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On the parameterized complexity of multiple-interval graph problems

2009
*
Theoretical Computer Science
*

In this sequel, we study

doi:10.1016/j.tcs.2008.09.065
fatcat:gdjhribxtvcitktdvwyhslnpie
*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 ...##
###
On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

Fellows et al. presented an FPT algorithm for k-CLIQUE in t-

doi:10.1007/978-3-642-13509-5_12
fatcat:6236yg4f3neyba7xlcgmt6hr7a
*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) ...##
###
On the parameterized complexity of some optimization problems related to multiple-interval graphs

2010
*
Theoretical Computer Science
*

Finally, we use

doi:10.1016/j.tcs.2010.09.001
fatcat:lg2rgcpqpnccxn5nx4hc6ugzc4
*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*. ...##
###
Parameterized Complexity

2002
*
Electronical Notes in Theoretical Computer Science
*

In this sequel, we study

doi:10.1016/s1571-0661(04)00301-9
fatcat:oecuoylw5jbe7o3esiqqtomlae
*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 ...##
###
k-Gap Interval Graphs
[article]

2011
*
arXiv
*
pre-print

We initiate

arXiv:1112.3244v2
fatcat:3mih66goi5hcrpzuvn3kbrsb7i
*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*. ...##
###
k-Gap Interval Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

We initiate

doi:10.1007/978-3-642-29344-3_30
fatcat:m7kymxr3hjhhvcyypxfshmqwuy
*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*. ...##
###
Parameterized Complexity in Multiple-Interval Graphs: Partition, Separation, Irredundancy
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present new results

doi:10.1007/978-3-642-22685-4_6
fatcat:7r4kzz5htnebthuz45eyurujmu
*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*. ...##
###
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable

2013
*
Theoretical Computer Science
*

We examine

doi:10.1016/j.tcs.2012.11.038
fatcat:vspgtpyrmbdqfjo57hudtc37dy
*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*. ...##
###
Parameterized complexity analysis in computational biology

1995
*
Bioinformatics
*

Lower bounds

doi:10.1093/bioinformatics/11.1.49
fatcat:bnu2gatf3ras5m6tptq4bkp2m4
*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 ...##
###
Parameterized complexity in multiple-interval graphs: Domination, partition, separation, irredundancy

2012
*
Theoretical Computer Science
*

Recall

doi:10.1016/j.tcs.2012.01.025
fatcat:7lon6rppsrbafejzvbswxiwgkq
*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. ...##
###
An Improved FPT Algorithm and Quadratic Kernel for Pathwidth One Vertex Deletion
[chapter]

2010
*
Lecture Notes in Computer Science
*

Recently Philip et al. [14] initiated

doi:10.1007/978-3-642-17493-3_11
fatcat:orqu3ziug5ez7geggcmlmvfhua
*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*...##
###
Parameterized complexity in multiple-interval graphs: domination, partition, separation, irredundancy
[article]

2011
*
arXiv
*
pre-print

In addition, we present various new results

arXiv:1110.0187v1
fatcat:d6vp67kqrnffjbyjkizbuuh3dy
*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*. ...##
###
Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs

2020
*
European Symposium on Algorithms
*

We discover that a number

doi:10.4230/lipics.esa.2020.49
dblp:conf/esa/FominG20a
fatcat:dh4jo3kb5rc3xgw7rqfted5doi
*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. ...##
###
On the Parallel Parameterized Complexity of the Graph Isomorphism Problem
[article]

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. ...

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

2022
*
arXiv
*
pre-print

We survey

arXiv:2207.12278v1
fatcat:va33yl356fh5xn64qge6tvhpuq
*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*. ...
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