Depth-first search in directed planar graphs, revisited

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2022-06-04 DOI:10.1007/s00236-022-00425-1

Eric Allender, Archit Chauhan, Samir Datta

引用次数: 0

Abstract

We present an algorithm for constructing a depth-first search tree in planar digraphs; the algorithm can be implemented in the complexity class \(\text{ AC}^1(\text{ UL }\cap \text{ co-UL})\), which is contained in \(\text{ AC}^2\). Prior to this (for more than a quarter-century), the fastest uniform deterministic parallel algorithm for this problem had a runtime of \(O(\log ^{10}n)\) (corresponding to the complexity class \(\text{ AC}^{10}\subseteq \text{ NC}^{11}\)). We also consider the problem of computing depth-first search trees in other classes of graphs and obtain additional new upper bounds.

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有向平面图中的深度优先搜索，重访

提出了一种构造平面有向图中深度优先搜索树的算法;该算法可以在复杂度类\(\text{ AC}^1(\text{ UL }\cap \text{ co-UL})\)中实现，该复杂度类包含在\(\text{ AC}^2\)中。在此之前(超过四分之一个世纪)，这个问题最快的统一确定性并行算法的运行时为\(O(\log ^{10}n)\)(对应于复杂度类\(\text{ AC}^{10}\subseteq \text{ NC}^{11}\))。我们还考虑了在其他类型的图中计算深度优先搜索树的问题，并获得了新的上界。

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

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.

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