Finding the closest extreme vertex to a fixed point

Abstract

Many results on parallel mergesort can be used to merge two sorted runs at-a-time [2-4,101. log,R merge passes are required to merge R initial runs, since two runs are merged at-a-time; hence, N log,R data accesses are required during merging by those algorithms when N elements are to be sorted. Such a large number of data accesses is undesirable for a system in which data access is expensive compared to typical instruction-execution times, such as the multiprocessor with private caches, since the data have to be transferred from the secondary memory many times [6]. In [9], an arbitrary number of sorted runs are merged using all processors in one pass in parallel, using an approximate partitioning technique, which splits multiple sorted runs according to the sort-key values among processors; however, the time complexity of both the number of comparisons and the data accesses during final merging is O(N) in the worst case. Iyer et al. [7,11] removed the skew effect of the sort-key values by splitting an arbitrary number of sorted runs among all the processors, but multiple processors should be able to read the same data element concur-