The integral stable allocation problem on graphs

Authors:
PéTer Biró;TamáS Fleiner
Affiliations:
Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computer Science and Information Theory, Budapest University of Technology and Economics, H-1117, Magyar tudósok körútja 2, Budapest, Hungary
Venue:
Discrete Optimization
Year:
2010

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Abstract

As a generalisation of the stable matching problem Baiou and Balinski (2002) [1] defined the stable allocation problem for bipartite graphs, where both the edges and the vertices may have capacities. They constructed a so-called inductive algorithm, that always finds a stable allocation in strongly polynomial time. Here, we generalise their algorithm for non-bipartite graphs with integral capacities. We show that the algorithm does not remain polynomial, although we also present a scaling technique that makes the algorithm weakly polynomial.