Abstract
In this paper we discuss the problem of finding edge-disjoint paths in a planar, undirected graph s.t. each path connects two specified vertices on the outer face boundary. We will focus on the “classical” case where an instance must additionally fulfill the so-called evenness-condition. The fastest algorithm for this problem known from the literature requires \(\mathcal{O}\left( {n^{{5 \mathord{\left/{\vphantom {5 3}} \right.\kern-\nulldelimiterspace} 3}} \left( {\log \log n} \right)^{{1 \mathord{\left/{\vphantom {1 3}} \right.\kern-\nulldelimiterspace} 3}} } \right)\) time, where n denotes the number of vertices. In this paper now, we introduce a new approach to this problem, which yields an \(\mathcal{O}\left( n \right)\) algorithm.
The authors acknowledge the Deutsche Forschungsgemeinschaft for supporting this research under grant Mö 446/1-3
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Wagner, D., Weihe, K. (1993). A linear-time algorithm for edge-disjoint paths in planar graphs. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_73
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DOI: https://doi.org/10.1007/3-540-57273-2_73
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