Nested convex bodies are chaseable

N. Bansal, M. Bohm, M. Elias, G. Koumoutsos, S.W. Umboh

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

11 Citations (Scopus)
97 Downloads (Pure)

Abstract



In the Convex Body Chasing problem, we are given an initial point v0 ∊ ℝd and an online sequence of n convex bodies F1, …, Fn. When we receive Fi, we are required to move inside Fi. Our goal is to minimize the total distance traveled. This fundamental online problem was first studied by Friedman and Linial (DCG 1993). They proved an lower bound on the competitive ratio, and conjectured that a competitive ratio depending only on d is possible. However, despite much interest in the problem, the conjecture remains wide open.

We consider the setting in which the convex bodies are nested: Fi ⊃ … ⊃ Fn. The nested setting is closely related to extending the online LP framework of Buchbinder and Naor (ESA 2005) to arbitrary linear constraints. Moreover, this setting retains much of the difficulty of the general setting and captures an essential obstacle in resolving Friedman and Linial's conjecture. In this work, we give a f(d)-competitive algorithm for chasing nested convex bodies in ℝd.



Original languageEnglish
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
Place of Publications.l.
PublisherSociety for Industrial and Applied Mathematics (SIAM)
Pages1253-1260
Number of pages8
ISBN (Electronic)9781611975031
DOIs
Publication statusPublished - 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018) - Astor Crowne Plaza, New Orleans, United States
Duration: 7 Jan 201810 Jan 2018
Conference number: 29
https://www.siam.org/meetings/da18/

Conference

Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)
Abbreviated titleSODA 2018
CountryUnited States
CityNew Orleans
Period7/01/1810/01/18
Internet address

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