Basic Studies on Submodular Structure of Largescale Combinatorial Systems
Project/Area Number  10680429 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
社会システム工学

Research Institution  Osaka University 
Principal Investigator 
FUJISHIGE Satoru Osaka University, Graduate School of Engineering Science, Professor, 大学院・基礎工学研究科, 教授 (10092321)

Project Period (FY) 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,300,000 (Direct Cost : ¥3,300,000)
Fiscal Year 1999 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥2,600,000 (Direct Cost : ¥2,600,000)

Keywords  Submodular functions / Combinatorial optimization / Discrete Algorithms 
Research Abstract 
The most important result of this project is the combinatorial, strongly polynomialtime algorithm for minimizing submodular functions. It has been a longstanding open problem to obtain such a combinatorial algorithm since 1981. With the aid of this algorithm we can construct efficient algorithms for a lot of combinatorial optimization problems such as the submodular flow problem for which existing algorithms assume the oracle for submodular function minimization. Moreover, we have obtained the following results. We gave a short proof of the validity of M. Queyranne's algorithm for minimizing symmetric submodular functions. We proposed an algorithm for minimizing submodular functions arising from concave functions by means of parametric maxflow algorithms. We also showed the laminarity property of posimodular functions, which generalize symmetric submodular functions. Furthermore, we proved that the dual greedy polyhedra investigated by Faigle and Kern belong to the class of submodular flow polyhedra. Concerning the minimumnorm point problem, related to submodular function minimization, we proposed an efficient algorithm for finding the minimumnorm point in the intersection of the convex hull of points and an affine space.

Report
(3results)
Research Products
(21results)