Depth-First Search in Directed Planar Graphs, Revisited

Authors Eric Allender , Archit Chauhan, Samir Datta

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Author Details

Eric Allender
  • Rutgers University, Piscataway, NJ, USA
Archit Chauhan
  • Chennai Mathematical Institute, India
Samir Datta
  • Chennai Mathematical Institute, India

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Eric Allender, Archit Chauhan, and Samir Datta. Depth-First Search in Directed Planar Graphs, Revisited. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We present an algorithm for constructing a depth-first search tree in planar digraphs; the algorithm can be implemented in the complexity class AC^1(UL∩co-UL), which is contained in AC². Prior to this (for more than a quarter-century), the fastest uniform deterministic parallel algorithm for this problem was O(log^{10}n) (corresponding to the complexity class AC^{10} ⊆ NC^{11}). We also consider the problem of computing depth-first search trees in other classes of graphs, and obtain additional new upper bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Parallel algorithms
  • Depth-First Search
  • Planar Digraphs
  • Parallel Algorithms
  • Space-Bounded Complexity Classes


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