Martin Charles Golumbic, Renu C. Laskar
Discrete Applied Mathematics
This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X1,...,Xg ⊆ V with each group Xi having a requirement ri between 0 and |Xi|, the goal is to find a minimum cost set of edges whose removal separates each group Xi into at least ri disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk·logg) approximation ratio for general graphs, where k=|∪gi=1=1gXi|≤n. © 2010 Elsevier B.V. All rights reserved.
Martin Charles Golumbic, Renu C. Laskar
Discrete Applied Mathematics
John S. Lew
Mathematical Biosciences
Juliann Opitz, Robert D. Allen, et al.
Microlithography 1998
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering