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Simultaneous Time-Space Upper Bounds for Red-Blue Path Problem in Planar DAGs

  • Diptarka Chakraborty
  • Raghunath Tewari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)

Abstract

In this paper, we consider the RedBluePath problem, which states that given a graph G whose edges are colored either red or blue and two fixed vertices s and t in G, is there a path from s to t in G that alternates between red and blue edges. The RedBluePath problem in planar DAGs is NL-complete. We exhibit a polynomial time and \(O(n^{\frac{1}{2}+\epsilon})\) space algorithm (for any ε > 0) for the RedBluePath problem in planar DAG. We also consider a natural relaxation of RedBluePath problem, denoted as EvenPath problem. The EvenPath problem in DAGs is known to be NL-complete. We provide a polynomial time and \(O(n^{\frac{1}{2}+\epsilon})\) space (for any ε > 0) bound for EvenPath problem in planar DAGs.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Diptarka Chakraborty
    • 1
  • Raghunath Tewari
    • 1
  1. 1.Department of Computer Science & EngineeringIndian Institute of TechnologyKanpurIndia

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