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We revisit the problem of finding k paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the k paths. We provide a ⌊k/2⌋-approximation algorithm for this problem, improving the best previous approximation factor of k − 1. We also provide the first approximation algorithm for the problem with a sublinear approximation factor of O(n 3/4 ), where n is the number of vertices in the input graph. For sparse graphs,doi:10.1007/s00453-014-9927-z fatcat:q64tdoecxfbhzhx7xdf7ymtbli