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On the parameterized complexity of multiple-interval graph problems

Michael R. Fellows, Danny Hermelin, Frances Rosamond, Stéphane Vialette
2009 Theoretical Computer Science  
In this sequel, we study multiple-interval graph problems from the perspective of parameterized complexity.  ...  Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it.  ...  The research of first and third authors has been supported by the Australian Research Council through the Australian Center for Bioinformatics, by the University of Newcastle Parameterized Complexity Research  ... 
doi:10.1016/j.tcs.2008.09.065 fatcat:gdjhribxtvcitktdvwyhslnpie

On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs [chapter]

Minghui Jiang
2010 Lecture Notes in Computer Science  
Fellows et al. presented an FPT algorithm for k-CLIQUE in t-interval graphs parameterized by both k and t.  ...  If the parameter t does not appear in the bound, then we would have an FPT algorithm for the W[1]hard problem of k-CLIQUE in general graphs. A genomic map is a sequence of gene markers.  ...  with a parametric time-bound of max{t O(k) , 2 O(k log k) }. (2)  ... 
doi:10.1007/978-3-642-13509-5_12 fatcat:6236yg4f3neyba7xlcgmt6hr7a

On the parameterized complexity of some optimization problems related to multiple-interval graphs

Minghui Jiang
2010 Theoretical Computer Science  
Finally, we use the W[1]hardness of k-Independent Set in t-track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called Maximal Strip Recovery  ...  We also give an FPT algorithm for k-Clique in t-interval graphs, parameterized by both k and t, with running time where n is the number of vertices in the graph.  ...  [15] recently initiated the study of the parameterized complexity of multiple-interval graph problems.  ... 
doi:10.1016/j.tcs.2010.09.001 fatcat:lg2rgcpqpnccxn5nx4hc6ugzc4

Parameterized Complexity

Michael R. Fellows
2002 Electronical Notes in Theoretical Computer Science  
In this sequel, we study multiple-interval graph problems from the perspective of parameterized complexity.  ...  Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it.  ...  The research of first and third authors has been supported by the Australian Research Council through the Australian Center for Bioinformatics, by the University of Newcastle Parameterized Complexity Research  ... 
doi:10.1016/s1571-0661(04)00301-9 fatcat:oecuoylw5jbe7o3esiqqtomlae

k-Gap Interval Graphs [article]

Fedor V. Fomin, Serge Gaspers, Petr Golovach, Karol Suchan, Stefan Szeider, Erik Jan van Leeuwen, Martin Vatshelle, Yngve Villanger
2011 arXiv   pre-print
We initiate the study of a new parameterization of graph problems.  ...  In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex  ...  On the other hand, the total number of gaps, k, in a multiple interval representation seems to be a more useful parameterization of problems on multiple interval graphs.  ... 
arXiv:1112.3244v2 fatcat:3mih66goi5hcrpzuvn3kbrsb7i

k-Gap Interval Graphs [chapter]

Fedor V. Fomin, Serge Gaspers, Petr Golovach, Karol Suchan, Stefan Szeider, Erik Jan van Leeuwen, Martin Vatshelle, Yngve Villanger
2012 Lecture Notes in Computer Science  
We initiate the study of a new parameterization of graph problems.  ...  In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex  ...  On the other hand, the total number of gaps, k, in a multiple interval representation seems to be a more useful parameterization of problems on multiple interval graphs.  ... 
doi:10.1007/978-3-642-29344-3_30 fatcat:m7kymxr3hjhhvcyypxfshmqwuy

Parameterized Complexity in Multiple-Interval Graphs: Partition, Separation, Irredundancy [chapter]

Minghui Jiang, Yong Zhang
2011 Lecture Notes in Computer Science  
We present new results on the parameterized complexities of k-VERTEX CLIQUE PARTITION and k-SEPARATING VERTICES in multiple-interval graphs and their complements, and present a very simple alternative  ...  proof of the W[1]hardness of k-IRREDUNDANT SET in general graphs  ...  [9] initiated the study of multiple-interval graph problems from the perspective of parameterized complexity.  ... 
doi:10.1007/978-3-642-22685-4_6 fatcat:7r4kzz5htnebthuz45eyurujmu

Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable

Michael Fellows, Tobias Friedrich, Danny Hermelin, Nina Narodytska, Frances Rosamond
2013 Theoretical Computer Science  
We examine the complexity of constraint satisfaction problems that consist of a set of AllDiff constraints.  ...  Our main contribution is an extensive study of the complexity of Multiple AllDiff CSPs for a set of natural parameters, like maximum domain size and maximum size of the constraint scopes.  ...  in the framework of parameterized complexity.  ... 
doi:10.1016/j.tcs.2012.11.038 fatcat:vspgtpyrmbdqfjo57hudtc37dy

