Linear-Time Recognition of Map Graphs with Outerplanar Witness

Map graphs generalize planar graphs and were introduced by Chen, Grigni and Papadimitriou [STOC 1998, J.ACM 2002]. They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup [FOCS 1998] published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n^{120}) for n-vertex graphs, and a full description of its details remains unpublished. We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n+m). In contrast to Thorup\u27s approach, it computes the witness graph W in the affirmative case

Linear-time recognition of map graphs with outerplanar witness

Map graphs generalize planar graphs and were introduced by Chen et al. (STOC 1998, J. ACM, 2002). They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup (FOGS 1998) published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n(120)) for n-vertex graphs, and a full description of its details remains unpublished. We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n + m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case. (C) 2017 Elsevier B.V. All rights reserved