On linear programs with random costs
Mathematical Programming: Series A and B
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Constructive bounds and exact expectation for the random assignment problem
Random Structures & Algorithms
The ζ (2) limit in the random assignment problem
Random Structures & Algorithms
Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures
Random Structures & Algorithms
Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality
IEEE Transactions on Information Theory
Graph construction and b-matching for semi-supervised learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
MAP estimation, message passing, and perfect graphs
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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The assignment problem concerns finding the minimum-cost perfect matching in a complete weighted n x n bipartite graph. Any algorithm for this classical question clearly requires Ω(n2) time, and the best known one (Edmonds and Karp, 1972) finds solution in O(n3). For decades, it has remained unknown whether optimal computation time is closer to n3 or n2. We provide answer to this question for random instance of assignment problem. Specifically, we establish that Belief Propagation finds solution in O(n2) time when edge-weights are i.i.d. with light tailed distribution.