Routing Permutations on Optical Baseline Networks with Node-Disjoint Paths

• Authors: Yuanyuan Yang;Jianchao Wang
• Venue: ICPADS '04 Proceedings of the Parallel and Distributed Systems, Tenth International Conference
• Year: 2004

Permutation is a frequently-used communication patternin parallel and distributed computing systems and telecommunicationnetworks. Node-disjoint routing has important applications in guidedwave optical interconnects where the optical "crosstalk" between messagespassing the same switch should be avoided. In this paper, weconsider routing arbitrary permutations on an optical baseline network(or reverse baseline network) with node-disjoint paths. We first provethe equivalence between the set of admissible permutations (or semi-permutations)of a baseline network and that of its reverse network basedon a step-by-step permutation routing. We then show that an arbitrarypermutation can be realized in a baseline network (or a reverse baselinenetwork) with node-disjoint paths in four passes, which beats the existingresults [Strictly nonblocking directional-coupler-based switching networks under crosstalk constraint], [Design of photinic rearrangeable networks with zero first-order switching-element-crosstalk] that a permutation can be realized in an n x n banyan networkwith node-disjoint paths in O(n^{\frac{1}{2}}) passes. This represents the currentlybest-known result for the number of passes required for routingan arbitrary permutation with node-disjoint paths in unique-path multi-stagenetworks. Unlike other unique path MINs (such as omega networksor banyan networks), only baseline networks have been found to possesssuch four-pass routing property. We present routing algorithms in bothself-routing style and central-controlled style. Different from the recentwork in [Routing permutations with link-disjoint and node-disjoint paths in a class of self-routable interconnects], which also gave a four-pass node-disjoint routing algorithmfor permutations, the new algorithm is efficient in transmission time formessages of any length, while the algorithm in [Routing permutations with link-disjoint and node-disjoint paths in a class of self-routable interconnects] can work efficientlyonly for long messages. Comparisons with previous results demonstratethat routing in a baseline network proposed in this paper could be a betterchoice for routing permutations due to its lowest hardware cost andnear-optimal transmission time.