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FCT
2005
Springer

Almost Optimal Explicit Selectors

13 years 9 months ago
Almost Optimal Explicit Selectors
We understand selection by intersection as distinguishing a single element of a set by the uniqueness of its occurrence in some other set. More precisely, given two sets A and B, if A ∩ B = {z}, then element z ∈ A is selected by set B. Selectors are such families S of sets B of some domain that allow to select many elements from sufficiently small subsets A of the domain. Selectors are used in communication protocols for the multiple-access channel, in implementations of distributed-computing primitives in radio networks, and in algorithms for group testing. We give new explicit (n, k, r)-selectors of size O(min n, k2 k−r+1 polylog n ), for any parameters r ≤ k ≤ n. We establish a lower bound Ω(min n, k2 k−r+1 · log(n/k) log(k/(k−r+1)) ) on the length of (n, k, r)-selectors, which demonstrates that our construction is within a polylog n factor close to optimal. The new selectors are applied to develop explicit implementations of selection resolution on the multipleacce...
Bogdan S. Chlebus, Dariusz R. Kowalski
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where FCT
Authors Bogdan S. Chlebus, Dariusz R. Kowalski
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