Abstract
We present a new approach to the minimum-cost integral flow problem for small values of the flow. It reduces the problem to the tests of simple multi-variable polynomials over a finite field of characteristic two for non-identity with zero. In effect, we show that a minimum-cost flow of value k in a network with n vertices, a sink and a source, integral edge capacities and positive integral edge costs polynomially bounded in n can be found by a randomized PRAM, with errors of exponentially small probability in n, running in O(klog(kn) + log2 (kn)) time and using 2k(kn)O(1) processors. Thus, in particular, for the minimum-cost flow of value O(logn), we obtain an RNC 2 algorithm.
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Lingas, A., Persson, M. (2012). A Fast Parallel Algorithm for Minimum-Cost Small Integral Flows. In: Kaklamanis, C., Papatheodorou, T., Spirakis, P.G. (eds) Euro-Par 2012 Parallel Processing. Euro-Par 2012. Lecture Notes in Computer Science, vol 7484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32820-6_68
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DOI: https://doi.org/10.1007/978-3-642-32820-6_68
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