We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ∈ > 0 produces an output XA with (1 - ∈)per(A) ≤ XA ≤ (1 + ∈)per(A) for almost all (0-1) matrices A. For any positive constant ∈ > 0, and almost all (0-1) matrices the algorithm runs in time O(n2ω), i.e., almost linear in the size of the matrix, where ω = ω(n) is any function satisfying ω(n) → ∞ as n → ∞. This improves the previous bound of O(n3ω) for such matrices. The estimator can also be used to estimate the size of a backtrack tree.
|Original language||English (US)|
|Number of pages||12|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|State||Published - Jan 1 2004|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)