On convex body chasing

Joel Friedman*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


A player moving in the plane is given a sequence of instructions of the following type: at step i a planar convex set Fi is specified, and the player has to move to a point in Fi. The player is charged for the distance traveled. We provide a strategy for the player which is competitive, i.e., for any sequence Fi the cost to the player is within a constant (multiplicative) factor of the "off-line" cost (i.e., the least possible cost when all Fi are known in advance). We conjecture that similar strategies can be developed for this game in any Euclidean space and perhaps even in all metric spaces. The analogous statement where convex sets are replaced by more general families of sets in a metric space includes many on-line/off-line problems such as the k-server problem; we make some remarks on these more general problems.

Original languageAmerican English
Pages (from-to)293-321
Number of pages29
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Dec 1993


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