Scaling and proximity properties of integrally convex functions

Satoko Moriguchi, Kazuo Murota, Akihisa Tamura, Fabio Tardella

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n ≤ 2, while a proximity theorem can be established for any n, but only with an exponential bound. This is, however, sufficient to extend the classical logarithmic complexity result for minimizing a discretely convex function in one dimension to the case of integrally convex functions in two dimensions. Furthermore, we identified a new class of discrete convex functions, called directed integrally convex functions, which is strictly between the classes of L-convex and integrally convex functions but enjoys the same scaling and proximity properties that hold for L-convex functions.

本文言語English
ホスト出版物のタイトル27th International Symposium on Algorithms and Computation, ISAAC 2016
編集者Seok-Hee Hong
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ページ57.1-57.13
ISBN(電子版)9783959770262
DOI
出版ステータスPublished - 2016 12 1
イベント27th International Symposium on Algorithms and Computation, ISAAC 2016 - Sydney, Australia
継続期間: 2016 12 122016 12 14

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
64
ISSN(印刷版)1868-8969

Other

Other27th International Symposium on Algorithms and Computation, ISAAC 2016
CountryAustralia
CitySydney
Period16/12/1216/12/14

ASJC Scopus subject areas

  • Software

引用スタイル