Subcomplete generalizations of graph isomorphism
TLDR
An O( n 2 · k ) algorithm for constructing the centralizer of a permutation group of degree n presented by a generating set of k permutations is given, and results about the group-theoretic structure of thecentralizer are recovered.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1982-12-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Graph automorphism & Graph isomorphism.read more
Citations
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Journal ArticleDOI
Graph isomorphism is low for PP
TL;DR: It is shown that the graph isomorphism problem, is low for PP and for C=P, i.e., it does not provide a PP or C= P computation with any additional power when used as an oracle.
Book ChapterDOI
Graph Isomorphism is Low for PP
TL;DR: It is shown that the graph isomorphism problem is low for PP and for C=P, i.e. it does not provide a PP or C= P computation with any additional power when used as oracle, andGraph Automorphism belongs to the class LWPP.
Journal ArticleDOI
Counting Complexity of Solvable Black-Box Group Problems
TL;DR: The results in this paper favor the belief that these problems over solvable black-box groups in the counting complexity classes SPP or LWPP are unlikely to be complete for NP.
Journal ArticleDOI
The Complexity of Modular Graph Automorphism
TL;DR: A randomized polynomial-time checker for modk-GA, the modular graph automorphism problems, which consist of deciding whether the number of automorphisms of a graph is divisible by k.
Journal ArticleDOI
Nearly Linear Time Algorithms for Permutation Groups: An Interplay Between Theory and Practice
TL;DR: In the last section, some new nearly linear time algorithms are presented, culminating in the computation of the upper central series in nilpotent groups.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
The complexity of computing the permanent
TL;DR: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations.
Book
The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.