Abstract
Abstract Given weighted graph , the minimum cut problem is classified with source and sink or without and . Given undirected weighted graph without and , Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs times. Given graph with and , Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from to . If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with and . This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs times and successfully divides into disjoint and sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within
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