Project/Area Number  10680353 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
計算機科学

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
KATOH Naoki Kyoto Univ. Graduate school of Engineering, Dept of Arch. and Arch. Systems, Professor, 工学研究科, 教授 (40145826)

CoInvestigator(Kenkyūbuntansha) 
FVJISAWA Katsuki Kyoto Univ. Graduate school of Engineering, Dept of Arch and Arch, systems. Research Asscciate, 工学研究科, 助手 (40303854)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  optimal partition / geometric data / vehicle routing / approximation algorithm / data mining / semidefinite programming / 最適分割 / 幾何学データ / 車両配置計画 / 近似アルゴリズム / データマイニング / 半正定値計画 / 車両配送計画 / 最適二次元相関ルール / 計算幾何学 / 耳両配送計画 / クラス間分散 / クラスタリング 
Research Abstract 
Over the last two years, we have tried to develop efficient algorithms for optimally partitioning geometric data such as point set in the plane and pixel data on twodimensional grid. The problems we studied and results we obtained are summarized as follows. (1) we deal with a vehicle routing on a treeshaped network with a single depot. Customers are located on vertices of the tree, and each customer has a positive demand. Demands of customers are served by a fleet of identical vehicles with limited capacity. It is assumed that the demand of a customer is splittable. We considered the problem for finding a set of tours with minimum total lengths. In the first year, we showed that the problem is NPcomplete and proposed a 1.5approximation algorithm for the problem. We also performed some computational experiments. In the second year, the approximation ration is improved to 1.35 by further refining the first algorithm. (2) We considered the problem of finding an optimal interval in onedimensional array and a region in twodimensional array under several optimality criteria. In particular, we shall consider the problem of finding an interval I∈[1,n] that maximizes the interclass variance. We shall present an O(n log n)time algorithm for this problem. We then extend this algorithm to twodimensional case. Namely, given a N×N twodimensional array, the problem seeks to find a rectangular subarray R with maximum interclass variance. We developed an O(NィイD13ィエD1)algorithm. (3) We considered the problem of finding twodimensional association rules for categorical attributes and developed an algorithm based on semidefinite programming.
