Finding nucleolus of flow game
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Related Research Unit(s)
|Journal / Publication||Journal of Combinatorial Optimization|
|Publication status||Published - Jul 2009|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-67651114225&origin=recordpage|
We study the algorithmic issues of finding the nucleolus of a flow game. The flow game is a cooperative game defined on a network D=(V,E; ω). The player set is E and the value of a coalition S ⊆ E is defined as the value of a maximum flow from source to sink in the subnetwork induced by S. We show that the nucleolus of the flow game defined on a simple network (ω(e)=1 for each e ∈ E) can be computed in polynomial time by a linear program duality approach, settling a twenty-three years old conjecture by Kalai and Zemel. In contrast, we prove that both the computation and the recognition of the nucleolus are N℘-hard for flow games with general capacity. © 2008 Springer Science+Business Media, LLC.
- Efficient algorithm, Flow game, Linear program duality, N℘-hard, Nucleolus