Project/Area Number  05680281 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
計算機科学

Research Institution  KOBE UNIVERSITY OF COMMERCE 
Principal Investigator 
KATOH Naoki Kobe University of commerce, Dept.Management Science, Professor, 商経学部, 教授 (40145826)

CoInvestigator(Kenkyūbuntansha) 
DAI Yang Kobe University of commerce, Dept.Management Science, Research Assistant, 商経学部, 助手 (40244678)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1994 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1993 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  network optimization / minimum range cut / minimum cut / randomized algorithm / parallel algorithm / color quantization / minimum kclustering / ネットワーク最適化 / 最小カット / 確率的アルゴリズム / 並列アルゴリズム / 最小kクラスタリング / カラー量子化 / 最大格差最小カット / 最小κクラスタリング / 最小kカット / 最大格差最小kカット / 確率的近似アルゴリズム / 回路分割 
Research Abstract 
Over the last two years, we have tried to construct new parallel, randomized algorithms for network optimization problems, in particular for minimum cut problems. Recently, there has been much progress in the research of parallel and randomized algorithms for minimum cut problems. In this research project, we have focused on developing simple and efficient algorithms that work for a broader class of problems including minimum cut problems. In addition, we have also studied minimum kclustering problems and could achieve new theoretical results on the problem under minimum variance criterion. In this project, we have first developed an O (m+nlogn) time algorithm for minimum range cut problems (n and m are the numbers of nodes and vertices in a graph). A minimum range cut problems asks to find a cut in weighted undirected graphs that minimizes the difference between maximum and minimum edge weights in the cut. Based on this algorithm, we developed a parallel, randomized algorithm for minimum cut problems. We then carried out extensive computer experiments to demonstrate the effectiveness of our approximate algorithm. As a result, we could show that our algorithm computes cuts that are very close to exact ones in time much faster than existing exact algorithms. We have further extended this algorithm to minimum kcut problems and performed similar experiments. A minimum kclustering problem asks to find a kpartition of a given set of n points in R^d based on certain optimality criteria. In our study, focusing on the application to color quantization problems arising in computer graphics, we have proposed randomized algorithms to find optimal kpartition under certain optimality criteria that are suitable for this application.
