complexity of graph isomorphism and related problems.

by Charles Joseph Colbourn

Written in English
The Physical Object
Pagination174 leaves
Number of Pages174
ID Numbers
Open LibraryOL14670546M

Ladner [18] proved the existence of an in nite hierarchy of problems of interme-diate complexity assuming that P is di erent from NP. The graph isomorphism problem, for reasons stated above, is believed to be a natural example. In this article, we study graph isomorphism and related problems. There is now a vast literature on graph isomorphism On parallel complexity of the subgraph homeomorphism and the subgraph isomorphism problem for classes of planar graphs We also show that the related subgraph isomorphism problem for two-connected outerplanar graphs is in NC 3. This is the first example of a restriction of subgraph isomorphism to a non-trivial graph family admitting an NC   Graph isomorphism is not known to be in BQP. There has been a lot of work done on trying to put it in. A very intriguing observation is that graph isomorphism could be solved if quantum computers could solve the non-abelian hidden subgroup problem for the symmetric group (factoring and discrete log are solved by using the abelian hidden subgroup problem, which in turn is solved by applying the   We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism(under groupaction) (SI) and Coset Intersection (CI) can be solved in quasipolynomial(exp (logn)O(1)) time. The best previousbound forGI wasexp(O(√ nlogn)), where nis the number of vertices (Luks, ); for the other two problems, the bound was

\$\begingroup\$ Please check complexity class GA and the book cited there. (The definition of the graph automorphism problem in the Complexity Zoo is technically incorrect; this problem is usually defined as the decision problem to decide whether a given graph has any nontrivial automorphism.) \$\endgroup\$ – Tsuyoshi Ito Sep 12 '12 at   equivalent to GI (so-called isomorphism-complete problems), problems to which GI is Turing reducible (like Group Factorization) and problems that seem to be incomparable with GI (like Group Intersection). The present work makes a contribution towards a better (structural) complexity classiﬁcation of Graph Isomporhism and other related The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.. Besides its practical importance, the graph isomorphism problem is a curiosity in computational complexity theory as it is one of a very small number of problems belonging to NP neither known to be solvable in polynomial time nor NP-complete: it is one of only 12 such problems +complexity/en-en. The graph isomorphism problem: its structural complexity. Boston, MA: Birkhäuser. Google Scholar; Michael Koren (). Pairs of sequences with a unique realization by bipartite graphs. Journal of Combinatorial Theory, Series B 21(3), Google Scholar Cross Ref; Andreas Krebs & Oleg Verbitsky ().

complexity of graph isomorphism and related problems. by Charles Joseph Colbourn Download PDF EPUB FB2

Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has been obtained. These results belong to the so-called structural part of Complexity Theory. Our idea behind this book is to summarize such results which might otherwise not be easily accessible in the literature, › Birkhäuser › Computer sciences and Informatics.

We reduce the isomorphism problem for undirected graphs without loops to the isomorphism problems for some class of finite-dimensional 2-step nilpotent Lie -Be book focuses on this issue and presents several recent results that provide a better understanding of the relative position of the graph isomorphism problem in the class NP as well as in other complexity classes.

It also uses the problem to illustrate important concepts in structural complexity, providing a look into the more general ://   One of these is the problem of determining whether a given graph has a fixed-point-free automorphism.

Some speculation is made on the possible implications of these results on deciding the complexity status of ISOMORPHISM. Various classes and hierarchies of problems in NP are ://   reductions between NP-intermediate problems, graph isomorphism, minimum circuit size problem, time-bounded Kolmogorov complexity AMS Subject Headings 68Q15, 68Q17, 68Q30   We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems).

We show that these problems are closely related for all amounts c ≥ 1 of deletion: 1. GI ≡l~spr/PUBL/trpdf. We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs.

We show that the problems are rather closely related for all amounts c of deletion: and inequalities is related to the complexity of the graphs isomorphism and subgraph isomorphim problems.

Mathematics Subject Classiﬁcation: 03D15, 05C50, 05C60, 15A48, 15A51,   Graph isomorphism (GI) gained prominence in the theory community in the s, when it emerged as one of the few natural problems in the complexity class NP that could neither be classified as being hard (NP-complete) nor shown to be solvable with The nonuniform complexity of the graph isomorphism (GI) and graph automorphism (GA) problems is studied, and the implications of different types of polynomial-time reducibilities from these On Borel complexity of the isomorphism problems for graph-related classes of Lie algebras and finite p-groups   () The complexity of computing the automorphism group of automata and related problems.

