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Nested Convex Bodies are Chaseable
[chapter]
2018
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
In the Convex Body Chasing problem, we are given an initial point v 0 ∈ R d and an online sequence of n convex bodies F 1 , . . . , F n . When we receive F i , we are required to move inside F i . 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 Ω( √ d) lower bound on the competitive ratio, and conjectured that a competitive ratio depending only on d is possible. However, despite much
doi:10.1137/1.9781611975031.81
dblp:conf/soda/BansalB0KU18
fatcat:qqg563nc55dshb5lvyz5rbdnum