On A New Competitive Measure For Oblivious Routing

Two new algorithms for worm-hole routing in the hypercube are presented. The first hypercube algorithm is adaptive, but non-minimal in the sense that some derouting is permitted. Then another deadlock-free adaptive worm-hole based routing algorithm for the hypercube interconnection is presented which is minimal. Finally some well-known worm-hole algorithms for the hypercube were evaluated together with the new ones on a hypercube of 2/sup 10/ nodes. One oblivious algorithm, the Dimension-Order, or E-Cube routing algorithm (W. Dally, C. Seitz, 1987) was tried. In addition, three partially adaptive algorithms were considered: the Hanging algorithm (Y. Birk, P. Gibbons, D. Soroker, J. Sanz, 1989 and S. Konstantinidou, 1990), the Zenith algorithm (S. Konstantinidou, 1990), and the Hanging-Order algorithm (G.-M. Chia, S. Chalasani, C.S. Raghavendra, 1991). Finally, a fully adaptive minimal algorithm presented independently by L. Gravano, G. Pifarre, S.A. Felperin and J. Sanz (1991) and J. Duato was tried. This algorithm allows each message to choose adaptively among all the shortest paths from its source to its destination. Only four virtual channels per physical link are needed to achieve this. This technique is referred to as Fully. The results obtained show that the two new algorithms are good candidates as a choice for worm-hole routing in the hypercube network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive routing is widely regarded as a promising approach to improving interconnection network performance. Many designers of adaptive routing algorithms have used synthetic communication patterns, such as uniform and transpose traffic, to compare the performance of various adaptive routing algorithms with each other and with oblivious routing. These comparisons have shown that the average message latency is usually lower with adaptive routing. On the other hand, when a parallel program is executed on a multiprocessor the goal is to reduce the total execution time. We explain why improving the average message latency of a routing algorithm does not necessarily lead to a lower execution time for real applications. We support this observation by reporting simulation results for both adaptive and oblivious routing using communication derived from real applications. Specifically, we report the performance of various routing algorithms for directed acyclic graphs (DAGs) derived from the Cholesky factorization of sparse matrices. Our results show that there is little correlation between average message latency and the total execution time of a parallel program. Hence, average message latency does not seem to be a useful measure of the performance of a routing algorithm. This strongly suggests that current comparisons of routing algorithms do not provide a reliable indication of the performance improvements to be realized by executing programs on a multiprocessor with such a routing algorithm. We interpret these results and suggest several alternatives for further research.

In this paper we describe anO(logN)-bit-step randomized algorithm for bit-serial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of on-line circuit switching in anO(1)-dilated hypercube (i.e., the problem of establishing edge-disjoint paths between the nodes of the dilated hypercube for any one-to-one mapping). Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least Ω(log2 N/log logN) bit steps with high probability for almost all permutations.

We study oblivious routing in which the packet paths are constructed independently of each other. We give a simple oblivious routing algorithm for geometric networks in which the nodes are embedded in the Euclidean plane. In our algorithm, a packet path is constructed by first choosing a random intermediate node in the space between the source and destination, and then the packet is sent to its destination through the intermediate node. We analyze the performance of the algorithm in terms of the stretch and congestion of the resulting paths. We show that the stretch is constant, and the congestion is near optimal when the network paths can be chosen to be close to the geodesic lines that connect the end points of the paths. We give applications of our general result to the mesh topology and uniformly distributed disc graphs. Previous oblivious routing algorithms with near optimal congestion use many intermediate nodes and do not control the stretch.

In this paper, we introduce a novel oblivious routing scheme based on valiant load-balancing for the model of polyhedral uncertainty (i.e., hose model), and the scheme is implemented with traffic-grooming approach in WDM mesh networks. Considering that a high-speed connection request in optical networks is difficult to be divided into low-speed connections, we propose the method of hose-model separation to support the multi-granularity connections for valiant load-balanced oblivious routing in WDM mesh networks. Our Objective is to minimize total network cost. Two fast heuristic algorithms-MPCF and MRUF are proposed. Simulation results show MRUF performs better than MPCF

In the oblivious path selection problem, each packet in the network independently chooses a path, which is an important property if the routing algorithm is to be independent of the traffic distribution. The quality of the paths is determined by the congestion, C, the maximum number of paths crossing an edge, and the dilation, D, the maximum path length. So far, the oblivious algorithms studied in the literature have focused on minimizing the congestion while ignoring the dilation. An open problem is to give algorithms for networks in which C and D can be controlled simultaneously. Here, we solve this problem for the d-dimensional mesh. We present an oblivious algorithm for which C and D are both within O(d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) of the optimal. The algorithm uses randomization and we show that the number of random bits required per packet is within O(d) of the minimum number of random bits required by any algorithm that obtains the same congestion. For a fixed d, our algorithm is asymptotically optimal.

Data networking now plays a major role in everyday life and new applications continue to appear at a blinding pace. Yet we still do not have a sound foundation for designing, evaluating and managing these networks. This book covers topics at the intersection of algorithms and networking. It builds a complete picture of the current state of research on Next Generation Networks and the challenges for the years ahead. Particular focus is given to evolving research initiatives and the architecture they propose and implications for networking. Topics: Network design and provisioning, hardware issues, layer-3 algorithms and MPLS, BGP and Inter AS routing, packet processing for routing, security and network management, load balancing, oblivious routing and stochastic algorithms, network coding for multicast, overlay routing for P2P networking and content delivery. This timely volume will be of interest to a broad readership from graduate students to researchers looking to survey recent research its open questions.

