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Explicit constructions of selectors and related combinatorial structures, with applications

In this paper we present explicit constructions of several combinatorial objects: selectors [CGR00] and selective families [CGGPR00], pseudo-random generators for proof systems [ABRW00] and fixed waking schedules [GPP00]. As a result, we obtain almost optimal deterministic protocols for broadcasting in unknown directed radio networks [CGR00] and wake-up problem [GPP00]. We also show application of selectors (and its variants) to explicit construction of test sets for coin-weighting problems [DH00]. The parameters of our constructions come close to the best known non-constructive bounds. The constructions are achieved using a common technique, which could be of use for other problems.