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Maximum matching width: new characterizations and a fast algorithm for dominating set [article]

Jisu Jeong, Sigve Hortemo Sæther, Jan Arne Telle
2015 arXiv   pre-print
Given only the graph G and using the best known algorithms to find decompositions, maximum matching width will be better for solving Dominating Set whenever tw(G) > 1.549 ×mmw(G).  ...  We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A,B,C ⊆ X  ...  Taking the subtrees of tree representation for treewidth, branchwidth and maximum matching width mentioned in the Introduction as input, our algorithm for dominating set can be seen as a generic one that  ... 
arXiv:1507.02384v1 fatcat:euc6vu3prrhvnmxwoynk6a6azu

Maximum matching width: New characterizations and a fast algorithm for dominating set

Jisu Jeong, Sigve Hortemo Sæther, Jan Arne Telle
2018 Discrete Applied Mathematics  
Given only the graph G and using the best known algorithms to find decompositions, maximum matching width will be better for solving Dominating Set whenever tw(G) > 1.549 × mmw(G).  ...  We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A, B, C ⊆  ...  Taking the subtrees of tree representation for treewidth, branchwidth and maximum matching width mentioned in the Introduction as input, our algorithm for dominating set can be seen as a generic one that  ... 
doi:10.1016/j.dam.2017.09.019 fatcat:heppqi43ffct7nrqbmxua7ulka

Maximum Matching Width: New Characterizations and a Fast Algorithm for Dominating Set

Jisu Jeong, Sigve Hortemo Saether, Jan Telle
unpublished
Given only the graph G and using the best known algorithms to find decompositions, maximum matching width will be better for solving Dominating Set whenever tw(G) > 1.549 × mmw(G).  ...  We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A, B, C ⊆  ...  Taking the subtrees of tree representation for treewidth, branchwidth and maximum matching width mentioned in the Introduction as input, our algorithm for dominating set can be seen as a generic one that  ... 
fatcat:l37ho7caajgopcraj2uichnseu

Access to Data and Number of Iterations: Dual Primal Algorithms for Maximum Matching under Resource Constraints [article]

Kook Jin Ahn, Sudipto Guha
2015 arXiv   pre-print
For any constant p>1, we provide an iterative sampling based algorithm for computing a (1-ϵ)-approximation of the weighted nonbipartite maximum matching that uses O(p/ϵ) rounds of sampling, and O(n^1+1  ...  In SPAA 2011, Lattanzi etal. provided a O(1) approximation of maximum matching using O(p) rounds of iterative filtering via mapreduce and O(n^1+1/p) space of central processing for a graph with n nodes  ...  Often these iterative algorithms converge fast and provide a solution which is much better than the worst case guarantees.  ... 
arXiv:1307.4359v3 fatcat:nv5p4qnkyralro53bq5msslwaq

Boolean-Width of Graphs [chapter]

B. -M. Bui-Xuan, J. A. Telle, M. Vatshelle
2009 Lecture Notes in Computer Science  
For an n-vertex graph given with a decomposition tree of boolean-width k, we solve Maximum Weight Independent Set in time O(n 2 k2 2k ) and Minimum Weight Dominating Set in time O(n 2 + nk2 3k ).  ...  With an additional n 2 factor in the runtime, we can also count all independent sets and dominating sets of each cardinality.  ...  Independent Dominating Sets Combining the requirements of independence and domination in the definition of tables and in the algorithm we can solve both the Minimum and Maximum Independent Dominating Set  ... 
doi:10.1007/978-3-642-11269-0_5 fatcat:xer24xhbnbh3bdqauzggqfw2b4

Boolean-width of graphs

Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
2011 Theoretical Computer Science  
For an n-vertex graph given with a decomposition tree of boolean-width k, we solve Maximum Weight Independent Set in time O(n 2 k2 2k ) and Minimum Weight Dominating Set in time O(n 2 + nk2 3k ).  ...  With an additional n 2 factor in the runtime, we can also count all independent sets and dominating sets of each cardinality.  ...  Independent Dominating Sets Combining the requirements of independence and domination in the definition of tables and in the algorithm we can solve both the Minimum and Maximum Independent Dominating Set  ... 
doi:10.1016/j.tcs.2011.05.022 fatcat:kfmhmeu7dbgzldtybqchilgwf4

Fully polynomial FPT algorithms for some classes of bounded clique-width graphs [article]

David Coudert COATI,
2017 arXiv   pre-print
We believe that our most important result is an O(k^4 · n + m)-time algorithm for computing a maximum matching where k is either the modular-width or the P_4-sparseness.  ...  , Gromov hyperbolicity, betweenness centrality) and maximum matching.  ...  New Parameterized algorithms for Maximum Matching A matching in a graph is a set of edges with pairwise disjoint end vertices. We consider the problem of computing a matching of maximum size.  ... 
arXiv:1707.05016v2 fatcat:qogbvqxlmba5npiyzxhb2xcwa4

The Algorithmic Complexity of Tree-Clique Width [article]

Chris Aronis
2021 arXiv   pre-print
Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems.  ...  Therefore, we introduce tree-clique width, denoted by tcl(G) for a graph G, a new width measure for tree decompositions.  ...  Acknowledgements The author thanks Hans Bodlaender and Jelle Oostveen for discussions and suggestions that helped to improve this paper.  ... 
arXiv:2111.02200v1 fatcat:vvl52cnvkbcznkabrs7acrnbvq

