XXXXXXXXXX An O ( log n ) Randomized Resource Discovery Algorithm

The problem of a distributed network of computers discovering one another by making network connections is called the resource discovery problem. In this paper, we present the first randomized algorithm, called ‘Absorption’, that can solve the resource discovery problem in O(log n) running time with high probability and with O(n2) expected pointer complexity. In particular, the expected running time of our Absorption algorithm is at most 4 log4/3 n + 1 steps on any strongly-connected network. We also describe a variation of the algorithm, which runs in O(log n) expected time but has O(n) expected message complexity.