A Structure Theory for the Parametric Submodular Intersection Problem

Authors:
Satoru Fujishige;Kiyohito Nagano
Affiliations:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan;Department of Mathematical and Computing Sciences, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
Venue:
Mathematics of Operations Research
Year:
2009

Citing 6
Cited 0

A fast parametric maximum flow algorithm and applications

SIAM Journal on Computing
A fast parametric submodular intersection algorithm for strong map sequences

Mathematics of Operations Research
Fast Algorithms for Parametric Scheduling Come From Extensions to Parametric Maximum Flow

Operations Research
A push-relabel framework for submodular function minimization and applications to parametric optimization

Discrete Applied Mathematics - Submodularity
Submodular function minimization

Mathematical Programming: Series A and B
Matrices and Matroids for Systems Analysis

Matrices and Matroids for Systems Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

A linearly parameterized polymatroid intersection problem appears in the context of principal partitions. We consider a submodular intersection problem on a pair of strong-map sequences of submodular functions, which is an extension of the linearly parameterized polymatroid intersection problem to a nonlinearly parameterized one. We introduce the concept of a basis frame on a finite nonempty set of cardinality n that gives a mapping from the set of all base polyhedra in n-dimensional space into n-dimensional vectors such that each base polyhedron is mapped to one of its bases. We show the existence of a simple universal representation of all optimal solutions of the parameterized submodular intersection problem by means of basis frames.