A Linear Time Algorithm for Deciding Interval Graph Isomorphism

Lueker, George S.; Booth, Kellogg S.

doi:10.1145/322123.322125

Cited by 178 publications

(111 citation statements)

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“…It is known that Graph Isomorphism is Graph Isomorphism-complete even for pairs (G, R) where G and R are chordal graphs [21]. From Theorem 4.1 we get an immediate polynomial time reduction from Graph Isomorphism on chordal graphs to Cover on chordal graphs, and vice versa.…”

Section: Complementary Results and An Open Questionmentioning

confidence: 94%

“…Hence Cover is Graph Isomorphism-complete for pairs (G, R) where G and R are chordal graphs. On the other hand, Cover is polynomial time solvable on interval graphs, and hence also on proper interval graphs, since isomorphism between two interval graphs can be checked in polynomial time [21]. Because every locally bijective homomorphism is locally surjective, we can use Theorem 2.6 to deduce that these three results stay valid for input pairs (G, R) where only G is required to be chordal and R may be an arbitrary graph.…”

Section: Complementary Results and An Open Questionmentioning

confidence: 99%

“…We first check if G[K ≤q ] is isomorphic to R. This can be done in linear time [21]. If G[K ≤q ] is not isomorphic to R, then we output NO due to Theorem 3.1.…”

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confidence: 99%

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Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Heggernes

Hof

Paulusma

2011

Lecture Notes in Computer Science

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Further information on publisher's website:http://dx.doi.org/10. 1016/j.jda.2011.12.004 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Journal of discrete algorithms. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Journal of discrete algorithms, 14, 2012, 10.1016/j.jda.2011.12.004 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractAn R-role assignment of a graph G is a locally surjective homomorphism from G to graph R. For a fixed graph R, the R-Role Assignment problem is to decide, for an input graph G, whether G has an R-role assignment. When both graphs G and R are given as input, the problem is called Role Assignment. In this paper, we study the latter problem. It is known that R-Role Assignment is NP-complete already when R is a path on three vertices. In order to obtain polynomial time algorithms for Role Assignment, it is therefore necessary to put restrictions on G. So far, the only known non-trivial case for which this problem is solvable in polynomial time is when G is a tree. We present an algorithm that solves Role Assignment in polynomial time when G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that Role Assignment is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.

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Section: Complementary Results and An Open Questionmentioning

confidence: 94%

Section: Complementary Results and An Open Questionmentioning

confidence: 99%

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Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Heggernes

Hof

Paulusma

2011

Lecture Notes in Computer Science

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“…A vector is said to be maximal with respect to a set of vectors if no vector in the set is greater than the given vector in all coordinates. Preparata [1978] has given a data structure SMS for This structure has the same performance as Lueker's [1979], but is substantially easier to code and prove correct; his structure, however, also supports deletions.…”

Section: Proofmentioning

confidence: 99%

Transforming static data structures to dynamic structures

Saxe

Bentley

1979

20th Annual Symposium on Foundations of Computer Science (Sfcs 1979)

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In this paper we will investigate transformations that serve as tools in the design of new data structures. Specifically, we study general methods for converting static structures (in which all elements are known before any searches are performed) to dynamic structures (in which insertions of new elements can be mixed with searches). We will exhibit three classes of such transformations, each based on a different counting scheme for representing the integers, and then »ise a combinatorial model to show the optimality of many of the transformations. Issues such as online data structures and deletion of elements are also examined. To demonstrate the applicability of these tools, we will study six new data structures that have been developed by applying the transformations.

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“…Most studies of graph isomorphism (Hopcroft and Wong, 1974;Lueker, 1979;Babai et al, 1980;Galil et al, 1987;Hirata and Inagaki, 1988;Akutsu, 1988) restrict graphs by their characteristics. Some studies are undertaken based on group theory.…”

Section: Introductionmentioning

confidence: 99%

Graph Isomorphism Algorithm by Perfect Matching

Fukuda

Nakamori²

2003

IFIP Advances in Information and Communication Technology

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No polynomial time algorithm is known for the graph isomorphism problern. In this paper, we determine graph isomorphism with the help of perfect matehing algorithm, to Iimit the range of search of 1 to 1 correspondences between the two graphs: We reconfigure the graphs into layered graphs, labeling vertices by partitioning the set of vertices by degrees. We prepare a correspondence table by means of whether Iabels on 2 layered graphs match or not. Using that table, we seek a 1 to 1 correspondence between the two graphs. By limiting the search for 1 to 1 correspondences between the two graphs to information in the table, we are able to determine graph isomorphism more efficiently than by other known algorithms. The algorithm was timed with on experimental data and we obtained a complextity of O(n 4 ) .

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A Linear Time Algorithm for Deciding Interval Graph Isomorphism

Cited by 178 publications

References 7 publications

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

Transforming static data structures to dynamic structures

Graph Isomorphism Algorithm by Perfect Matching

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