Developing New Algorithms for Enumerating Feasible Solutions in Linear Programming and Combinatorial Optimization
Project/Area Number  03832008 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
社会システム工学

Research Institution  University of Tsukuba 
Principal Investigator 
FUKUDA Komei University of Tsukuba, GSSM, Associate Professor, 社会工学系, 助教授 (40156782)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1992 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1991 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Linear Programming / Combinatorial Optimization / Enumerating Algorithms / Computational Geometry / 線形計画法 / 組合せ最適化 / 列挙アルゴリズム / 計算幾何学 / 並列アルゴリズム 
Research Abstract 
The purpose of this research project was to study new enumeration algorithms in linear programming and combinatorial optimization and to implement them on computers. The main results of this two year research can be summerized as follows: 1. We have made a Mathematica implementation of the AvisFukuda algorithm for enumerating all vertices of a convex polytype, and made it publicly available. 2. We have developed the notion of reverse search, which is a new general framework of enumeration. We have shown that this technique can be applied to solve various enumeration problems efficiently. 3. A Mathematica implementation of the reverse search algorithm has been developed as a unified platform for enumerating several different objects, including the connected induced subgraphs in a graph, the cells in an arrangement of hyperplanes in R^n and the triangulations of a finite set of points in the plane. 4. New (Nonreversesearch) algorithms have been developed for two problems,namely, the enumeration of common bases of two matroids and the combinatorial face enumeration in convex polytypes.

Report
(4results)
Research Output
(14results)