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

Scheduling techniques for packet routing, load, balancing and disk scheduling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.Includes bibliographical references (p. 163-170).by Matthew Andrews.Ph.D

Greedy Dynamic Routing on Arrays

We study the problem of dynamic routing on arrays. We prove that a large class of greedy algorithms perform very well on average. In the dynamic case, when the arrival rate of packets in an N \Theta N array is at most 99% of network capacity, we establish an exponential bound on the tail of the delay distribution. Moreover, we show that, in any window of T steps, the maximum queue-size is O(1 + log T= log N ) with high probability. We extend these results to the case of bit-serial routing, and to the static case. We also calculate the exact value of the ergodic expected delay and queue-sizes under the farthest-first protocol for the one dimensional array, and for the ring when the arrivals are Poisson. 1 Introduction Many parallel machines, such as the MPP, Ametek and Intel Touchstone are configured as a low-dimensional array containing a large number of processors. These machines generally route packets using simple greedy algorithms. While these algorithms tend to behave well experi..