Practical Algorithms for Linear Boolean-width

Chiel B. Ten Brinke, Frank J. P. Van Houten, Hans L. Bodlaender, Marc Herbstritt
2015 International Symposium on Parameterized and Exact Computation  
In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms.  ...  We first give an exact algorithm for computing optimal linear boolean decompositions, improving upon existing algorithms, and subsequently investigate several new heuristics through experiments, improving  ...  This class of problems consists of finding a (σ, ρ)-set of maximum or minimum cardinality and contains well known problems such as the maximum independent set, the minimum dominating set and the maximum  ... 
doi:10.4230/lipics.ipec.2015.187 dblp:conf/iwpec/BrinkeHB15 fatcat:zeaozky3ibbylbil6s2yfjcy3u

Practical Algorithms for Linear Boolean-width [article]

Chiel B. Ten Brinke, Frank J. P. van Houten, Hans L. Bodlaender
2015 arXiv   pre-print
In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms.  ...  We also evaluated dynamic programming algorithms on linear boolean decompositions for several vertex subset problems.  ...  This class of problems consists of finding a (σ, ρ)-set of maximum or minimum cardinality and contains well known problems such as the maximum independent set, the minimum dominating set and the maximum  ... 
arXiv:1509.07687v1 fatcat:s6yyllxdd5aebgxxdvixrogdrm

Node Multiway Cut and Subset Feedback Vertex Set on Graphs of Bounded Mim-width [article]

Benjamin Bergougnoux, Charis Papadopoulos, Jan Arne Telle
2022 arXiv   pre-print
The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a given set of terminals, and for  ...  We design a meta-algorithm that allows to solve both problems in time 2^O(rw^3)· n^4, 2^O(q^2log(q))· n^4, and n^O(k^2) where rw is the rank-width, q the ℚ-rank-width, and k the mim-width of a given decomposition  ...  [7] to design a meta-algorithm, also giving XP algorithms by mim-width, for so-called (σ, ρ) generalized domination problems.  ... 
arXiv:1910.00887v8 fatcat:iuxxwa6gdncmrfowgnqm4ax32i

Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming

Li-Hsuan Chen, Felix Reidl, Peter Rossmanith, Fernando Sánchez Villaamil
2018 Algorithms  
Specifically, we design two novel algorithms for DOMINATING SET on graphs of treedepth d: A pure branching algorithm that runs in time d O(d 2 ) · n and uses space O(d 3 log d + d log n) and a hybrid of  ...  SET for any > 0.  ...  Lokshtanov, Marx and Saurabh showed-assuming the Strong Exponential Time Hypothesis (SETH)-that for 3-COLORING, VERTEX COVER and DOMINATING SET algorithms on a tree decomposition of width w with running  ... 
doi:10.3390/a11070098 fatcat:4diwb3o3fzfn7jz6joixddfbry

Twin-width III: Max Independent Set, Min Dominating Set, and Coloring [article]

Édouard Bonnet, Colin Geniet, Eun Jung Kim, Stéphan Thomassé, Rémi Watrigant
2021 arXiv   pre-print
We present 2^O(k)n-time algorithms for k-Independent Set, r-Scattered Set, k-Clique, and k-Dominating Set when an O(1)-sequence is provided.  ...  The inevitable price to pay for such a general result is that f is a tower of exponentials of height roughly k. In this paper, we show that algorithms based on twin-width need not be impractical.  ...  For Min Dominating Set on bounded twin-width graphs, we ask for a constantapproximation algorithm with ratio independent on the twin-width bound, or even for a PTAS.  ... 
arXiv:2007.14161v2 fatcat:25jkfscxwvbqljzupiftzowacu

Fully polynomial FPT algorithms for some classes of bounded clique-width graphs [chapter]

David Coudert, Guillaume Ducoffe, Alexandra Popa
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We believe that our most important result is an O(k 4 · n + m)-time algorithm for computing a maximum matching where k is either the modular-width or the P4-sparseness.  ...  In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems, distance problems and maximum matching.  ...  New Parameterized algorithms for Maximum Matching A matching in a graph is a set of edges with pairwise disjoint end vertices. We consider the problem of computing a matching of maximum cardinality.  ... 
doi:10.1137/1.9781611975031.176 dblp:conf/soda/CoudertDP18 fatcat:ktq2zmjnyjbfvkkbbz5udkpi3y

Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width Graphs

David Coudert, Guillaume Ducoffe, Alexandru Popa
2019 ACM Transactions on Algorithms  
We believe that our most important result is an algorithm in O(k 4 · n + m)-time for computing a maximum matching where k is either the modular-width of the graph or the P 4 -sparseness.  ...  The well known algorithm in [85] , that runs in O(m √ n)-time, is essentially the best so far for Maximum Matching.  ...  1819-01-01"Modeling, simulation, optimization of complex systems and decision support in new areas of IT&C research", funded by the Ministry of Research and Innovation, Romania, and by a grant of Romanian  ... 
doi:10.1145/3310228 fatcat:yx262bgipvebfi7p3sh6xl5kfq
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