@TECHREPORT{Høyer96permutationrouting, author = {Peter Høyer and Kim S. Larsen}, title = {Permutation Routing via Matchings}, institution = {}, year = {1996} }

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Abstract

The following routing problem on an undirected graph is considered: Initially, each node of the graph contains exactly one packet. Each node is the destination node of exactly one packet, so the initial state can be considered a permutation of the packets. The packets are routed to their destination nodes by a sequence of steps. In one step, each packet can either remain at its current location, or it can be swapped with a neighbor, i.e., a step is determined by a matching of the participating nodes. The time complexity of the previously best algorithm for routing all packets to their destination nodes given any initial permutation in a graph with n nodes was bounded by 13 5 n. We present an algorithm running in at most 2n \Gamma 3 steps, where n 2, at the same time simplifying the analysis of the time complexity.