Doing-it-All with bounded work and communication
We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured i...
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| Published in: | Information and computation Vol. 254; pp. 1 - 40 |
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01.06.2017
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| Abstract | We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of workcomplexity and communication complexity. When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work O(t+plogp(plogp+tlogt)) and a nonconstructive algorithm that has work O(t+plog2p). The latter result is close to the lower bound Ω(t+plogp/loglogp) on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by cp, for some positive constant c<1. We also present a nonconstructive algorithm that has effort O(t+p1.77). |
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| AbstractList | We consider the Do-All problem, where p cooperating processors need to complete t similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of workcomplexity and communication complexity. When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work O(t+plogp(plogp+tlogt)) and a nonconstructive algorithm that has work O(t+plog2p). The latter result is close to the lower bound Ω(t+plogp/loglogp) on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by cp, for some positive constant c<1. We also present a nonconstructive algorithm that has effort O(t+p1.77). |
| Author | Kowalski, Dariusz R. Chlebus, Bogdan S. Gąsieniec, Leszek Schwarzmann, Alexander A. |
| Author_xml | – sequence: 1 givenname: Bogdan S. surname: Chlebus fullname: Chlebus, Bogdan S. email: bogdan.chlebus@ucdenver.edu organization: Department of Computer Science and Engineering, University of Colorado Denver, Denver, CO 80217, USA – sequence: 2 givenname: Leszek surname: Gąsieniec fullname: Gąsieniec, Leszek organization: Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK – sequence: 3 givenname: Dariusz R. surname: Kowalski fullname: Kowalski, Dariusz R. organization: Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK – sequence: 4 givenname: Alexander A. surname: Schwarzmann fullname: Schwarzmann, Alexander A. organization: Department of Computer Science and Engineering, University of Connecticut, Storrs, CT 06269, USA |
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| Cites_doi | 10.1109/12.272432 10.1007/PL00008926 10.1137/S0097539704440442 10.1007/BF02277667 10.1137/0216066 10.1137/0217061 10.1137/S0097539793255527 10.1016/j.ic.2005.08.002 10.1145/357172.357176 10.1145/2450142.2450147 10.1016/j.jda.2008.03.001 10.1016/0012-365X(88)90189-6 10.1145/7351.7478 10.1006/inco.1994.1099 10.1007/s00446-005-0153-4 10.1016/j.tcs.2013.04.017 10.1016/j.tcs.2004.06.034 10.1016/j.jcss.2006.08.001 10.1007/s00446-003-0099-3 10.1016/j.tcs.2014.10.015 10.1007/BF02126799 10.1007/s002240010009 10.1016/j.tcs.2005.05.019 10.1002/rsa.10104 10.1007/s004530010030 10.1137/0605030 |
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| Keywords | Ramanujan graphs Message passing Scheduling tasks Crash failures Load balancing Distributed algorithm |
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| SubjectTerms | Crash failures Distributed algorithm Load balancing Message passing Ramanujan graphs Scheduling tasks |
| Title | Doing-it-All with bounded work and communication |
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