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In this paper we consider the worst case ratio between the capaciry of minimum-cuts and the value of maximum-flow for multicommodity flow problems. We improve the best known bounds for the rein-cut rnax-flow ratio for multicommodi~flows in undirected graphs, by replacing the O(log D) in the bound by O(log k), where D denotes the sum of all demands, and k denotes the number of commodities.
Plotkin et al. (Fri,) studied this question.