A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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Bax and Franklin (2002) gave a randomized algorithm for exactly computing the permanent of any n × n zero-one matrix in expected time exp[-Ω(n1/3/(2lnn))]2n. Building on their work, we show that for any constant C 0 there is a constant ε 0 such that the permanent of any n × n (real or complex) matrix with at most Cn nonzero entries can be computed in deterministic time (2 - ε)n and space O(n). This improves on the Ω(2n) runtime of Ryser's algorithm for computing the permanent of an arbitrary real or complex matrix.