On Routing in Circulant Graphs
نویسندگان
چکیده
We investigate various problems related to circulant graphs { nding the shortest path between two vertices, nding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the length of the shortest loop. We claim NPhardness results, and establish a worst-case/average-case connection for the shortest loop problem. A pseudo-polynomial time algorithm for these problems is also given. Our main tools are results and methods from the geometry of numbers.
منابع مشابه
Frobenius circulant graphs of valency four
A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group K o H such that S = a for some a ∈ K with 〈a〉 = K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as ...
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تاریخ انتشار 1999