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.
Research supported by Research-I Foundation.
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Chakraborty, D., Tewari, R. (2015). Simultaneous Time-Space Upper Bounds for Red-Blue Path Problem in Planar DAGs. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_23
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DOI: https://doi.org/10.1007/978-3-319-15612-5_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15611-8
Online ISBN: 978-3-319-15612-5
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