Near-Linear Time Approximation Schemes for some Implicit Fractional Packing Problems
نویسندگان
چکیده
We consider several implicit fractional packing problems and obtain faster implementations of approximation schemes based on multiplicative-weight updates. This leads to new algorithms with near-linear running times for some fundamental problems in combinatorial optimization. We highlight two concrete applications. The first is to find the maximum fractional packing of spanning trees in a capacitated graph; we obtain a (1− )-approximation in Õ ( m/ 2 ) time, where m is the number of edges in the graph. Second, we consider the LP relaxation of the weighted unsplittable flow problem on a path and obtain a (1− )-approximation in Õ ( n/ 2 ) time, where n is the number of demands.
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