A bound and algorithm for four sender contention resolution

A number of important contention resolution and distributed ordering problems arising in time-slotted multiuser broadcast communication systems can be viewed as generic search problems in which M independent random variables, uniformly distributed in (0, 1), are to be located by testing a sequence of subsets of (0, 1). The authors discuss a search problem in which M=4 and each test returns a 0, a 1, or an e, depending on whether the tested subset contained 0, 1, or >1 random variables. The average number of tests required to locate the four random variables is shown to be lower bounded by 6.495, and a testing algorithm that requires, on average, 6.782 tests is constructed