|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)
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.