Neighbor systems, jump systems, and bisubmodular polyhedra

Akiyoshi Shioura

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The concept of neighbor system, introduced by Hartvigsen (2009), is a set of integral vectors satisfying a certain combinatorial property. In this paper, we reveal the relationship of neighbor systems with jump systems and with bisubmodular polyhedra. We firstly prove that for every neighbor system, there exists a jump system which has the same neighborhood structure as the original neighbor system. This shows that the concept of neighbor system is essentially equivalent to that of jump system. We next show that the convex closure of a neighbor system is an integral bisubmodular polyhedron. In addition, we give a characterization of neighbor systems using bisubmodular polyhedra. Finally, we consider the problem of minimizing a separable convex function on a neighbor system. By using the relationship between neighbor systems and jump systems shown in this paper, we prove that the problem can be solved in weakly-polynomial time for a class of neighbor systems.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings
Number of pages13
EditionPART 1
Publication statusPublished - 2010
Event21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, Korea, Republic of
Duration: 2010 Dec 152010 Dec 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6506 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other21st Annual International Symposium on Algorithms and Computations, ISAAC 2010
Country/TerritoryKorea, Republic of
CityJeju Island

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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