1993 Fiscal Year Final Research Report Summary
Fundamental Studies on Large-Scale combinatorial Systems Based on Submodular Analysis
| Project/Area Number |
04832006
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
社会システム工学
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| Research Institution | University of Tsukuba |
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Principal Investigator |
FUJISHIGE Satoru Univ.Tsukuba Professor Inst.Socio-Econ.Plann., 社会工学系, 教授 (10092321)
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| Project Period (FY) |
1992 – 1993
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| Keywords | submodular analysis / submodular function / network / graph / large-scale system / combinatorial optimization |
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| Research Abstract |
We have investigated the following three based on the submodular analysis for large-scale combinatorial systems.
(1) The structures of combinatorial polyhedra determined by submodular functions and bisubmodular function,
(2) network optimization problems related to flows and cuts,
(3) algorithms for the minimun-norm point problem that gives us practical algorithms for minimizing submodular functions, basic tools in submodular analysis.
Concerning (1), we derived an algorithm for discerning whether a given crossing-submodular function defines a nonempty base polyhedron, and proposed new algorithms for solving the intersection problem of two submodular systems. Moreover, we examined the structures of combinatorial polyhedra determined byu bisubmodular functions and gave a greedy algorithm for minimizing separable convex functions over the polyhedra. We also revealed the relationship between bisubmodular functions and bidirected flows.
Concerning (2), we developed an efficient algorithm for finding a maximum mean cut and invented a new method, called a speculative contraction method, for minimum-cost flows. The effectiveness of these algorithms were shown by computational experiments.
For (3), we gave algorithms for finding a nearest pair of points in two polyhedra and for finding the minimum-norm point in the intersection of a polyhedron and a hyperplane, and showed their applicability for large-scale problems.
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