Packet routing and job-shop scheduling in O(congestion+dilation) steps Authors
Received: 02 January 1991 Revised: 30 October 1993 DOI:
Cite this article as: Leighton, F.T., Maggs, B.M. & Rao, S.B. Combinatorica (1994) 14: 167. doi:10.1007/BF01215349 Abstract
In this paper, we prove that there exists a schedule for routing any set of packets with edge-simple paths, on any network, in
O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and job-shop scheduling. AMS subject classification code (1991) 68 M 20 68 M 10 68 M 07
This research was conducted while the authors were at MIT. Support was provided by the Defense Advanced Research Projects Agency under Contract N00014-87-K-825, the Office of Naval Research under Contract N00014-86-K-0593, the Air Force under Contract OSR-86-0076, and the Army under Contract DAAL-03-86-K-0171. Tom Leighton is supported by an NSF Presidential Young Investigator Award with matching funds provided by IBM.
N. Alon: A parallel algorithmic version of the Local Lemma. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science (1991), 586–593.
J. Beck: An algorithmic approach to the Lovász Local Lemma I. Random Structures and Algorithms, to appear.
R. Koch, T. Leighton, B. Maggs, S. Rao, and A. Rosenberg: Work-preserving emulations of fixed-connection networks. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing May 1989, 227–240.
E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys: Sequencing and scheduling: Algorithms and complexity. Technical Report BS-R8909, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, June 1989.
F. T. Leighton: Introduction to Parallel Algorithms and Architectures: Arrays • Tree • Hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.
F. T. Leighton, B. M. Maggs, A. G. Ranade, and S. B. Rao: Randomized routing and sorting on fixed-connection networks, Journal of Algorithms, to appear.
T. Leighton, B. Maggs, and S. Rao: Fast algorithms for finding O(congestion+dilation) packet routing schedules. Manuscript in preparation.
T. Leighton, B. Maggs, and S. Rao: Universal packet routing algorithms. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, October 1988, 256–271.
A. G. Ranade: How to emulate shared memory. In Proceedings of the 28th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, October 1987, 185–194.
S. V. Sevast'yanov: Bounding algorithm for routing problem with arbitrary paths and alternate servers. Kibernetika
22(6) (1986), 74–79 Translation in Cybernetics 22 773–780.
D. B. Shmoys, C. Stein, and J. Wein: Improved approximation algorithms for shop scheduling problems. In Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms January 1991, 148–157.
J. Spencer: Ten Lectures on the Probabilistic Method. SIAM, Philadelphia, PA, 1987.