Nested Convex Bodies are Chaseable

@inproceedings{Bansal2018NestedCB,
  title={Nested Convex Bodies are Chaseable},
  author={Nikhil Bansal and Martin B{\"o}hm and Marek Eli{\'a}s and Grigorios Koumoutsos and Seeun William Umboh},
  booktitle={SODA},
  year={2018}
}
In the Convex Body Chasing problem, we are given an initial point v0 ∈ R 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 Ω( √ d) lower bound on the competitive ratio, and conjectured that a competitive ratio depending only on d is possible. However, despite much interest in the… CONTINUE READING

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