A Fast Selection Algorithm and the Problem of Optimum Distribution of Effort

ABSTRATI. An algorithm IS developed whtch finds the nth largeat element of a Ilnearly ordered \el S. glven In the form of rn pairwise dlsjo~nt subsets. Each of the rn subsets satisfies the property that 11s kth largest element can be computed tn a constant amount of time. The algor~thm terminate5 in time O(rn.logL(lSl/rn)! The selection algorithm applies to the problem of optimum distr~bution of effort. namely. the maumizat~on o f the total utility of allocating n persons to rn acttbiuea, where the utility u fk persons assigned to activity j la a concave function u,(k). Consequently, this problem can be solved in time 0(rn.log2n).