research-article

Online set packing and competitive scheduling of multi-part tasks

Authors:

Magnús M. Halldórsson,

Yishay Mansour,

Boaz Patt-Shamir,

Jaikumar Radhakrishnan,

Dror RawitzAuthors Info & Claims

PODC '10: Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing

Pages 440 - 449

https://doi.org/10.1145/1835698.1835800

Published: 25 July 2010 Publication History

Abstract

We consider a scenario where large data frames are broken into a few packets and transmitted over the network. Our focus is on a bottleneck router: the model assumes that in each time step, a set of packets (a burst) arrives, from which only one packet can be served, and all other packets are lost. A data frame is considered useful only if none of its constituent packets is lost, and otherwise it is worthless. We abstract the problem as a new type of online set packing, present a randomized distributed algorithm and a matching lower bound on the competitive ratio for any randomized online algorithm. Our bounds are expressed in terms of the maximal burst size and the maximal number of packets per frame. We also present refined bounds that depend on the uniformity of these parameters.

References

[1]

N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, and J. Naor. The online set cover problem. In Proc. 35th Ann. ACM Symp. on Theory of Computing, pages 100--105. ACM, 2003.

Digital Library

[2]

N. Alon, U. Arad, and Y. Azar. Independent sets in hypergras with applications to routingvia fixed paths. In Proc. 2nd APPROX, pp. 16--27, 1999.

Digital Library

[3]

B. Awerbuch and R. Khandekar. Stateless distributed gradient descent for positive linear programs. SIAM J. Comput., 38(6):2468--2486, 2009.

Digital Library

[4]

P. Berman. A d/2-approximation for maximum weight independent set in d-claw free graphs. Nordic J. Comput., 7(3):178--184, 2000.

Digital Library

[5]

N. Buchbinder and J. Naor. Online primal-dual algorithms for covering and packing. Math. Oper. Res., 34(2):270--286, 2009.

Digital Library

[6]

J. Håstad. Clique is hard to approximate within n^1-ε. Acta Mathematica, 182(1):105--142, 1999.

[7]

M. M. Halldórsson, K. Iwama, S. Miyazaki, and S. Taketomi. Online independent sets. Theoretical Computer Science, 289(2):953--962, 2002.

Digital Library

[8]

M. M. Halldórsson, J. Kratochvil, J. A. Telle. Independent sets with domination constraints. Disc. Applied Math., 99(1-3):39--54, 2000.

Digital Library

[9]

E. Hazan, S. Safra, and O. Schwartz. On the complexity of approximating k-dimensional matching. In Proc. 6th Int. Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 83--97, 2003.

[10]

C. A. J. Hurkens and A. Schrijver. On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM J. Disc. Math., 2(1):68--72, 1989.

Digital Library

[11]

R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for on-line bipartite matching. In Proc. 22nd Ann. ACM Symp. on Theory of Computing, pages 352--358. ACM, 1990.

Digital Library

[12]

A. Kesselman, B. Patt-Shamir, and G. Scalosub. Competitive buffer management with packet dependencies. In 23rd IEEE Int. Symp. on Parallel and Distributed Processing (IPDPS) 2009, Rome, Italy, May 23-29, 2009, pages 1--12. IEEE, 2009.

Digital Library

[13]

V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov. Random Allocations. Winston & Sons, Washington, 1978.

[14]

F. Kuhn, T. Moscibroda, and R. Wattenhofer. The price of being near-sighted. In Proc. 17th Ann. ACM-SIAM Symposium on Discrete Algorithms, pages 980--989, New York, NY, USA, 2006. ACM.

Digital Library

[15]

M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 15(4):1036--1053, Nov. 1986.

Digital Library

[16]

C. H. Papadimitriou and M. Yannakakis. Linear programming without the matrix. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 121--129, New York, NY, USA, 1993. ACM.

Digital Library

[17]

M. Raab and A. Steger. "Balls into Bins" - A Simple and Tight Analysis. In Proc. 2nd Intl. Workshop on Randomization and Approximation Techniques in Computer Science, pages 159--170, 1998.

Digital Library

[18]

T. Sandholm. Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence, 135(1-2):1--54, 2002.

Digital Library

[19]

A. C.-C. Yao. Probabilistic computations: Toward a unified measure of complexity. In Proceedings of the 18th Annual ACM Symposium on Theory of Computing, pages 222--227, 1977.

