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Solving Graph Isomorphism Using Parameterized Matching
[chapter]
2013
Lecture Notes in Computer Science
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We propose a new approach to 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. ...
doi:10.1007/978-3-319-02432-5_26
fatcat:et66ctddmrbhtly5etm5d5g4oa
On the complexity of various parameterizations of common induced subgraph isomorphism
2017
Theoretical Computer Science
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feedback vertex sets of the input 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 ...
doi:10.1016/j.tcs.2017.07.010
fatcat:dabbehi67bcwlmjt2ygu67b5dy
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
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Given two 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] . ...
doi:10.4230/lipics.stacs.2014.542
dblp:conf/stacs/MarxP14
fatcat:dy4trfjwkvhj3i2tzcvrguedyi
On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[chapter]
2015
Lecture Notes in Computer Science
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It remains NP-hard on many 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). ...
doi:10.1007/978-3-319-19315-1_1
fatcat:knzdi3nve5ao7kvxr7ubulpdnq
On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
[article]
2017
arXiv
pre-print
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It remains NP-hard on many 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). ...
arXiv:1412.1261v2
fatcat:ownbquhznvcrnmz4uthnys5o3m
Foreword: Special Issue on IPEC 2014
2016
Algorithmica
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In The 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. ...
doi:10.1007/s00453-016-0151-x
fatcat:2xhmdtkgtzbbppmbxnhugehgr4
Parameterized Aspects of Strong Subgraph Closure
2020
Algorithmica
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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 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 . ...
doi:10.1007/s00453-020-00684-9
fatcat:nhbdwiiu35hndapxu3wdxes7ou
Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)
2015
Dagstuhl Reports
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Over the last two decades 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. ...
doi:10.4230/dagrep.4.11.1
dblp:journals/dagstuhl-reports/KratschLMR14
fatcat:vwgmhttkgrf4pb34jpsb2rfvnm
Isomorphism for Graphs of Bounded Feedback Vertex Set Number
[chapter]
2010
Lecture Notes in Computer Science
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We prove that the 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. ...
doi:10.1007/978-3-642-13731-0_9
fatcat:ys6cnyk3qfaatfczzh24vkxlvm
Stable Matching Games: Manipulation via Subgraph Isomorphism
2017
Algorithmica
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Our algorithm is a nontrivial combination of a 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 ...
doi:10.1007/s00453-017-0382-5
fatcat:txog53msovgvxlpc7mvtw5x67q
Graph Square Roots of Small Distance from Degree One Graphs
[article]
2020
arXiv
pre-print
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We are interested in the 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. ...
arXiv:2010.05733v1
fatcat:43jifxqrfjcyvjplbcvdejbl4e
GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism
[chapter]
2015
Lecture Notes in Computer Science
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This paper describes an extended version of a Binary Linear Program (BLP) for 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. ...
doi:10.1007/978-3-319-18224-7_13
fatcat:fogd2zn6krbbrbfeq7eeis2a3q
What's Next? Future Directions in Parameterized Complexity
[chapter]
2012
Lecture Notes in Computer Science
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In particular, we set up a framework for understanding which problems can be 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? ...
doi:10.1007/978-3-642-30891-8_20
fatcat:enftdcd27rd5jmglgw4khqffty
Mine 'Em All: A Note on Mining All Graphs
[chapter]
2016
Lecture Notes in Computer Science
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For instance, the problem can be 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. ...
doi:10.1007/978-3-319-40566-7_8
fatcat:x2kqtt2znff7dkvcpkgu574qee
Counting Problems in Parameterized Complexity
2019
International Symposium on Parameterized and Exact Computation
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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] . ...
doi:10.4230/lipics.ipec.2018.1
dblp:conf/iwpec/Curticapean18
fatcat:tdfs7zngzrgv5fixf2qawrccuy
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