Selection on Mesh Connected Computers with Fixed and Reconfigurable Buses 1 Sanguthevar Rajasekaran Department of CISE University of Florida Gainesville, FL 32611-2024. Abstract Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject of extensive previous research. The problem of our interest is selection. Selection is a critical comparison problem with numerous applications. Our algorithms have considerably better time bounds than the best known algorithms for selection. 1 Introduction Given a set of N numbers and an i ≤ N , the problem of selection is to find the ith smallest element from out of the N given numbers. The problem of selection has many applications. For example, in the design of divide and conquer algorithms, one has to partition the problem into as equally sized subproblems as possible. A median finding algorithm could be employed to achieve even partitions. Many computational problems (both sequential and parallel) have been solved using this strategy. An elegant linear time sequential algorithm is known for selection. The problem of parallel selection has been studied extensively. Several optimal and near optimal algorithms are known for various models of computing (see e.g., [16]). In this paper 1 This research was supported in part by an NSF Research Initiation Award CCR-92-09260 and an NSF Grant CCR-95-03007. Preliminary versions of some of the results in this paper were presented in the First Annual European Symposium on Algorithms, 1993. 1