Abstract
Recent results by Valiant indicate that computing the permanent of an n×n matrix probably requires a computation time exponential in n. The problem is at least as difficult as the NP-complete problems. This paper presents a fast algorithm to compute an approximate value of the permanent. Given two arbitrary parameters 0<r<1 and 0<ε<1, the algorithm ensures that, with probability r, its answer will be within a factor of ε of the true value of the permanent. Furthermore, the running time of the algorithm degrades by no worse than a polynomial as ε is decreased or r is increased.
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© 1980 Springer-Verlag
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Goldschlager, L.M. (1980). An approximation algorithm for computing the permanent. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088907
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DOI: https://doi.org/10.1007/BFb0088907
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