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Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes

Authors Archit Chauhan , Samir Datta , M. Praveen

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ACM Subject Classification
  • Theory of computation → Parallel algorithms
Keywords
  • Parallel Complexity
  • Graph Algorithms
  • Depth First Search
  • Maximal Path
  • Planar Graphs
  • Minor-Free
  • Treewidth
  • Logspace

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Abstract

Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more recently, deterministic quasipolynomial parallel algorithms) are known for constructing a DFS tree in general (di)graphs. However a deterministic parallel algorithm for DFS in general graphs remains an elusive goal. Working towards this, a series of works gave deterministic NC algorithms for DFS in planar graphs and digraphs. We further extend these results to more general graph classes, by providing NC algorithms for (di)graphs of bounded genus, and for undirected H-minor-free graphs where H is a fixed graph with at most one crossing. For the case of (di)graphs of bounded treewidth, we further improve the complexity to a Logspace bound. Constructing a maximal path is a simpler problem (that reduces to DFS) for which no deterministic parallel bounds are known for general graphs. For planar graphs a bound of O(log n) parallel time on a CRCW PRAM (thus in NC²) is known. We improve this bound to Logspace.

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Archit Chauhan, Samir Datta, and M. Praveen. Parallel Complexity of Depth-First-Search and Maximal Path in Restricted Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSTTCS.2025.23

Author Details

Archit Chauhan
  • Department of Computer Science and Engineering, IIT Bombay, India
Samir Datta
  • Chennai Mathematical Institute, India
  • UMI ReLaX, Indo-French joint research unit, Chennai, India
M. Praveen
  • Chennai Mathematical Institute, India
  • UMI ReLaX, Indo-French joint research unit, Chennai, India

Funding

  • Datta, Samir: Partially supported by a grant from Infosys foundation.
  • Praveen, M.: Partially funded by a grant from the Infosys foundation.

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