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Nested Convex Bodies are Chaseable [article]

Nikhil Bansal, Martin Böhm, Marek Eliáš, Grigorios Koumoutsos, Seeun William Umboh
2017 arXiv   pre-print
We consider the setting in which the convex bodies are nested: F_1 ⊃ ... ⊃ F_n.  ...  In the Convex Body Chasing problem, we are given an initial point v_0 in 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.  ...  Nested Convex Body Chasing. In this paper, we consider the nested convex body chasing problem where the requested convex bodies are nested, i.e., F i ⊂ F i−1 for each i ≥ 1.  ... 
arXiv:1707.05527v1 fatcat:b22pz2ekdjfwzbxbilqwzbbyna

Nested Convex Bodies are Chaseable [chapter]

Nikhil Bansa, Martin Böhm, Marek Eliáš, Grigorios Koumoutsos, Seeun William Umboh
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We consider the setting in which the convex bodies are nested: F 1 ⊃ . . . ⊃ F n .  ...  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 .  ...  Nested Convex Body Chasing. In this paper, we consider the nested convex body chasing problem where the requested convex bodies are nested, i.e., F i ⊂ F i−1 for each i ≥ 1.  ... 
doi:10.1137/1.9781611975031.81 dblp:conf/soda/BansalB0KU18 fatcat:qqg563nc55dshb5lvyz5rbdnum

Competitively Chasing Convex Bodies [article]

Sébastien Bubeck and Yin Tat Lee and Yuanzhi Li and Mark Sellke
2018 arXiv   pre-print
In 1991, Linial and Friedman conjectured that the family of convex sets in Euclidean space is chaseable. We prove this conjecture.  ...  The family F is said to be chaseable if there exists an online algorithm with finite competitive ratio.  ...  Combining both points we would obtain a O(d 2 log d)-competitive algorithm for nested convex body chasing.  ... 
arXiv:1811.00887v1 fatcat:q6aonfedmnbylp72c6v56qahwy