A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
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Bax and Franklin (2002) gave a randomized algorithm for exactly computing the permanent of any nxn zero-one matrix in expected time exp[-@W(n^1^/^3/(2lnn))]2^n. Building on their work, we show that for any constant C0 there is a constant @?0 such that the permanent of any nxn (real or complex) matrix with at most Cn nonzero entries can be computed in deterministic time (2-@?)^n and space O(n). This improves on the @W(2^n) runtime of Ryser's algorithm for computing the permanent of an arbitrary real or complex matrix.