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...

• Type: Conference
• Year: 2005
• Where: FCT
• Authors: Bogdan S. Chlebus, Dariusz R. Kowalski
• Keywords: FCT 2005, Group Testing, Radio Networks, Single Element