2010/06/10 by Vladimir Kolmogorov, Kolmogorov, Vladimir
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Optimization and Search Problems #cs.DS
paper · pdf · doi:10.48550/arxiv.1006.1990
accepted to "Discrete Applied Mathematics"
openalex publication_date 2010/06/10 · arxiv created 2012/06/11 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of minimizing a function represented as a sum of submodular terms. We assume each term allows an efficient computation of \em exchange capacities. This holds, for example, for terms depending on a small number of variables, or for certain cardinality-dependent terms. A naive application of submodular minimization algorithms would not exploit the existence of specialized exchange capacity subroutines for individual terms. To overcome this, we cast the problem as a \em submodular flow (SF) problem in an auxiliary graph, and show that applying most existing SF algorithms would rely only on these subroutines. We then explore in more detail Iwata's capacity scaling approach for submodular flows (Math. Programming, 76(2):299--308, 1997). In particular, we show how to improve its complexity in the case when the function contains cardinality-dependent terms.