A constant-time parallel sorting algorithm and its optical implementation

Sorting is a fundamental operation that has important implications in a vast number of areas. For instance, sorting is heavily utilized in applications such as database machines, where hashing techniques are used to accelerate data processing algorithms. It is also the basis for interprocessor message routing and has strong implications in video telecommunications. However, high-speed electronic sorting networks are di cult to implement with VLSI technology because of the dense, global connectivity required. Optics eliminates this bottleneck by o ering global interconnects, massive parallelism, and non-interfering communications. In this paper, we present a parallel sorting algorithm and its e cient optical implementation using currently available optical hardware. The algorithm sorts n data elements in few steps, independent of the number of elements to be sorted. Thus, it is a constant-time sorting algorithm (i.e. O(1) time). This is a signi cant performance improvement over state-of-the-art electronic sorting systems where the fastest sorting algorithm for n elements takes O(log n) but requires O(n 2 ) processors. We provide the detailed description of an optical system for generating the rank of a data set and physically reordering it. This is evidence that problems considered \solved" using conventional approaches need to be reconsidered so that the bene ts of optics can be properly utilized to obtain new, faster solutions to old problems. 1 This research was supported by an NSF grant No. MIP 9113688