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An FPT Algorithm for Elimination Distance to Bounded Degree Graphs

Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, Saket Saurabh, Markus Bläser, Benjamin Monmege
2021
They showed that Graph Isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of  ...  bounded degree graphs is fixed-parameter tractable.  ...  A second direction is to investigate the parameterized complexity of various S TA C S 2 0 2 1 5:10 An FPT Algorithm for Elimination Distance to Bounded Degree Graphs graphs problems parameterized by  ... 
doi:10.4230/lipics.stacs.2021.5 fatcat:z5kxoecfufcpdjsqammeo7ql3i

Fixed-Parameter Tractable Distances to Sparse Graph Classes

Jannis Bulian, Anuj Dawar
2016 Algorithmica  
The second shows that determining the elimination distance of a graph G to a minor-closed class C is FPT.  ...  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  ...  Another recently introduced measure is elimination distance, defined in [3] where it was shown that graph isomorphism is FPT when parameterized by elimination distance to a class of graphs of bounded  ... 
doi:10.1007/s00453-016-0235-7 fatcat:yk3piechqnec5gusen2sl7jp4u

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

Jannis Bulian, Anuj Dawar
2015 arXiv   pre-print
The second shows that determining the elimination distance of a graph G to a minor-closed class C is FPT.  ...  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  ...  A natural open question raised by these two results is whether elimination distance to the class of graphs of degree d is FPT.  ... 
arXiv:1502.05910v1 fatcat:uhxviaio4nfo3aahfvdks3eeuq

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree [chapter]

Jannis Bulian, Anuj Dawar
2014 Lecture Notes in Computer Science  
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al.  ...  that need to be deleted from a graph to place it in some class for which efficient algorithms are known.  ...  Corollary 6.8 Graph Isomorphism is FPT parameterized by elimination distance to bounded degree.  ... 
doi:10.1007/978-3-319-13524-3_12 fatcat:elbyocaifvdfrdwxkhj7zdofmq

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Jannis Bulian, Anuj Dawar
2015 Algorithmica  
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al.  ...  that need to be deleted from a graph to place it in some class for which efficient algorithms are known.  ...  Corollary 6.8 Graph Isomorphism is FPT parameterized by elimination distance to bounded degree.  ... 
doi:10.1007/s00453-015-0045-3 fatcat:aojf733y7vap5hpms43uhazuwq

Deleting, Eliminating and Decomposing to Hereditary Classes Are All FPT-Equivalent [article]

Akanksha Agrawal, Lawqueen Kanesh, Daniel Lokshtanov, Fahad Panolan, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi
2022 arXiv   pre-print
For a graph class H, the graph parameters elimination distance to H (denoted by ed_ H) [Bulian and Dawar, Algorithmica, 2016], and H-treewidth (denoted by tw_ H) [Eiben et al.  ...  As an example, we prove that an FPT algorithm for the vertex-deletion problem implies a non-uniform FPT algorithm for computing ed_ H and tw_ H.  ...  In fact, they proved a more general result and obtained the result for elimination distance to graphs of bounded degree as a consequence.  ... 
arXiv:2104.09950v3 fatcat:2itpufur5neqzi5fhxj53dxqvy

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree [article]

Jannis Bulian, Anuj Dawar
2014 arXiv   pre-print
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (2012).  ...  for which efficient algorithms are known.  ...  Canonisation parameterized by elimination distance to bounded degree In this section we show that graph canonisation, and thus graph isomorphism, is FPT parameterized by elimination distance to bounded  ... 
arXiv:1406.4718v2 fatcat:ibwbqostf5cchan4wufjeytsba

Engineering Exact Quasi-Threshold Editing

Lars Gottesbüren, Michael Hamann, Philipp Schoch, Ben Strasser, Dorothea Wagner, Sven Zühlsdorf, Domenico Cantone, Simone Faro
2020 Symposium on Experimental and Efficient Algorithms  
For the FPT algorithm, we introduce a fast heuristic for computing high-quality lower bounds and an improved branching strategy. For the ILP, we engineer several variants of row generation.  ...  We evaluate both methods for quasi-threshold editing on a large set of protein similarity graphs. For most instances, our optimizations speed up the FPT algorithm by one to three orders of magnitude.  ...  For the FPT algorithm, we propose a novel lower bound algorithm based on local search heuristics for independent sets as well as an improved branching strategy.  ... 
doi:10.4230/lipics.sea.2020.10 dblp:conf/wea/GottesburenHSSW20 fatcat:oca4fzswhzdoxj7ohrbun3yhj4

