Covering skew-supermodular functions by hypergraphs of minimum total size

Authors:
Attila BernáTh;TamáS KiráLy
Affiliations:
MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest H-1117, Hungary;MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest H-1117, Hungary
Venue:
Operations Research Letters
Year:
2009

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Abstract

The paper presents results related to a theorem of Szigeti on covering symmetric skew-supermodular set functions by hypergraphs. We prove the following generalization using a variation of Schrijver's supermodular colouring theorem: if p"1 and p"2 are skew-supermodular functions with the same maximum value, then it is possible to find in polynomial time a hypergraph of minimum total size that covers both p"1 and p"2. We also give some applications concerning the connectivity augmentation of hypergraphs.