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Solving Graph Isomorphism Using Parameterized Matching
[chapter]

2013
*
Lecture Notes in Computer Science
*

We propose a new approach to

doi:10.1007/978-3-319-02432-5_26
fatcat:et66ctddmrbhtly5etm5d5g4oa
*solve**graph**isomorphism**using**parameterized**matching*. ... To find*isomorphism*between two*graphs*, one*graph*is linearized, i.e., represented as a*graph*walk that covers all nodes and edges such that each element is represented by a parameter. ... A good algorithm for*graph**isomorphism*should find*isomorphic**graphs*quickly in many cases. In this paper we apply*parameterized**matching*to*solve**graph**isomorphism*. ...##
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On the complexity of various parameterizations of common induced subgraph isomorphism

2017
*
Theoretical Computer Science
*

feedback vertex sets of the input

doi:10.1016/j.tcs.2017.07.010
fatcat:dabbehi67bcwlmjt2ygu67b5dy
*graphs*, that is*solving*them in polynomial time is very unlikely when this parameter is a constant. ... MCIS remains NP-hard on many*graph*classes including bipartite*graphs*, planar*graphs*and k-trees. Little is known, however, about the*parameterized*complexity of the problem. ... However, that algorithm cannot help*us*much for*solving*MCCIS since it relies on the existence of a feasible solution of size at least ≈ n − k which consists of mapping the two big independent sets of ...##
###
Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)

2014
*
Symposium on Theoretical Aspects of Computer Science
*

Given two

doi:10.4230/lipics.stacs.2014.542
dblp:conf/stacs/MarxP14
fatcat:dy4trfjwkvhj3i2tzcvrguedyi
*graphs*H and G, the Subgraph*Isomorphism*problem asks if H is*isomorphic*to a subgraph of G. While NP-hard in general, algorithms exist for various*parameterized*versions of the problem. ... Our goal is to systematically investigate the possible*parameterized*algorithms that can exist for Subgraph*Isomorphism*. ... In fact, the only way we were able to*solve*these*matching*problems is by the randomized algebraic*matching*algorithm of Mulmuley et al. [28] . ...##
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On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[chapter]

2015
*
Lecture Notes in Computer Science
*

It remains NP-hard on many

doi:10.1007/978-3-319-19315-1_1
fatcat:knzdi3nve5ao7kvxr7ubulpdnq
*graph*classes including forests. In this paper, we study the*parameterized*complexity of MCIS. ... We complement this result by showing that, unless the ETH fails, it cannot be*solved*in time 2 o(k log k) . ... Obviously, if there is a k-clique S in G, then the*graph*I(G)[S ∪ E(S)] is*isomorphic*to I(K k ). Now, let*us*assume that I(K k ) is*isomorphic*to an induced subgraph of I(G). ...##
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On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[article]

2017
*
arXiv
*
pre-print

It remains NP-hard on many

arXiv:1412.1261v2
fatcat:ownbquhznvcrnmz4uthnys5o3m
*graph*classes including forests. In this paper, we study the*parameterized*complexity of MCIS. ... We complement this result by showing that, unless the ETH fails, it cannot be*solved*in time 2^o(k k). ... Obviously, if there is a k-clique S in G, then the*graph*I(G)[S ∪ E(S)] is*isomorphic*to I(K k ). Now, let*us*assume that I(K k ) is*isomorphic*to an induced subgraph of I(G). ...##
###
Foreword: Special Issue on IPEC 2014

2016
*
Algorithmica
*

In The

doi:10.1007/s00453-016-0151-x
fatcat:2xhmdtkgtzbbppmbxnhugehgr4
*Parameterized*Complexity of Geometric*Graph**Isomorphism*, V. ... Jannis Bulian and Anuj Dawar consider the*Graph**Isomorphism*problem in*Graph**Isomorphism**Parameterized*by Elimination Distance to Bounded Degree. ...##
###
Parameterized Aspects of Strong Subgraph Closure

2020
*
Algorithmica
*

Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the

doi:10.1007/s00453-020-00684-9
fatcat:nhbdwiiu35hndapxu3wdxes7ou
*parameterized*study ... An induced*matching*, denoted byqK 2 , is a*matching*M of q edges such that G[V (M )] is*isomorphic*to qK 2 .Let*us*give a couple of observations on the nature of our problem.An F -*graph*of a subgraph H ... If two*graphs*H and F are*isomorphic*then we write H F , and if they are not*isomorphic*then we write H F . ...##
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Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)

2015
*
Dagstuhl Reports
*

Over the last two decades

doi:10.4230/dagrep.4.11.1
dblp:journals/dagstuhl-reports/KratschLMR14
fatcat:vwgmhttkgrf4pb34jpsb2rfvnm
*parameterized*complexity has become one of the main tools for handling intractable problems. ... This report documents the program and the outcomes of Dagstuhl Seminar 14451 "Optimality and tight results in*parameterized*complexity". ... For both of these families, ETH can be*used*to pinpoint the optimum form of the running time of a*parameterized*algorithm*solving*the problem. ...##
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Isomorphism for Graphs of Bounded Feedback Vertex Set Number
[chapter]

