| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥1,500,000 (Direct Cost: ¥1,500,000)
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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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