Summary: SIAM J. COMPUT.
Vol. 18, No. 2, pp. 258-267, April 1989
(C) 1989 Society for Industrial and Applied Mathematics
FINDING AN APPROXIMATE MAXIMUM*
N. ALON':]: AND Y. AZAR'
Abstract. Suppose that there are n elements from a totally ordered domain. The objective is to find,
in a minimum possible number of rounds, an element that belongs to the biggest n/2, where in each round
one is allowed to ask n binary comparisons. It is shown that log* n +19(1) rounds are both necessary and
sufficient in the best algorithm for this problem.
Key words, searching, approximate maximum, parallel comparison algorithms
AMS(MOS) subject classification. 68E05
1. Introduction. Parallel comparison algorithms have received much attention
during the last decade. The problems that have been considered include sorting [AA87],
[AA88], [AAV86], [Ak853, [AKS833, [A185], [AV87], [BT83], [BHe85], [HH81],
[HH82], [Kn73], [Kr83], [Le84], [Pi86]; merging [BHo82], [HH82], [Kr83], [SV81];
selecting [AA88], [AKSS86a], lAP89], [Pi87], [Va75]; and approximate sorting
[AA88], [AAV86], [AKSS86b], [BB87], [BR82]. The common model of computation
considered is the parallel comparison model, introduced by Valiant [Va75], where only
comparisons are counted. In this model, during each time unit (called a round) a set