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Nested Convex Bodies are Chaseable
[article]
2017
arXiv
pre-print
Preserved Fulltext
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]
2018
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
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]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
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