Upper and Lower Bounds for Selection on the Mesh

A distance-optimal algorithm for selection on the mesh has proved to be elusive, although distance-optimal algorithms for the related problems of routing and sorting have recently been discovered. In this paper we explain, using the notion of adaptiveness, why techniques used in the currently best selection algorithms cannot lead to a distance-optimal algorithm. For worst-case inputs we apply new techniques to improve the previous best upper bound of 1.22n of Kaklamanis et al. [7] to 1.15n . This improvement is obtained in part by increasing the adaptiveness of previous algorithms. Received May 25, 1995; revised June 1, 1996.