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)


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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  1. 1.
    Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci. 4, 177–192 (1970)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Wigderson, A.: The complexity of graph connectivity. In: Mathematical Foundations of Computer Science, pp. 112–132 (1992)Google Scholar
  3. 3.
    Barnes, G., Buss, J.F., Ruzzo, W.L., Schieber, B.: A sublinear space, polynomial time algorithm for directed s-t connectivity. In: Proceedings of the Seventh Annual Structure in Complexity Theory Conference, pp. 27–33 (1992)Google Scholar
  4. 4.
    Imai, T., Nakagawa, K., Pavan, A., Vinodchandran, N.V., Watanabe, O.: An O(n1/2 + ε)-Space and Polynomial-Time Algorithm for Directed Planar Reachability. In: 2013 IEEE Conference on Computational Complexity (CCC), pp. 277–286 (2013)Google Scholar
  5. 5.
    Chakraborty, D., Pavan, A., Tewari, R., Vinodchandran, N.V., Yang, L.: New time-space upperbounds for directed reachability in high-genus and $h$-minor-free graphs. Electronic Colloquium on Computational Complexity (ECCC) 21, 35 (2014)Google Scholar
  6. 6.
    Kulkarni, R.: On the power of isolation in planar graphs. TOCT 3(1), 2 (2011)CrossRefGoogle Scholar
  7. 7.
    LaPaugh, A.S., Papadimitriou, C.H.: The even-path problem for graphs and digraphs. Networks 14(4), 507–513 (1984)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Nedev, Z.P.: Finding an Even Simple Path in a Directed Planar Graph. SIAM J. Comput. 29, 685–695 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Pach, J., Tóth, G.: Graphs drawn with few crossings per edge. Combinatorica 17(3), 427–439 (1997)zbMATHMathSciNetCrossRefGoogle Scholar

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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