A parallelization of Miller's \(n^{\log n}\) isomorphism technique
type: Item
instance of: scholarly article
title: A parallelization of Miller's \(n^{\log n}\) isomorphism technique
zbMATH Open document ID: 0769.05085
DOI: 10.1016/0020-0190(92)90243-O
author: Charles J. Colbourn
author: Luc Teirlinck
author: D. R. Stinson
published in: Information Processing Letters
publication date: 1993-01-16T00:00:00Z
review text: The authors first present G. L. Miller's sequential algorithm of complexity \(O(n^{\log n+c})\) for isomorphism testing of Steiner triple systems of order \(n\), \(\text{STS}(n)\), as Algorithm Canonical, a recursive procedure returning a canonical form of an \(\text{STS}(n)\). Two main steps in the algorithm have been called forcing and choosing and the forcing step is shown as the computation of a closure of a set defined in a suitable way needing at most \(3\log n\) iterations. The algorithm is then parallelized using a CREW-PRAM model needing \(O(n^{\log n+2})\) processors and a total running time of \(O((\log n)^ 2)\). Whether the problem lies in NC is left open. It is also shown that both the sequential and parallel algorithms can be generalized to compute canonical forms of quasi-semigroups.
Mathematics Subject Classification ID: 05C85
Mathematics Subject Classification ID: 68W15
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 92121
zbMATH Keywords: sequential algorithm
zbMATH Keywords: complexity
zbMATH Keywords: isomorphism
zbMATH Keywords: Steiner triple systems
zbMATH Keywords: parallel algorithms
MaRDI profile type: Publication
cites work: Sorting in \(c \log n\) parallel steps
cites work: Embedding Partial Steiner Triple Systems
cites work: Q3916602
cites work: Q3861412
cites work: Q3728911
cites work: Concerning the complexity of deciding isomorphism of block designs
cites work: On the nlog n isomorphism technique (A Preliminary Report)
cites work: Q3708032
cites work: Implementation of simultaneous memory address access in models that forbid it
full work available at URL: 0020-0190(92)90243-o
OpenAlex ID: W2048558076
description: scientific article; zbMATH DE number 92121