2010
*
Lecture Notes in Computer Science
*

We prove that the

doi:10.1007/978-3-642-13731-0_9
fatcat:ys6cnyk3qfaatfczzh24vkxlvm
*Graph**Isomorphism*problem is fixed-parameter tractable when*parameterized*by the feedback vertex set number. ... For*graphs*of bounded feedback vertex set number the presented algorithm runs in time O(n 2 ), and is thereby the first fixed-parameter tractable*Graph**Isomorphism*algorithm for a non-trivial parameter ... We now design an FPT-algorithm that*solves**Graph**Isomorphism**parameterized*with the feedback vertex set number. ...##
###
Stable Matching Games: Manipulation via Subgraph Isomorphism

2017
*
Algorithmica
*

Our algorithm is a nontrivial combination of a

doi:10.1007/s00453-017-0382-5
fatcat:txog53msovgvxlpc7mvtw5x67q
*parameterized*algorithm for Subgraph*Isomorphism*, a relationship between stable*matching*and finding an out-branching in an appropriate*graph*and enumerating ... We will*use*(L M , L W ) to denote the set of preference lists of men and women, and the men-optimal*matching*with respect to these lists is denoted by GS(L M , L W ). ...*graph*[2, 17] , and a*parameterized*algorithm for Colored Subgraph*Isomorphism*[1, 7, 8] , we can search for a subgraph in the universal suitor*graph*that is*isomorphic*to an out-branching corresponding ...##
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Graph Square Roots of Small Distance from Degree One Graphs
[article]

2020
*
arXiv
*
pre-print

We are interested in the

arXiv:2010.05733v1
fatcat:43jifxqrfjcyvjplbcvdejbl4e
*parameterized*complexity of the problem for classes ℋ that are composed by the*graphs*at vertex deletion distance at most k from*graphs*of maximum degree at most one, that is, ... In particular, we prove that the VC-k Root problem, that asks whether an input*graph*has a square root with vertex cover of size at most k, cannot be*solved*in time 2^2^o(k)· n^O(1) unless Exponential ... We*use*the following properties of*matched*and nested twins. Lemma 1. ...##
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GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism
[chapter]

2015
*
Lecture Notes in Computer Science
*

This paper describes an extended version of a Binary Linear Program (BLP) for

doi:10.1007/978-3-319-18224-7_13
fatcat:fogd2zn6krbbrbfeq7eeis2a3q
*solving*this class of*graph**matching*problem. ... The substitution-tolerant subgraph*isomorphism*is a particular error-tolerant subgraph*matching*that allows label substitutions for both vertices and edges. ... ), and the command-line utility GEM++sub, that*solves*our subgraph*isomorphism*problem. ...##
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What's Next? Future Directions in Parameterized Complexity
[chapter]

2012
*
Lecture Notes in Computer Science
*

In particular, we set up a framework for understanding which problems can be

doi:10.1007/978-3-642-30891-8_20
fatcat:enftdcd27rd5jmglgw4khqffty
*solved*by branching algorithms. ... Finally, we discuss that the domain of directed*graph*problems is a challenging area which can potentially see significant progress in the following years. ... A planar problem which is not fully understood yet is Subgraph*Isomorphism*: given*graphs*H and G, does G has a subgraph*isomorphic*to H? ...##
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Mine 'Em All: A Note on Mining All Graphs
[chapter]

2016
*
Lecture Notes in Computer Science
*

For instance, the problem can be

doi:10.1007/978-3-319-40566-7_8
fatcat:x2kqtt2znff7dkvcpkgu574qee
*solved*with polynomial delay for databases of planar*graphs*when the enumerated*graphs*should be output from large to small but it cannot be*solved*even in incremental-polynomial ... We show that there are hereditary classes of*graphs*for which the complexity of this problem depends on the order in which the*graphs*should be enumerated (e.g. from frequent to infrequent or from small ... The problem ALL F →I cannot be*solved*in incremental polynomial time for the class G of planar*graphs*and subgraph*isomorphism*as pattern*matching*operator. Proof. ...##
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Counting Problems in Parameterized Complexity

2019
*
International Symposium on Parameterized and Exact Computation
*

*graphs*, and counting perfect

*matchings*and Hamiltonian cycles in well-structured

*graphs*. ...

*parameterized*complexity,

*graph*motifs, perfect

*matchings*,

*graph*minor theory, Hamiltonian cycles Digital Object Identifier 10.4230/LIPIcs.IPEC.2018.1 Category Invited Tutorial Funding BARC is supported ... We

*use*(1) for a

*parameterized*reduction from the colorful subgraph

*isomorphism*problem to the uncolored version [78, 33] . ...

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