Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization
We consider the gap between the cost of an optimal assignment in a complete bipartite graph with random edge weights, and the cost of an optimal traveling salesman tour in a complete directed graph with the same edge weights. Using an improved "patching" heuristic, we show that with high probability the gap is O((ln n) 2/n), and that its expectation is Ω(1/n). One of the underpinnings of this result is that the largest edge weight in an optimal assignment has expectation ⊖(ln n/n). A consequence of the small assignment-TSP gap is an e Õ(√n)-time algorithm which, with high probability, exactly solves a random asymmetric traveling salesman instance. In addition to the assignment-TSP gap, we also consider the expected gap between the optimal and second-best assignments; it is at least Ω(1/n 2) and at most O(ln n/n 2). © 2007 Society for Industrial and Applied Mathematics.
Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization
Yigal Hoffner, Simon Field, et al.
EDOC 2004
Gal Badishi, Idit Keidar, et al.
IEEE TDSC
Raymond Wu, Jie Lu
ITA Conference 2007