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Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03
We devise the first constant factor approximation algorithm for minimum quotient vertex-cuts in planar graphs. Our algorithm achieves approximation ratio 1+ 4 3 (1+ ) with running time O(W · n 3+2/ ), where W is the total weight of the vertices. The approximation ratio improves to 4 3 (1 + + o(1)) if there is an optimal quotient vertex-cut (A * , B * , C * ) where the weight of C * is of low order compared to those of A * and B * ; this holds, for example, when the input graph has uniformdoi:10.1145/780555.780557 fatcat:bbrufwdo3fg2rb4ajuxaxdqvja