| Summary: | 碩士 === 淡江大學 === 數學學系碩士班 === 103 === The problem of routing permutations over graphs arose in different fields , such as the study of communicating processes on networks, the data flow on parallel computation, and the analysis of routing algorithms on VLSI chips. This problem can be described as follows: Let G = (V,E) be a connected graph with vertices {v1, v2 ...vn} and π be a permutation on [n]. Initially, each vertex vi of G is occupied by a “pebble.” The pebble on vi will be labeled as pj if π(i) = j. Pebbles can be moved around by the following rule. At each step a disjoint collection of edges of G is selected, and the pebbles at each edge’s two endpoints are interchanged. The goal is to move/route each pebble pi to its destination vi. Define rt(G, π) to be the minimum number of steps to route the permutation π. Finally, define rt(G) the routing number of G by rt(G) = max π rt(G, π).
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