Instance-Optimal Geometric Algorithms

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Instance-Optimal Geometric Algorithms
We prove the existence of an algorithm A for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every set S of n points and for every algorithm A in a certain class A, the maximum running time of A on input s1, . . . , sn is at most a constant factor times the maximum running time of A on s1, . . . , sn , where the maximum is taken over all permutations s1, . . . , sn of S. In fact, we can establish a stronger property: for every S and A , the maximum running time of A is at most a constant factor times the average running time of A over all permutations of S. We call algorithms satisfying these properties instance-optimal in the order-oblivious and random-order setting. Such instance-optimal algorithms simultaneously subsume output-sensitive algorithms and distribution-dependent average-case algorithms, and all algorithms that do not take advantage of the order of the input or that assume the input is given in a random order. The class A...
Peyman Afshani, Jérémy Barbay, Timot
Added 20 May 2010
Updated 20 May 2010
Type Conference
Year 2009
Where FOCS
Authors Peyman Afshani, Jérémy Barbay, Timothy M. Chan
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