Filters








8,357 Hits in 4.9 sec

Fixed-parameter Tractable Distances to Sparse Graph Classes [article]

Jannis Bulian, Anuj Dawar
2015 arXiv   pre-print
graph G to C is fixed-parameter tractable.  ...  We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given  ...  In this paper we consider the fixed-parameter tractability of a variety of different notions of distance to various different classes C of sparse graphs.  ... 
arXiv:1502.05910v1 fatcat:uhxviaio4nfo3aahfvdks3eeuq

Fixed-Parameter Tractable Distances to Sparse Graph Classes

Jannis Bulian, Anuj Dawar
2016 Algorithmica  
graph G to C is fixed-parameter tractable.  ...  We show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given  ...  In this paper we consider the fixed-parameter tractability of a variety of different notions of distance to various different classes C of sparse graphs.  ... 
doi:10.1007/s00453-016-0235-7 fatcat:yk3piechqnec5gusen2sl7jp4u

Constant Thresholds Can Make Target Set Selection Tractable

Morgan Chopin, André Nichterlein, Rolf Niedermeier, Mathias Weller
2013 Theory of Computing Systems  
corresponding fixed-parameter tractability and (parameterized) hardness results.  ...  We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some "cliquish" graphs and developing  ...  For the larger (thus "weaker" [19] ) parameter "distance to clique" (the minimum number of vertices to delete to make a graph a clique), however, TSS is fixed-parameter tractable for both constant and  ... 
doi:10.1007/s00224-013-9499-3 fatcat:ykvmkfbzhje2dbfcyuhkzvunnm

Constant Thresholds Can Make Target Set Selection Tractable [chapter]

Morgan Chopin, André Nichterlein, Rolf Niedermeier, Mathias Weller
2012 Lecture Notes in Computer Science  
corresponding fixed-parameter tractability and (parameterized) hardness results.  ...  We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some "cliquish" graphs and developing  ...  For the larger (thus "weaker" [19] ) parameter "distance to clique" (the minimum number of vertices to delete to make a graph a clique), however, TSS is fixed-parameter tractable for both constant and  ... 
doi:10.1007/978-3-642-34862-4_9 fatcat:xhx6vk3kjzgmlgcuhcmrgigrn4

Structure and Specification as Sources of Complexity

Anuj Dawar, Marc Herbstritt
2009 Foundations of Software Technology and Theoretical Computer Science  
Automata and Locality The following is a sampling of results on the fixed-parameter tractability of the first-order satisfaction problem on classes of sparse graphs.  ...  It is easy to establish that problems such as INDEPENDENT SET are fixed-parameter tractable on such classes.  ... 
doi:10.4230/lipics.fsttcs.2009.2336 dblp:conf/fsttcs/Dawar09 fatcat:gubhh5istngmjcauyzu33d3cja

The Complexity of Satisfaction on Sparse Graphs [chapter]

Anuj Dawar
2010 Lecture Notes in Computer Science  
It subsumes many natural parameterized graph problems (where, fixing the parameter, we can express the problem in first-order logic). • Vertex Cover; • Independent Set; • Dominating Set; • Network Centres  ...  That is, given a graph G and a formula ϕ of first-order logic in the language of graphs: What is the complexity of this, parameterized by the length of ϕ?  ...  First-order logic is fixed-parameter tractable on M k .  ... 
doi:10.1007/978-3-642-17493-3_1 fatcat:p2md6mgdnneollnsmsf23tondu

A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems [article]

Nicolas Bousquet and Amer E. Mouawad and Naomi Nishimura and Sebastian Siebertz
2022 arXiv   pre-print
The emphasis will be on positive results and the most common techniques for the design of fixed-parameter tractable algorithms.  ...  We survey both older and more recent work on the parameterized complexity of all three problems when parameterized by the number of tokens k.  ...  ., Independent Set, Dominating Set, and Connected Dominating Set parameterized by solution size k become fixed-parameter tractable when restricted to sparse graph classes, such as planar, bounded degree  ... 
arXiv:2204.10526v1 fatcat:ua3pkqxtabatbbl6jydhy3i3b4

Spanners of bounded degree graphs

Fedor V. Fomin, Petr A. Golovach, Erik Jan van Leeuwen
2011 Information Processing Letters  
We prove that for fixed k, w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree.  ...  In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree.  ...  They proved that the problem of finding a k-spanner of treewidth at most w in a given planar graph G is fixed-parameter tractable parameterized by k and w, and for every fixed k and w, this problem can  ... 
doi:10.1016/j.ipl.2010.10.021 fatcat:gw6jr2js4fchzbi62lscizrhj4

