Routing Permutations in the Hypercube
نویسندگان
چکیده
Olivier Baudon y, Guillaume Fertin y and Ivan Havel z y LaBRI U.M.R. CNRS 5800, Universit e Bordeaux I 351 Cours de la Lib eration, F33405 Talence Cedex z Faculty of Mathematics and Physics, Charles University Malostransk e n am. 25, 118 00 Praha, Czech Republic fbaudon,[email protected], [email protected] Abstract We study an n-dimensional directed symmetric hypercube Hn, in which every pair of adjacent vertices is connected by two arcs of opposite directions. Using the computer, we show that for H4 and for any permutation on its vertices, there exists a system of pairwise arc-disjoint directed paths from each vertex to its target in the permutation. This gives the answer to Szymanski's conjecture [Szy89] for dimension 4. In addition to this study, we consider in Hn the so-called 2-1 routing requests, that is routing requests where any vertex of Hn can be used twice as a source, but only once as a target. We give two such routing requests which cannot be routed in H3. Moreover, we show that for any dimension n 3, it is possible to nd a 2-1 routing request gn such that gn cannot be routed in Hn : in other words, for any n 3, Hn is not (2-1)-rearrangeable.
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تاریخ انتشار 1999