A linear delay algorithm in SD set system and its application to subgraph enumeration

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-02-21 DOI:10.1016/j.jcss.2025.103637

Takumi Tada, Kazuya Haraguchi

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引用次数: 0

Abstract

For a set system

(V, C \subseteq 2^{V})

, we call each

C \in C

a component. A nonempty subset

Y ⊊ C

is a removable set (RS) of C if

C ∖ Y

is a component. We say that a set system has subset-disjoint (SD) property if, for any two components

C, C^{'}

with

C^{'} ⊊ C

, every minimal RS Y of C satisfies either

Y \subseteq C^{'}

Y \cap C^{'} = \emptyset

. Assuming that an SD set system is implicitly given by an oracle that returns a minimal RS of a component, we provide an algorithm that enumerates all components in linear time/space with respect to

| V |

and oracle running time/space. We then extend this algorithm to linear-delay enumeration of all 2-edge-connected (or 2-vertex-connected) induced subgraphs in an undirected graph and of all strongly connected subgraphs in a digraph.

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SD集合系统中的一种线性延迟算法及其在子图枚举中的应用

对于集合系统（V,C≤2V），我们称每个C∈C为一个分量。如果C≠Y是一个分量，一个非空子集Y≠C是C的一个可移动集（RS）。如果对于任意两个分量C，C′与C′≠C，则C的每一个极小RS Y满足Y≠C′或Y∩C′=∅，则我们说一个集合系统具有子集不相交（SD）性质。假设一个SD集合系统是由一个oracle隐式给出的，它返回一个组件的最小RS，我们提供了一个算法，该算法在线性时间/空间中枚举关于|V|和oracle运行时间/空间的所有组件。然后，我们将该算法推广到无向图中所有2边连通（或2点连通）诱导子图和有向图中所有强连通子图的线性延迟枚举。

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 Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.