Fast approximation of the permanent for very dense problems

Approximation of the permanent of a matrix with nonnegative entries is a well studied problem. The most successful approach to date for general matrices uses Markov chains to approximately sample from a distribution on weighted permutations, and Jerrum, Sinclair, and Vigoda developed such a method they proved runs in polynomial time in the input. The current bound on the running time of their method is O(n7 (log n)4 ). Here we present a very different approach using sequential acceptance/rejection, and show that for a class of dense problems this method has an O(n4 log n) expected running time. 1 The Permanent.

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Mark Huber, Jenny Law
• Keywords: Algorithms, Matrices Uses Markov, Nonnegative Entries, SODA 2008, Successful Approach