ROMM is a class of Randomized, Oblivious, Multi--phase, Minimal routing algorithms. ROMM routing offers a potential for improved performance compared to both fully randomized algorithms and deterministic oblivious algorithms, under both light and heavy loads. ROMM routing also offers close to best case performance for many common routing problems. In previous work, these claims were supported by extensive simulations on binary cube networks [30, 31]. Here we present analytical and empirical results for ROMM routing on wormhole routed mesh and torus networks. Our simulations show that ROMM algorithms can perform several representative routing tasks 1.5 to 3 times faster than fully randomized algorithms, for medium--sized networks. Furthermore, ROMM algorithms are always competitive with deterministic, oblivious routing, and in some cases, up to 2 times faster.

We study oblivious routing in fat-tree-based system area networks with deterministic routing under the assumption that the traffic demand is uncertain. The performance of a routing algorithm under uncertain traffic demands is characterized by the oblivious performance ratio that bounds the relative performance of the routing algorithm with respect to the optimal algorithm for any given traffic demand. We consider both single-path routing, where only one path is used to carry the traffic between each source-destination pair, and multipath routing, where multiple paths are allowed. For single-path routing, we derive lower bounds of the oblivious performance ratio for different fat-trees and develop routing schemes that achieve the optimal oblivious performance ratios for commonly used topologies. Our evaluation results indicate that the proposed oblivious routing schemes not only provide the optimal worst-case performance guarantees but also outperform existing schemes in average cases. For multipath routing, we show that it is possible to obtain an optimal scheme for all traffic demands (an oblivious performance ratio of 1). These results quantitatively demonstrate the performance difference between single-path routing and multipath routing in fat-trees.

Direct network performance is affected by different design parameters which include number of virtual channels, number of ports, routing algorithm, switching technique, deadlock handling technique, packet size, and buffer size. Another factor that affects network performance is the traffic pattern. In this thesis, we study the effect of hotspot traffic on system performance. Specifically, we study the effect of hotspot factor, hotspot number, and hot spot location on the performance of mesh-based networks. Simulations are run on two network topologies, both the mesh and torus. We pay more attention to meshes because they are widely used in commercial machines. Comparisons between oblivious wormhole switching and chaotic packet switching are reported. Overall packet switching proved to be more efficient in terms of throughput when compared to wormhole switching. In the case of uniform random traffic, it is shown that the differences between chaotic and oblivious routing are indistinguishable. Networks with low number of hotspots show better performance. As the number of hotspots increases network latency tends to increase. It is shown that when the hotspot factor increases, performance of packet switching is better than that of wormhole switching. It is also shown that the location of hotspots affects network performance particularly with the oblivious routers since their achieved latencies proved to be more vulnerable to changes in the hotspot location. It is also shown that the smaller the size of the network the earlier network saturation occurs. Further, it is shown that the chaos router’s adaptivity is useful in this case. Finally, for tori, performance is not greatly affected by hotspot presence. This is mostly due to the symmetric nature of tori.

In a (randomized) oblivious routing scheme the path chosen for a request between a source s and a target t is independent from the current traffic in the network. Hence, such a scheme consists of probability distributions over s-t paths for every source-target pair s,t in the network.In a recent result [11] it was shown that for any undirected network there is an oblivious routing scheme that achieves a polylogarithmic competitive ratio with respect to congestion. Subsequently, Azar et al. [4] gave a polynomial time algorithm that for a given network constructs the best oblivious routing scheme, i.e. the scheme that guarantees the best possible competitive ratio. Unfortunately, the latter result is based on the Ellipsoid algorithm; hence it is unpractical for large networks.In this paper we present a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log4n) for undirected networks. Furthermore, our approach yields a proof for the existence of an oblivious routing scheme with competitive ratio O(log3n), which is much simpler than the original proof from [11].

A VLSI implementation of a flexible router scheme for parallel interconnection network architectures is presented in this paper. The router implements implicit oblivious routing algorithms in 1.5 clock cycles, this being the fastest approach for flexible routers. To further increase performance, the router operation has been made pipelined with a throughput of 1 routing decision per cycle. The implementation is based on a combination of a content addressable memory that supports per entry unique bit masking, a fast priority scheme that allows only one entry to be selected, and a memory that stores the port assignment. The number of required CAM entries is extremely small; it is of the same order as the output ports (or node degree). >

We consider the all-or-nothing multicommodity flow problem in general graphs. We are given a capacitated undirected graph G=(V,E,u) and set of k pairs s1t1, s2t2, …, sktk. Each pair has a unit demand. The objective is to find a largest subset S of 1,2,…,k such that for every i in S we can send a flow of one unit between si and ti. Note that this differs from the edge-disjoint path problem (EDP) in that we do not insist on integral flows for the pairs. This problem is NP-hard, and APX-hard, even on trees. For trees, a 2--approximation is known for the cardinality case and a 4--approximation for the weighted case. In this paper we build on a recent result of Racke on low congestion oblivious routing in undirected graphs to obtain a poly-logarithmic approximation for the all-or-nothing problem in general undirected graphs. The best previous known approximation for all-or-nothing flow problem was O(min(n

A variety of models have been proposed for the study of synchronous parallel computation. We review these models and study further some prototype problems. We distinguish two classes of models, fixed connection networks and models based on a shared memory. Routing is the prototype problem for the networks. In particular, routing provides the basis for simulating the more powerful shared memory models. We show that a simple but important class of deterministic strategies (oblivious routing) is necessarily inefficient with respect to worst case analysis. Routing can be viewed as a special case of sorting and the existence of a deterministic O(logn) routing or sorting algorithm for an n processor fixed connection network remains open. However, if we consider the more powerful class of shared memory models, we are -&-ldquo;almost-&-rdquo; able to achieve such an efficient sort via Valiant's parallel merging algorithm. Within a spectrum of models, we show that log log n - log log r is asymptotically optimal for rn processors to merge two sorted lists of n elements.

Demand-oblivious routing in complex networks under uncertainty