A generalization of the monotonicity theorem in group testing with applications to random multiaccess channels

The binomial group-testing problem consists of finding by group tests all defectives in a given set of items, each of which independently has probability p of being defective. The conjecture that the expected number of tests under an optimal testing algorithm is nondecreasing in p has recently been proved by transplanting the probability structure of the set of defective items. It is proved that this approach works in a much broader setting in which the states of items are dependent and the tests have k possible outputs. The results apply to the collision-resolution problem in random-multiple-access-channel communication