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  As G has treewidth at most k, there is an elimination order of G in which each vertex has degree at most k upon elimination [8, Section 7] .  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number

Michael Fellows, Daniel Lokshtanov, Neeldhara Misra, Matthias Mnich, Frances Rosamond, Saket Saurabh
2009 Theory of Computing Systems  
We do two things: (1) We describe much improved FPT algorithms for a large number of graph problems, for input graphs G for which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically  ...  graphs of bounded max leaf number?  ...  we get an O * (4 k ) FPT algorithm for the Minimum Dominating Set problem, for graphs of max leaf number bounded by k.  ... 
doi:10.1007/s00224-009-9167-9 fatcat:ezqsz2ggzzgd5iicukjjenzoai

The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number [chapter]

Michael Fellows, Frances Rosamond
2007 Lecture Notes in Computer Science  
We do two things: (1) We describe much improved FPT algorithms for a large number of graph problems, for input graphs G for which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically  ...  graphs of bounded max leaf number?  ...  we get an O * (4 k ) FPT algorithm for the Minimum Dominating Set problem, for graphs of max leaf number bounded by k.  ... 
doi:10.1007/978-3-540-73001-9_28 fatcat:6ctmbq7kgrbfpeer6mpc5pqaja

Solving Routing Problems via Important Cuts [article]

Bin Sheng, Gregory Gutin
2022 arXiv   pre-print
The only known FPT algorithm for MV parameterized by p (the same parameter as for MSE) was for chordal graphs (Aoki et al., JCO 2018). We design an FPT algorithm for MV on all undirected graphs.  ...  We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman  ...  Algorithm ABBCP Results of Sections 3 and 4.1 allow us to design an algorithm for solving Bounded BCPP.  ... 
arXiv:2201.12790v2 fatcat:e3g6w2q5hjdbfhgo43ldiyguei

Foreword: Special Issue on IPEC 2014

Marek Cygan, Pinar Heggernes
2016 Algorithmica  
Jannis Bulian and Anuj Dawar consider the Graph Isomorphism problem in Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree.  ...  Arvind and Gaurav Rattan present improved FPT algorithm for Geometric Graph Isomorphism problem, where one is to decide whether there is a distance preserving bijection between two sets of points in k-dimensional  ... 
doi:10.1007/s00453-016-0151-x fatcat:2xhmdtkgtzbbppmbxnhugehgr4

Domination Problems in Nowhere-Dense Classes of Graphs [article]

Anuj Dawar, Stephan Kreutzer
2009 arXiv   pre-print
Our result also establishes that the distance-d dominating-set problem is FPT on classes of bounded expansion, answering a question of Nešetřil and Ossona de Mendez.  ...  This generalises known results about the dominating set problem on H-minor free classes, classes with locally excluded minors and classes of graphs of bounded expansion.  ...  If we are not interested in their distance-d-version than an even simpler algorithm than the one presented above can be used to show that these problems are in FPT on nowhere-dense classes of graphs, which  ... 
arXiv:0907.4283v1 fatcat:apxhpisvb5ew5otmn7mmngpcna

Elimination Distance to Bounded Degree on Planar Graphs

Alexander Lindermayr, Sebastian Siebertz, Alexandre Vigny, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem.  ...  function f and constant c whether the elimination distance of G to the class of degree d graphs is at most k.  ...  Conclusion Our proofs show that all difficulties for elimination distance to bounded degree arise already in bounded degree graphs.  ... 
doi:10.4230/lipics.mfcs.2020.65 dblp:conf/mfcs/LindermayrSV20 fatcat:q7l6fqaqujhj7kewuxyjrbzg6a
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