2018 Fiscal Year Final Research Report
Approximation of cost functions by tree metrics and approximation of the Shapley values of minimum cost spanning tree games
| Project/Area Number |
15K00033
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
前原 貴憲 国立研究開発法人理化学研究所, 革新知能統合研究センター, ユニットリーダー (20751407)
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| Research Collaborator |
SATO Koki
INAGAKI Ryosuke
SHOJI Kazuya
TAKASE Koichi
ISHIKAWA RUI
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | アルゴリズム / 協力ゲーム / Shapley値 |
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| Outline of Final Research Achievements |
In this study, we have developed two approximation algorithms for computing the Shapley values of the minimum cost spanning tree games. One is an approximation algorithm based on sampling. The other is an algorithm which approximates the Shapley value of the given minimum cost spanning tree games by approximating a given cost function with another "special" cost function, for which an efficient algorithm for computing the Shapley value of the associated minimum cost spanning tree game is available. Furthermore, we have obtained an efficient algorithm for finding a representation of a subtree distance, which is such a special cost function. Also, we studied properties and algorithms for the cycle-complete distance, which is an another such special cost function.
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| Free Research Field |
離散最適化
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| Academic Significance and Societal Importance of the Research Achievements |
本研究で開発したShapley値の近似計算のためのサンプリング・アルゴリズムは，既存研究より少ないサンプル数で近似解を出力することを示した．もう一つは，費用関数の近似によってShapley値の近似計算を行うアルゴリズムである．後者のアルゴリズムも既存の同様のアルゴリズムよりも高精度の近似解を出力することを数値計算によって示した．このような研究はこれまでほとんど行われて来なかったため，学術的な意義は大きい．また，最小費用全域木ゲームのShapley値の計算の厳密計算は現実的には不可能であるため，最小費用全域木ゲームを現実問題に適用する際には，このような効率的なアルゴリズムの存在は不可欠である．
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