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Several Graph Layout Problems for Grids. Vladimir Lipets Ben-Gurion University of the Negev Advisors: Prof. Daniel Berend Prof. Ephraim Korach. Graph layout problems. A large number of theoretical and practical problems in various areas may be formulated as graph layout problems.
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Several Graph Layout Problems for Grids Vladimir Lipets Ben-Gurion University of the Negev Advisors: Prof. Daniel Berend Prof. Ephraim Korach
Graph layout problems A large number of theoretical and practical problems in various areas may be formulated as graph layout problems.
Applications Such problems arise in connection with: • VLSI circuit design, • graph drawing, • embedding problems, • numerical analysis, • optimization of networks for parallel computer architectures.
History Historically, bandwidth was the the first layout problem, as a means to speed up several computations on sparse matrices during the fifties. The bandwidth problem for graphs was first posed as an open problem during a graph theoretical meeting in 1967 by Harary. For more detailed survey of graph layout problems see. The Minimal Cutwidth Linear Arrangement problem (MINCUT) was first used in the seventies as a theoretical model for the number of channels in an optimal layout of a circuit [Adolphson and Hu 1973]
Known Results All above problems are NP-hard in general, MINCUT remains NP-hard even when restricted, for example, to • polynomially (edge-) weighted trees • planar graphs with maximum degree 3. MINCUT remains NP-hard even when restricted, for example, to • trees, with maximum degree 3