A hybrid algorithm for computing permanents of sparse matrices

The permanent of matrices has wide applications in many fields of science and engineering. It is, however, a #P-complete problem in counting. The best-known algorithm for computing the permanent, which is due to Ryser [Combinatorial Mathematics, The Carus Mathematical Monographs, vol. 14, Mathematical Association of America, Washington, DC, 1963], runs O(n2 ) in time. It is possible to speed up algorithms for matrices with special structures, which arise commonly in applications. Most algorithms discussed before focus on 0,1 matrix. In this paper, a hybrid algorithm is proposed. It is efficient for sparse matrices. 2004 Elsevier Inc. All rights reserved. 0096-3003/$ see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2004.11.020 q Supported by National Science Foundation of China G10228101 and National Key Basic Research Special Fund G1998020306. * Corresponding author. E-mail addresses: [email protected] (H. Liang), [email protected] (S. Huang), [email protected] (F. Bai). H. Liang et al. / Appl. Math. Comput. 172 (2006) 708–716 709