A Nearly-Linear Bound for Chasing Nested Convex Bodies
A Nearly-Linear Bound for Chasing Nested Convex Bodies
复制标题
追逐嵌套凸体的近线性界限
DOI：
10.1137/1.9781611975482.8
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Y. Lee
中科院分区：
文献类型：
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作者：
C. Argue;Sébastien Bubeck;Michael B. Cohen;Anupam Gupta;Y. Lee
Friedman和Linial [8]引入了凸的身体追逐问题，以探索在凸起的凸台上的几何形状和竞争比之间的相互作用。凸面kt⊂rd，必须输出一个点XT∈Kt。被理解。 ）嵌套凸的算法算法，我们的算法适用于任何规范。
Friedman and Linial [8] introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step t ∈ N, the online algorithm receives a request in the form of a convex body Kt ⊂ Rd and must output a point xt ∈ Kt. The goal is to minimize the total movement between consecutive output points, where the distance is measured in some given norm. This problem is still far from being understood. Recently Bansal et al. [4] gave an 6d (d!)2-competitive algorithm for the nested version, where each convex body is contained within the previous one. We propose a different strategy which is O(dlog d)-competitive algorithm for this nested convex body chasing problem. Our algorithm works for any norm. This result is almost tight, given an Ω(d) lower bound for the l∞ norm [8].
DOI：
10.4230/lipics.approx-random.2015.96
发表时间：
2015
期刊：
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影响因子：
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作者：
N. Bansal;Anupam Gupta;Ravishankar Krishnaswamy;K. Pruhs;Kevin Schewior;C. Stein
通讯作者：
N. Bansal;Anupam Gupta;Ravishankar Krishnaswamy;K. Pruhs;Kevin Schewior;C. Stein