A nonoblivious bus access scheme yields an optimal partial sorting algorithm

This paper focuses on a linear array of n nodes with multiple shared buses as a practically feasible model for parallel processing. Let k be the number of shared buses. A nonoblivious scheme for mutually exclusive access to k shared buses is proposed. The effectiveness of the scheme is demonstrated by proposing an algorithm for solving a partial sort problem, which can be efficiently executed on the array according to the scheme. The partial sort problem with parameter m is the problem of sorting a subset S′ of a given set S, where S′ is the set of elements less than or equal to the mth smallest element in S. If m = 1, then it is solved by an algorithm for finding the smallest element in S, and if m = n, then it is solved by adapting normal sorting algorithm. The time complexity (9mlk) log₂ log₂ n + 3.467 √nlk + O(mlk + (nlk)^1/4) of the proposed algorithm matches a lower bound Ω (√nlk + mlk) with respect to n and k, if m is small enough to satisfy m = O(√nkllog log n).