Cited By

Kawahara JKobayashi KMiyazaki S(2017)Better bounds for online k-frame throughput maximization in network switchesTheoretical Computer Science10.1016/j.tcs.2016.10.009657:PB(173-190)Online publication date: 2-Jan-2017
https://dl.acm.org/doi/10.1016/j.tcs.2016.10.009
Fernández Anta AGeorgiou CKowalski DZavou E(2015)Online parallel scheduling of non-uniform tasksTheoretical Computer Science10.1016/j.tcs.2015.01.027590:C(129-146)Online publication date: 26-Jul-2015
https://dl.acm.org/doi/10.1016/j.tcs.2015.01.027
Georgiou CKowalski D(2015)On the competitiveness of scheduling dynamically injected tasks on processes prone to crashes and restartsJournal of Parallel and Distributed Computing10.1016/j.jpdc.2015.07.00784:C(94-107)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.jpdc.2015.07.007
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Index Terms

Online set packing and competitive scheduling of multi-part tasks
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Conferences

PODC '10: Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing

July 2010

494 pages

ISBN:9781605588889

DOI:10.1145/1835698

General Chairs:
Andrea Richa
Arizona State University, USA
,
Rachid Guerraoui
EPFL, Switzerland

Copyright © 2010 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 25 July 2010

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PODC '10

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PODC '10: ACM Symposium on Principles of Distributed Computing

July 25 - 28, 2010

Zurich, Switzerland

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Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

Kawahara JKobayashi KMiyazaki S(2017)Better bounds for online k-frame throughput maximization in network switchesTheoretical Computer Science10.1016/j.tcs.2016.10.009657:PB(173-190)Online publication date: 2-Jan-2017
https://dl.acm.org/doi/10.1016/j.tcs.2016.10.009
Fernández Anta AGeorgiou CKowalski DZavou E(2015)Online parallel scheduling of non-uniform tasksTheoretical Computer Science10.1016/j.tcs.2015.01.027590:C(129-146)Online publication date: 26-Jul-2015
https://dl.acm.org/doi/10.1016/j.tcs.2015.01.027
Georgiou CKowalski D(2015)On the competitiveness of scheduling dynamically injected tasks on processes prone to crashes and restartsJournal of Parallel and Distributed Computing10.1016/j.jpdc.2015.07.00784:C(94-107)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.jpdc.2015.07.007
Bienkowski MKraska ASchmidt P(2015)A Randomized Algorithm for Online Scheduling with Interval ConflictsPost-Proceedings of the 22nd International Colloquium on Structural Information and Communication Complexity - Volume 943910.1007/978-3-319-25258-2_7(91-103)Online publication date: 14-Jul-2015
https://dl.acm.org/doi/10.1007/978-3-319-25258-2_7
Jeź ŁMansour YPatt-Shamir B(2015)Scheduling Multipacket Frames with Frame DeadlinesPost-Proceedings of the 22nd International Colloquium on Structural Information and Communication Complexity - Volume 943910.1007/978-3-319-25258-2_6(76-90)Online publication date: 14-Jul-2015
https://dl.acm.org/doi/10.1007/978-3-319-25258-2_6
Scalosub GMarbach PLiebeherr J(2013)Buffer Management for Aggregated Streaming Data with Packet DependenciesIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2012.6524:3(439-449)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1109/TPDS.2012.65
Kawahara JKobayashi KMiyazaki S(2013)Better Bounds for Online k-Frame Throughput Maximization in Network SwitchesAlgorithms and Computation10.1007/978-3-642-45030-3_21(218-228)Online publication date: 2013
https://doi.org/10.1007/978-3-642-45030-3_21
Anta AGeorgiou CKowalski DZavou E(2013)Online parallel scheduling of non-uniform tasksProceedings of the 19th international conference on Fundamentals of Computation Theory10.1007/978-3-642-40164-0_16(145-158)Online publication date: 19-Aug-2013
https://dl.acm.org/doi/10.1007/978-3-642-40164-0_16
Kawahara JKobayashi K(2013)Optimal Buffer Management for 2-Frame Throughput MaximizationStructural Information and Communication Complexity10.1007/978-3-319-03578-9_23(274-285)Online publication date: 2013
https://doi.org/10.1007/978-3-319-03578-9_23
Mansour YPatt-Shamir BRawitz D(2012)Overflow management with multipart packetsComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2012.07.00156:15(3456-3467)Online publication date: 1-Oct-2012
https://dl.acm.org/doi/10.1016/j.comnet.2012.07.001
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