The T-join Problem in Sparse Graphs: Applications to Phase Assignment Problem in VLSI Mask Layout
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Given a graph G with weighted edges, and a subset of nodes T, the T-join problem asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A iff u ∈ T. We describe the applications of the T-join problem in sparse graphs to the phase assignment problem in VLSI mask layout and to conformal refinement of finite element meshes. We suggest a practical algorithm for the Tjoin problem. In sparse graphs, this algorithm is faster than previously known methods. Computational experience with industrial VLSI layout benchmarks shows the advantages of the new algorithm.
KeywordsPlanar Graph Perfect Match Dual Graph Sparse Graph Conflict Graph
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- 2.F. Barahona, “Planar multicommodity flows, max cut and the Chinese postman problem”, In W. Cook and P. D. Seymour, eds., Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1 (1990), pp. 189–202.Google Scholar
- 3.P. Berman, A. B. Kahng, D. Vidhani, H. Wang and A. Zelikovsky, “Optimal Phase Conflict Removal for Layout of Dark Field Alternating Phase Shifting Masks”, Proc. ACM/IEEE Intl. Symp. on Physical Design, 1999, to appear.Google Scholar
- 5.W. Cook and A. Rohe, “Computing Minimum-Weight Perfect Matchings”, http://www.or.uni-bonn.de/home/rohe/matching.html, manuscript, August, 1998.
- 9.A. B. Kahng and H. Wang, “Toward Lithography-Aware Layout: Preliminary Litho Notes”, manuscript, July 1997.Google Scholar
- 10.A. B. Kahng, H. Wang and A. Zelikovsky, “Automated Layout and Phase Assignment Techniques for Dark Field Alternating PSM”, SPIE 11th Annual BACUS Symposium on Photomask Technology, SPIE 1604 (1998), pp. 222–231.Google Scholar
- 14.M. Müller-Hannemann and K. Weihe, “Improved Approximations for Minimum Cardinality Quadrangulations of Finite Element Meshes”, Proc. ESA’97, Graz, Austria, pp. 364–377.Google Scholar
- 17.SIA, The National Technology Roadmap for Semiconductors, Semiconductor Industry Association, December 1997.Google Scholar