Algorithmic Properties of Sparse Digraphs

Stephan Kreutzer, Irene Muzi, Patrice Ossona De Mendez, Roman Rabinovich, Sebastian Siebertz, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
The classes of directed graphs having those properties are very general classes of sparse directed graphs, as they include, on one hand, all classes of directed graphs whose underlying undirected class  ...  has bounded expansion, such as planar, bounded-genus, and H-minor-free graphs, and on the other hand, they also contain classes whose underlying undirected class is not even nowhere dense.  ...  Once fixed-parameter tractability is established, we turn our attention to the kernelisation problem for Distance-r Dominating Set.  ... 
doi:10.4230/lipics.stacs.2019.46 dblp:conf/stacs/KreutzerMMRS19 fatcat:k3zs6tfrpfbaxpkk4bfrnu5s7i

Progressive Algorithms for Domination and Independence

Grzegorz Fabianski, Michal Pilipczuk, Sebastian Siebertz, Szymon Torunczyk, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
We demonstrate our approach by giving linear-time fixed-parameter algorithms for the Distance-r Dominating Set problem (parameterized by the solution size) in a wide variety of restricted graph classes  ...  Similarly, for the Distance-r Independent Set problem the technique can be used to give a linear-time fixed-parameter algorithm on any nowhere dense class.  ...  Acknowledgements We thank Ehud Hrushovski for pointing us to the nfcp property.  ... 
doi:10.4230/lipics.stacs.2019.27 dblp:conf/stacs/FabianskiPST19 fatcat:wutum5aw6bho3clozgv7nl4hxy

Recovering Sparse Graphs

Jakub Gajarský, Daniel Král', Michael Wagner
2018 International Symposium on Mathematical Foundations of Computer Science  
We derive as a corollary that if G is a graph class with bounded expansion, then the first order model checking is fixed parameter tractable in the class of all graphs that can obtained from a graph G  ...  We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set  ...  Both these problems are fixed parameter tractable when parameterized by d and k.  ... 
doi:10.4230/lipics.mfcs.2018.29 dblp:conf/mfcs/GajarskyK18 fatcat:bzr43lgahrewhbz6lb67dd67si

Recovering sparse graphs [article]

Jakub Gajarsky, Daniel Kral
2018 arXiv   pre-print
We derive as a corollary that if G_0 is a graph class with bounded expansion, then the first order model checking is fixed parameter tractable in the class of all graphs that can obtained from a graph  ...  We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set  ...  Both these problems are fixed parameter tractable when parameterized by d and k.  ... 
arXiv:1709.09985v3 fatcat:glc4eiz5l5ckjnafhycgxaxqma

On the Treewidth of Dynamic Graphs [chapter]

Bernard Mans, Luke Mathieson
2013 Lecture Notes in Computer Science  
We show the application of these results to problems in dynamic graph theory and dynamic extensions to static problems.  ...  In addition we demonstrate that certain widely used dynamic graph classes have bounded local treewidth.  ...  Let C be any class of structures of bounded local treewidth. MC(C , FO) is fixed-parameter tractable when parameterized by the length of the FO sentence. [16] .)  ... 
doi:10.1007/978-3-642-38768-5_32 fatcat:miynieup6rfdrkc46vf4w3zp7i

On the treewidth of dynamic graphs

Bernard Mans, Luke Mathieson
2014 Theoretical Computer Science  
We show the application of these results to problems in dynamic graph theory and dynamic extensions to static problems.  ...  In addition we demonstrate that certain widely used dynamic graph classes have bounded local treewidth.  ...  Let C be any class of structures of bounded local treewidth. MC(C , FO) is fixed-parameter tractable when parameterized by the length of the FO sentence. [16] .)  ... 
doi:10.1016/j.tcs.2013.12.024 fatcat:cbpjf6h62vdxxjdssqrw74h5vu

Domination Above r-Independence: Does Sparseness Help?

Carl Einarson, Felix Reidl, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
does the restriction to sparse graph classes help here?  ...  In the spirit of gap-parameters, we consider a parametrisation by the size of the "residual" set Our work aims to answer two questions: How does the constant r affect the tractability of the problem and  ...  For r = 3, the problem is W [2] -hard in general graphs but admits an XP-algorithm. In nowhere dense and bounded expansion classes, it is fixed-parameter tractable.  ... 
doi:10.4230/lipics.mfcs.2019.40 dblp:conf/mfcs/EinarsonR19 fatcat:2ufaxeeggvcgbmgjidmiqkkxk4
« Previous Showing results 1 — 15 out of 8,357 results