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)

Research Abstract 
We have investigated the following three based on the submodular analysis for largescale 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 minimunnorm 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 crossingsubmodular 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 minimumcost 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 minimumnorm point in the intersection of a polyhedron and a hyperplane, and showed their applicability for largescale problems.
