Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization

• 成果类型: Article
• 署名作者: McCormick, S. Thomas; Fujishige, Satoru
• 署名单位: University of British Columbia; Kyoto University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-008-0242-9
• 发表日期: 2010
• 页码: 87-120
• 关键词: submodular function minimization; separation algorithm

摘要

Bisubmodular functions are a natural directed, or signed, extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function minimization (SFM) to bisubmodular function minimization (BSFM). However, they were able to extend only the weakly polynomial version of IFF to BSFM. Here we investigate the difficulty that prevented them from also extending the strongly polynomial version of IFF to BSFM, and we show a way around the difficulty. This new method gives a somewhat simpler strongly polynomial SFM algorithm, as well as the first combinatorial strongly polynomial algorithm for BSFM. This further leads to extending Iwata's fully combinatorial version of IFF to BSFM.