Parameterized complexity analysis in computational biology

H.L. Bodlaender, R.G. Downey, M.R. Fellows, M.T. Hallett, H.T. Wareham
1995 Bioinformatics  
Lower bounds on the complexity of this basic combinatorial problem imply lower bounds on more general sequence alignment and consensus discovery problems.  ...  We also describe a number of open problems pertaining to the parameterized complexity of problems in computational biology where small parameter values are important.  ...  Note that these problems can also be stated on colored graphs, yielding alternate (and more biologically useful) versions of the problem Intervalizing colored graphs studied in Fellows et al. (1993) and  ... 
doi:10.1093/bioinformatics/11.1.49 fatcat:bnu2gatf3ras5m6tptq4bkp2m4

Parameterized complexity in multiple-interval graphs: Domination, partition, separation, irredundancy

Minghui Jiang, Yong Zhang
2012 Theoretical Computer Science  
Recall the sharp contrast in parameterized complexities of the two problems k-independent set and k-clique in multiple-interval graphs and their complements.  ...  In addition, we present various new results on the parameterized complexities of k-vertex clique partition and k-separating vertices in multiple-interval graphs and their complements, and present a very  ...  Is it still W[1]-hard in co-2-track interval graphs or co-unit 3-track interval graphs? Many questions can be asked in the same spirit.  ... 
doi:10.1016/j.tcs.2012.01.025 fatcat:7lon6rppsrbafejzvbswxiwgkq

An Improved FPT Algorithm and Quadratic Kernel for Pathwidth One Vertex Deletion [chapter]

Marek Cygan, Marcin Pilipczuk, Michał Pilipczuk, Jakub Onufry Wojtaszczyk
2010 Lecture Notes in Computer Science  
Recently Philip et al. [14] initiated the study of the parameterized complexity of POVD and have shown a quartic kernel and a 7 k n O(1) algorithm.  ...  The PATHWIDTH ONE VERTEX DELETION (POVD) problem, given an undirected graph G and an integer k, asks whether one can delete at most k vertices from G so that the remaining graph has pathwidth at most 1  ...  One of the most extensively studied problems in the parameterized complexity community, FEEDBACK VERTEX SET, asks for a set of vertices of size at most k such that their deletion results in a graph of  ... 
doi:10.1007/978-3-642-17493-3_11 fatcat:orqu3ziug5ez7geggcmlmvfhua

Parameterized complexity in multiple-interval graphs: domination, partition, separation, irredundancy [article]

Minghui Jiang, Yong Zhang
2011 arXiv   pre-print
In addition, we present various new results on the parameterized complexities of k-Vertex Clique Partition and k-Separating Vertices in multiple-interval graphs and their complements, and present a very  ...  On the other hand, we show that these problems belong to W[1] when restricted to multiple-interval graphs and their complements. This answers an open question of Fellows et al.  ...  [11] initiated the study of multiple-interval graph problems from the perspective of parameterized complexity.  ... 
arXiv:1110.0187v1 fatcat:d6vp67kqrnffjbyjkizbuuh3dy

Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs

Fedor V. Fomin, Petr A. Golovach, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
We discover that a number of fundamental intractable optimization problems being parameterized by k admit subexponential algorithms on graphs from Chordal-ke.  ...  On the other hand, we show that for some fundamental optimization problems, like finding an optimal graph coloring or finding a maximum clique, are FPT on Chordal-ke when parameterized by k but do not  ...  Acknowledgements We thank Torstein Strømme, Daniel Lokshtanov, and Pranabendu Misra for fruitful discussions on the topic of this paper.  ... 
doi:10.4230/lipics.esa.2020.49 dblp:conf/esa/FominG20a fatcat:dh4jo3kb5rc3xgw7rqfted5doi

On the Parallel Parameterized Complexity of the Graph Isomorphism Problem [article]

Bireswar Das, Murali Krishna Enduri, I. Vinod Reddy
2017 arXiv   pre-print
The parallel parameterized complexity of parameterized by the size of a feedback vertex set remains an open problem.  ...  In this paper, we study the parallel and the space complexity of the graph isomorphism problem () for several parameterizations. Let H={H_1,H_2,...  ...  Cographs are P 4 -free graphs i.e., they do not contain any induced paths on four vertices. Interval graphs are the intersection graphs of a family of intervals on the real line.  ... 
arXiv:1711.08885v2 fatcat:xufsxkkaafblxo6e4p2q7h3ohe

A Survey on Graph Problems Parameterized Above and Below Guaranteed Values [article]

Gregory Gutin, Matthias Mnich
2022 arXiv   pre-print
We survey the field of algorithms and complexity for graph problems parameterized above or below guaranteed values, a research area which was pioneered by Venkatesh Raman.  ...  Those problems seek, for a given graph G, a solution whose value is at least g(G)+k or at most g(G)-k, where g(G) is a guarantee on the value that any solution on G takes.  ...  A survey by Serna and Thilikos [53] on parameterized complexity of graph layout problems lists ten such problems.  ... 
arXiv:2207.12278v1 fatcat:va33yl356fh5xn64qge6tvhpuq
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