1994 Fiscal Year Final Research Report Summary
On Construction and Evaluation of Parallel and Randomized Algorithms for Network Optimization Problems
| Project/Area Number |
05680281
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
計算機科学
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| Research Institution | KOBE UNIVERSITY OF COMMERCE |
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Principal Investigator |
KATOH Naoki Kobe University of commerce, Dept.Management Science, Professor, 商経学部, 教授 (40145826)
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| Co-Investigator(Kenkyū-buntansha) |
DAI Yang Kobe University of commerce, Dept.Management Science, Research Assistant, 商経学部, 助手 (40244678)
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| Project Period (FY) |
1993 – 1994
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| Keywords | network optimization / minimum range cut / minimum cut / randomized algorithm / parallel algorithm / color quantization / minimum k-clustering |
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| 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 k-clustering 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 k-cut problems and performed similar experiments.
A minimum k-clustering problem asks to find a k-partition 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 k-partition under certain optimality criteria that are suitable for this application.
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