International Journal of Computer Mathematics() A New Algorithm for Graph Monomorphism Based on the Projections of the Product :// Their relationship and the computational complexity of problems related to these notions have been studied in [2, 3, 7, 11, 15, 16]. We denote by ≤ iso the partial ordering on the set of degrees We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular   In this section, we need some of the group-theoretic and graph-theoretic foundations presented in Section In particular, recall the notion of permutation group from Definition and the graph isomorphism problem (, for short) and the graph automorphism problem (, for short) from Definition ; see also Example in Chapter start by providing some more background from complexity Support sets of polynomials span Newton polytopes and a related problems is the polytope isomorphism problem, see [18] for its complexity, which is as hard as the graph isomorphism problem.

Depending on the graph class, the design and analysis of algorithms for GI use tools from various fields, such as combinatorics, algebra and logic. In this paper, we collect several complexity results on graph isomorphism testing and related algorithmic problems for restricted graph   Abstract.

We introduce the maximum graph homomorphism (MGH) problem: given a graph G, and a target graph H, find a mapping ϕ:V G ↦V H that maximizes the number of edges of G that are mapped to edges of problem encodes various fundamental NP-hard problems including Maxcut and also consider the multiway uncut problem.

We are given a graph G and a set of 21 hours ago  The paper On graph classes with logarithmic boolean-width claims that some graph problems are fixed parameter tractable with parameter the boolean width.

In The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. Besides its practical importance, the graph isomorphism problem is a curiosity in computational complexity theory as it is one of a very small number of problems belonging to NP neither known to be solvable in polynomial time nor NP-complete: it is one of only 12 such problems isomorphism problem/en-en.

polytopes. The general graph isomorphism problem can be Karp-reduced to each of the three geometric polytope isomorphism problems stated above (Theorem 3). Furthermore, the graph isomorphism problem restricted to graphs of polytopes (formed by their vertices and edges) is graph isomorphism complete, even for the The paradigm case of concern in this chapter is isomorphism of two graphs.

In this case, an isomorphism consists of a bijection between the vertex sets of the graphs which induces a bijection between the edge sets of the graphs. One can also take the second graph to be a copy of the first, so that isomorphisms map a graph onto ://   We show that the graph isomorphism problem is hard under DLOGTIME uniform AC 0 many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class Mod k L and for the class DET of problems NC 1 reducible to the determinant.

These are the strongest known hardness results for the graph Get this from a library. The graph isomorphism problem: its structural complexity. [Johannes Köbler; Uwe Schöning; Jacobo Torán] -- "The graph isomorphism problem belongs to the part of Complexity Theory that focuses on the structure of complexity classes involved in the classification of computational problems and in the   The complexity of these problems depends not only on the particular underlying algebraic structure, but also on the way the input instances are encoded.

As in the case of better studied isomorphism questions, like graph isomorphism, Arthur-Merlin games provide a good tool for proving upper bounds for these problems in terms of complexity ://   We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems).

We show that these problems are closely related for all amounts c ⩾ 1 of deletion: (1)   Furthermore, we derive that the problems to decide whether two polytopes, given either by vertex or by facet descriptions, are projectively or affinely isomorphic are graph isomorphism hard.

The original version of the paper (June11 pages) had the title ``On the Complexity of Isomorphism Problems Related to Polytopes''. On the Complexity of Polytope Isomorphism Problems 9 Akutsu [1] also gave a Karp reduction of the congruence problem to the (labeled) graph isomorphism problem, thus showing that the former one is graph isomorphism  › 百度文库 › 行业资料.

Corollary The Graph Isomorphism problem and the Coset Intersection problem can be solved in quasipolynomial time. The SI and CI problems were introduced by Luks [Lu82] (cf. [Lu93]) who also pointed out that these problems are polynomial-time equivalent (under Karp reductions) and GI easily reduces to ://   Two graphs G, H are isomorphic if there is a relabeling of the vertices of G that produces H, and vice-versa.

The graph isomorphism problem (GI) is to decide whether two given are ://. results on the complexity aspects of the reconstruction of a graph from a subdeck are described in Section We again show a strong relationship between these problems and the graph isomorphism problem.

Harary and Plantholt [16] introduced a parameter, called the ally-reconstruction number of a graph G (which we  Since graph isomorphism is not known to be in P nor is it known to be NP-complete, it is “natural” to define the complexity class related to graph isomorphism, GI, which is made up of problems with a polynomial time reduction to the graph isomorphism ://  \$\begingroup\$ I do not think that there are many versions of subgraph isomorphism problem.

The subgraph isomorphism problem is exactly the one you described: given graphs G_1 and G_2, decide whether G_1 contains a subgraph that is isomorphic to G_2. And this is different from the problem stated in the question.

In the problem stated in the question, the task is to decide whether G_1 contains