Modeling polarization for Hyper-NA lithography tools and masks
Kafai Lai, Alan E. Rosenbluth, et al.
SPIE Advanced Lithography 2007
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.
Kafai Lai, Alan E. Rosenbluth, et al.
SPIE Advanced Lithography 2007
Pradip Bose
VTS 1998
Yvonne Anne Pignolet, Stefan Schmid, et al.
Discrete Mathematics and Theoretical Computer Science
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007