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. >

[1]  J. Capetanakis,et al.  Generalized TDMA: The Multi-Accessing Tree Protocol , 1979, IEEE Trans. Commun..

[2]  Frank K. Hwang,et al.  Cutoff points for roll-call protocols in multiple-access systems , 1984, The 23rd IEEE Conference on Decision and Control.

[3]  J. Hayes,et al.  An Adaptive Technique for Local Distribution , 1978, IEEE Trans. Commun..

[4]  Frank K. Hwang,et al.  A Fundamental Monotonicity in Group Testing , 1988, SIAM J. Discret. Math..

[5]  Mart Molle,et al.  On the capacity of infinite population multiple access protocols , 1982, IEEE Trans. Inf. Theory.