A Pipelined Single-Bit Controlled Sorting Network with O(N log^2 N) Bit Complexity

• Authors: Rajgopal Kannan
• Venue: INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
• Year: 1997

We propose a pipelined optical sorting network to sort N w-bit inputs using O(w N log N) single bit-controlled 2x2 switching elements. The network is compared to the standard Batcher sorter which requires O(N log^2 N) two-input comparators for sorting N log N-bit words. However each comparator in the Batcher sorter has to perform a word comparison between two log N bit inputs, as opposed to single-bit controlled switching elements in the proposed scheme. An alternative implementation of the proposed network maintains the same hardware complexity while showing an O(log log N) improvement in latency over the Batcher sorter.The proposed network is based on binary radix sort and utilizes a pair of self-routing reverse banyan networks to implement each step of the radix-sort algorithm. A distributed single-bit control scheme due to a particular non-blocking property of the reverse banyan network is used to route packets through each reverse banyan. Given the high cost of optical switches, the low hardware and control complexity of the network makes it easy to replace electronic switching elements with 2x2 Lithium Niobate directional couplers, thus making the network attractive for high-speed optical applications.