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Packing random intervals

✍ Scribed by E. G. Coffman; Bjorn Poonen; Peter Winkler


Publisher
Springer
Year
1995
Tongue
English
Weight
678 KB
Volume
102
Category
Article
ISSN
1432-2064

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πŸ“œ SIMILAR VOLUMES


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It is known that given N random subintervals of [0, 1], one can find a disjoint subcollection that covers all of [0, 1] except a set of length about (log N)2/N. We investigate what happens when the distribution of the intervals is biased to favor shorter intervals or intervals close to the endpoints

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In this problem, we are given N uniformly distributed random intervals of 0 1 . For each random interval I, we are given a weight X I . These weights are independent, independent of the intervals, and satisfy P X I ≀ t = t Ξ± , where Ξ± > 0. A packing of the family is a disjoint subfamily of intervals

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We consider models for random interval graphs that are based on stochastic service systems, with vertices corresponding to customers and edges corresponding to pairs of customers that are in the system simultaneously. The number N of vertices in a connected component thus corresponds to the number o