Abstract: We propose a priority-based balanced routing scheme, called the priority STAR routing scheme, which leads to optimal throughput and average delay at the same time for random broadcasting and routing. In particular, the average reception delay for random broadcasting required in n1timesn2times...timesnd tori with ni=O(1), n-ary d-cubes with n=O(1), or d-dimensional hypercubes is O(d+1/(1-rho)). We also study the case where multiple communication tasks for random 1-1 routing and/or random broadcasting are executed at the same time. When a constant fraction of the traffic is contributed by broadcast requests, the average delay for random 1-1 routing required in any d-dimensional hypercube, any n-ary d-cube with n = O(1), and most n1timesn2times...timesnd tori with ni=O(1) are O(d) based on priority STAR. Our simulation results show that the priority-based balanced routing scheme considerably outperform the best previous routing schemes for these networks

Abstract: Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be routed along specific paths to their destinations without conflicts. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy algorithm for arbitrary direct routing problems whch is worst-case optimal, i.e., there exist instances for which no direct routing algorithm is better than the greedy. We apply variants of this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time using for the tree and d-dimensional mesh, given arbitrary sources and destinations; for the butterfly and the hypercube, the same result holds for random destinations. (ii) Complexity. By a reduction from Vertex Coloring, we show that Direct Routing is inapproximable, unless P=NP. (iii) Lower Bounds for Buffering. We show the existence of routing problems which cannot be solved efficiently with direct routing. To solve these problems, any routing algorithm needs buffers. We give nontrivial lower bounds on such buffering requirements for general routing algorithms.

Abstract: Partitioned Optimal Passive Stars network, POPS(d,g), is an optical interconnection network of N processors (N=dg) which uses g2 optical passive star couplers. The processors of this network are partitioned into g groups of d processors each and the g2 couplers are used for connecting each group with each of the groups, including itself. In this paper, we present an optimal embedding of the hypercube on this network for all combinations of values of d and g. Specifically, we show how to optimally simulate the most common hypercube communication pattern where each hypercube node sends a packet along the same dimension. Optimal simulation of this communication on the POPS(d,g) network has already been presented for d {\^a}‰¤ g in the literature, but for the case d> g, the optimality remained an open problem. Now, we show that an optimal simulation is feasible in this case too.

Abstract: Partitioned Optimal Passive Stars network, POPS(d,g), is an optical interconnection network of N processors (N=dg) with g 2 optical passive star couplers. In this network, there are g groups of d processors each and the g 2 couplers are used for connecting each group with each of the groups, including itself. In this paper, we present a technique for optimally simulating a frequently arising hypercube communication pattern on this network for all combinations of values of d and g. Specifically, we show that one-hop movements on the hypercube along the same dimension can be simulated on the POPS(d,g) network in $\lceil \frac{d}{g}\rceil$ slots for d≠g and in 2 slots for d=g.