| Presentation | 1994/7/25 The Minimum Base Game on Matroids Hiroshi Nagamochi, Naohisa Kabutoya, Dao-Zhi Zeng, Toshihide Ibaraki, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper studies complexties for computing solution concepts of cooperative games,introducing the minimum base game (MBG)(E,c) on a pair of a matroid M = (E,〓) and a weight funciton ω : E 〓 〓 , where a characteristic function c : 2^E 〓 〓 is defined as c(S) = the weight of a minimum weighted base on S ⊆ E.The minimum base game contains,as its special case,the minimum spanning tree game(MSTG)in an edge-weighted graph in which players are located on the edges.By interpreting solution concepts such as core and Shapley value in terms of matroid theory,we obtain the followings: (1)The core of MBG is non empty if and only if the matroid M has no circuit consisting of only edges with negative weights.Any minimum base on E gives an imputation in the core if the core is not empty.(2)Checking concavitiy(or subadditivity)of the MBG can be done in oracle-polynomial time.(3)The τ-value of the MBG exists if and only if the matroid M has no circuit consisting of only edges with negative weights.The τ-value of MSTG can be computed in polynomial time by the shortest path algorithm,while there is no oracle-polynomial algorithm for computing the τ-value of the MBG.( 4)Computing the Shapley value of the MSTG is #P-complete,while there is no oracle-polynomial algorithm for computing the Shapley- value of the MBG. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | cooperative game / Matroid / graph / computational complexity / polyromial algorithm / submodular |
| Paper # | COMP94-32 |
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| Conference Information | |
| Committee | COMP |
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| Conference Date | 1994/7/25(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Theoretical Foundations of Computing (COMP) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | The Minimum Base Game on Matroids |
| Sub Title (in English) | |
| Keyword(1) | cooperative game |
| Keyword(2) | Matroid |
| Keyword(3) | graph |
| Keyword(4) | computational complexity |
| Keyword(5) | polyromial algorithm |
| Keyword(6) | submodular |
| 1st Author's Name | Hiroshi Nagamochi |
| 1st Author's Affiliation | Department of Applied Mathematics and Physics,Faculty of Engineering,Kyoto University() |
| 2nd Author's Name | Naohisa Kabutoya |
| 2nd Author's Affiliation | Department of Applied Mathematics and Physics,Faculty of Engineering,Kyoto University |
| 3rd Author's Name | Dao-Zhi Zeng |
| 3rd Author's Affiliation | Department of Applied Mathematics and Physics,Faculty of Engineering,Kyoto University |
| 4th Author's Name | Toshihide Ibaraki |
| 4th Author's Affiliation | Department of Applied Mathematics and Physics,Faculty of Engineering,Kyoto University |
| Date | 1994/7/25 |
| Paper # | COMP94-32 |
| Volume (vol) | vol.94 |
| Number (no) | 181 |
| Page | pp.pp.- |
| #Pages | 10 |
| Date of Issue | |