Technical Report CS0104

Title: Covering a Graph by Circuits
Authors: Alon Itai and Michael Rodeh
Abstract: A circuit cover ts a set of circuits which cover all the edges of a graph; Its length ts the sum of the lengths of the circuits. In analyzing irrigation systems and electrical circuits it is necessary to find a short circuit cover. It Is shown ,that every bridge-free connected undirected graph with n vertices and e edges has a circuit cover the length of which Is less than or equal to e+2nlogn. A probabilistic algorithm for flnding such a cover Is presented; Its expected running time Is O(n^2), independent of the input graph. This constitutes one of the first examples of solving a graph-theoretical problem by a probabilistic algorithm -the class of algortihms Introduced by Rabin. If the graph contains two edge-disjoint s-pannlng trees then there exists a circuIt cover of length at most e+n-l. The relationship of the circuit cover problem to the Chinese postman problem is also discussed.
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