on sparse networks and study an application to the identification of overlapping protein complexes for a network of binary protein-protein interactions.  ...  There is a linear time algorithm for computing minimum clique cover for graphs with fixed treewidth k. Modifications for clique partition problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611972924.10">doi:10.1137/1.9781611972924.10</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/alenex/BlanchetteKV12.html">dblp:conf/alenex/BlanchetteKV12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oo2qzwd7s5c57nst5kgn4upxti">fatcat:oo2qzwd7s5c57nst5kgn4upxti</a> </span>
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A characterisation of clique-width through nested partitions

Bruno Courcelle, Pinar Heggernes, Daniel Meister, Charis Papadopoulos, Udi Rotics
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Clique-width of graphs is defined algebraically through operations on graphs with vertex labels.  ...  We characterise the clique-width in a combinatorial way by means of partitions of the vertex set, using trees of nested partitions where partitions are ordered bottom-up by refinement.  ...  Fixed-parameter tractability results are often of the form: a graph problem is tractable on graphs of bounded width, and the width of the input graph is a measure for the complexity of determining the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2015.02.016">doi:10.1016/j.dam.2015.02.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j3a3jgbnavfwldxzawpnmb6a7e">fatcat:j3a3jgbnavfwldxzawpnmb6a7e</a> </span>
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Algorithmic Lower Bounds for Problems Parameterized by Clique-width [chapter]

Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtanov, Saket Saurabh
<span title="2010-01-17">2010</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
On the other hand if we restrict ourselves to graphs of clique-width at most t, then there are many natural problems for which the running time of the best known algorithms is of the form n f (t) , where  ...  As a first step toward obtaining lower bounds for clique-width parameterizations, in [SODA 2009 ], we showed that unless FPT =W[1], there is no algorithm with run time O(g(t) · n c ), for some function  ...  Oum and Seymour [26] describe an algorithm that, for any fixed t, runs in time O(|V (G)| 9 log |V (G)|) and computes (2 3t+2 − 1)expressions for a graph G of clique-width at most t.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973075.42">doi:10.1137/1.9781611973075.42</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/FominGLS10.html">dblp:conf/soda/FominGLS10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tglopfqqmjfdlosg7pu4xqnzsy">fatcat:tglopfqqmjfdlosg7pu4xqnzsy</a> </span>
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On the threshold-width of graphs [article]

M. Chang, L. Hung, T. Kloks, S. Peng
<span title="2012-10-30">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms.  ...  We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs.  ...  Obviously, the class of graphs with TH-width at most k is hereditary. Let k be fixed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1210.8365v1">arXiv:1210.8365v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bmxlvws5bbfb7e5sg7sfoohr6u">fatcat:bmxlvws5bbfb7e5sg7sfoohr6u</a> </span>
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Acyclic coloring of special digraphs [article]

Frank Gurski and Dominique Komander and Carolin Rehs
<span title="2020-11-20">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce the first polynomial-time algorithm for the acyclic coloring problem on digraphs of constant directed clique-width.  ...  An acyclic r-coloring of a directed graph G=(V,E) is a partition of the vertex set V into r acyclic sets.  ...  Parameterized algorithms for directed clique-width For undirected graphs the clique-width [CO00] is one of the most important parameters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.13911v3">arXiv:2006.13911v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/metx5oprwzefjnjf445a7ord2y">fatcat:metx5oprwzefjnjf445a7ord2y</a> </span>
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On the Maximum Cardinality Cut Problem in Proper Interval Graphs and Related Graph Classes [article]

Arman Boyacı and Tınaz Ekim and Mordechai Shalom
<span title="2020-06-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we give FPT algorithms for the maximum cardinality cut problem in classes of graphs containing proper interval graphs and mixed unit interval graphs when parameterized by some new parameters  ...  These new parameters are related to a generalization of the so-called bubble representations of proper interval graphs and mixed unit interval graphs and to clique-width decompositions.  ...  Clique-width Decompositions The MaxCut problem can be solved in polynomial time for graphs with bounded clique-width.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.03856v1">arXiv:2006.03856v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ub2e6rcrq5gozjuvw2h3iyxqgi">fatcat:ub2e6rcrq5gozjuvw2h3iyxqgi</a> </span>
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When Trees Grow Low: Shrubs and Fast MSO1 [chapter]

Robert Ganian, Petr Hliněný, Jaroslav Nešetřil, Jan Obdržálek, Patrice Ossona de Mendez, Reshma Ramadurai
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also introduce a common extension of cographs and of graphs with bounded shrubdepth -m-partite cographs (still of bounded clique-width), which are well quasi-ordered by the relation "is an induced subgraph  ...  Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class.  ...  Note that this claim is in contrast with the well known algorithms of Courcelle [2] for MSO 2 and Courcelle et al. [3] for MSO 1 model checking problems on the graphs of bounded tree-and clique-width  ... 
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Block-Graph Width [chapter]

Maw-Shang Chang, Ling-Ju Hung, Ton Kloks, Sheng-Lung Peng
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For the class B of block graphs we show that graphs with B-width at most 4 are perfect. We also show that B-width is NP-complete and show that it is fixed-parameter tractable.  ...  A graph G has G-width k if there are k independent sets N 1 , . . . , N k in G such that G can be embedded into a graph H ∈ G such that for every edge e in H which is not an edge in G, there exists an  ...  He gratefully acknowledges the funding for this research by the National Science Council of Taiwan.  ... 
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