Disjoint Paths in Densely Embedded Graphs

13 years 7 months ago

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We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network — the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share an edge in the network. This classical problem has been brought into focus recently in papers discussing applications to routing in high-speed networks, where the current lack of understanding of the mdpp is an obstacle to the design of practical heuristics. We consider the class of densely embedded, nearly-Eulerian graphs, which includes the two-dimensional mesh and many other planar and locally planar interconnection networks. We obtain a constant-factor approximation algorithm for the maximum disjoint paths problem for this class of graphs; this improves on an O(log n)-approximation for the special case of the two-dimensional mesh due to Aumann–Rabani and the authors. For networks that ...

Jon M. Kleinberg, Éva Tardos

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