Deterministic 1-k routing on meshes with applications to worm-hole routing

In $1$-$k$ routing each of the $n^2$ processing units of an $n \times n$ mesh connected computer initially holds $1$ packet which must be routed such that any processor is the destination of at most $k$ packets. This problem reflects practical desire for routing better than the popular routing of permutations. $1$-$k$ routing also has implications for hot-potato worm-hole routing, which is of great importance for real world systems. We present a near-optimal deterministic algorithm running in \sqrt{k} \cdot n / 2 + \go{n} steps. We give a second algorithm with slightly worse routing time but working queue size three. Applying this algorithm considerably reduces the routing time of hot-potato worm-hole routing. Non-trivial extensions are given to the general $l$-$k$ routing problem and for routing on higher dimensional meshes. Finally we show that $k$-$k$ routing can be performed in \go{k \cdot n} steps with working queue size four. Hereby the hot-potato worm-hole routing problem can be solved in \go{k^{3/2} \cdot n} steps

Routing with locality in partitioned-bus meshes

We show that adding partitioned-buses (as opposed to long buses that span an entire row or column) to ordinary meshes can reduce the routing time by approximately one-third for permutation routing with locality. A matching time lower bound is also proved. The result can be generalized to multi-packet routing.published_or_final_versio

The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

Aspects of k-k-Routing in Meshes and OTIS Networks

Aspects of k-k Routing in Meshes and OTIS-Networks Abstract Efficient data transport in parallel computers build on sparse interconnection networks is crucial for their performance. A basic transport problem in such a computer is the k-k routing problem. In this thesis, aspects of the k-k routing problem on r-dimensional meshes and OTIS-G networks are discussed. The first oblivious routing algorithms for these networks are presented that solve the k-k routing problem in an asymptotically optimal running time and a constant buffer size. Furthermore, other aspects of the k-k routing problem for OTIS-G networks are analysed. In particular, lower bounds for the problem based on the diameter and bisection width of OTIS-G networks are given, and the k-k sorting problem on the OTIS-Mesh is considered. Based on OTIS-G networks, a new class of networks, called Extended OTIS-G networks, is introduced, which have smaller diameters than OTIS-G networks.Für die Leistungfähigkeit von Parallelrechnern, die über ein Verbindungsnetzwerk kommunizieren, ist ein effizienter Datentransport entscheidend. Ein grundlegendes Transportproblem in einem solchen Rechner ist das k-k Routing Problem. In dieser Arbeit werden Aspekte dieses Problems in r-dimensionalen Gittern und OTIS-G Netzwerken untersucht. Es wird der erste vergessliche (oblivious) Routing Algorithmus vorgestellt, der das k-k Routing Problem in diesen Netzwerken in einer asymptotisch optimalen Laufzeit bei konstanter Puffergröße löst. Für OTIS-G Netzwerke werden untere Laufzeitschranken für das untersuchte Problem angegeben, die auf dem Durchmesser und der Bisektionsweite der Netzwerke basieren. Weiterhin wird ein Algorithmus vorgestellt, der das k-k Sorting Problem mit einer Laufzeit löst, die nahe an der Bisektions- und Durchmesserschranke liegt. Basierend auf den OTIS-G Netzwerken, wird eine neue Klasse von Netzwerken eingeführt, die sogenannten Extended OTIS-G Netzwerke, die sich durch einen kleineren Durchmesser von OTIS-G Netzwerken unterscheiden

Communication algorithms for isotropic tasks in hypercubes and wraparound meshes

Cover title.Includes bibliographical references (p. 29-30).Research supported by the NSF. NSF-ECS-8519058 Research supported by the ARO. DAAL03-86-K-0171by Emmanouel A. Varvarigos and Dimitri P. Bertsekas

Partial multinode broadcast and partial exchange algorithms for d-dimensional meshes

Caption title. "Revision of January 1992."Includes bibliographical references (p. 24-26).Supported by NSF. NSF-ECS-8519058 Supported by ARO. DAAL03-86-K-0171by Emmanouel A. Varvarigos and Dimitri P. Bertsekas

Sample sort on meshes

This paper provides an overview of lower and upper bounds for mesh-connected processor networks. Most attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Grammatikakis, Hsu and Kraetzl on multicomputer routing, submitted to JPDC