Algorithms and complexity for counting configurations in Steiner triple systems

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-04-18 DOI:10.1002/jcd.21839

Daniel Heinlein, Patric R. J. Östergård

引用次数: 2

Abstract

Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad hoc algorithms for counting or listing configurations are typically fast enough for practical needs, but with many systems or large systems, the relevance of computational complexity and algorithms of low complexity is highlighted. General theoretical results as well as specific practical algorithms for important configurations are presented.

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Steiner三重系统中计数组态的算法及其复杂性

施泰纳三系统是组合设计中研究最多的一类。包括子系统在内的配置在斯坦纳三重系统的研究中起着核心作用。对于小系统的零星实例，用于计数或列出配置的自组织算法通常足够快以满足实际需求，但对于许多系统或大系统，计算复杂性和低复杂性算法的相关性突出。给出了重要构型的一般理论结果和具体的实用算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.