Scheduling Parallel Communication: The h-relation Problem

This paper is concerned with the efficient scheduling and routing of point-to-point messages in a distributed computing system with n processors. We examine the h-relation problem, a routing problem where each processor has at most h messages to send and at most h messages to receive. Communication is carried out in rounds. Direct communication is possible from any processor to any other, and in each round a processor can send one message and receive one message. The off-line version of the problem arises when every processor knows the source and destination of every message. In this case the messages can be routed in at most h rounds. More interesting, and more typical, is the on-line version, in which each processor has knowledge only of h and of the destinations of those messages which it must send. The on-line version of the problem is the focus of this paper.

[1]  Michael D. Noakes,et al.  System design of the J-Machine , 1990 .

[2]  Thanasis Tsantilas,et al.  Efficient optical communication in parallel computers , 1992, SPAA '92.

[3]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[4]  Sajal K. Das,et al.  Book Review: Introduction to Parallel Algorithms and Architectures : Arrays, Trees, Hypercubes by F. T. Leighton (Morgan Kauffman Pub, 1992) , 1992, SIGA.

[5]  W. Daniel Hillis,et al.  The Network Architecture of the Connection Machine CM-5 , 1996, J. Parallel Distributed Comput..

[6]  Leslie Ann Goldberg,et al.  An Ω(√ log log n) lower bound for routing in optical networks , 1994, SPAA '94.

[7]  Ramesh Subramonian,et al.  LogP: towards a realistic model of parallel computation , 1993, PPOPP '93.

[8]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[9]  Abhiram G. Ranade,et al.  Fluent parallel computation , 1989 .

[10]  Leslie G. Valiant,et al.  Direct Bulk-Synchronous Parallel Algorithms , 1994, J. Parallel Distributed Comput..

[11]  Yossi Matias,et al.  The QRQW PRAM: accounting for contention in parallel algorithms , 1994, SODA '94.

[12]  Jehoshua Bruck,et al.  Efficient algorithms for all-to-all communications in multi-port message-passing systems , 1994, SPAA '94.

[13]  Torsten Suel,et al.  Efficient communication using total-exchange , 1995, Proceedings of 9th International Parallel Processing Symposium.

[14]  Richard J. Anderson.  Optical Communication for Pointer Based Algorithms , 1988 .

[15]  Leslie G. Valiant,et al.  General Purpose Parallel Architectures , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[16]  Yossi Matias,et al.  Efficient low-contention parallel algorithms , 1994, SPAA '94.

[17]  Frank Thomson Leighton,et al.  A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer , 1993, SPAA '93.

[18]  S. Zafar.  Abstract , 2002, Veterinary Record.

[19]  Richard Cole,et al.  Parallel merge sort , 1988, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[20]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[21]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .