General scheduling non-approximability results in presence of hierarchical communications

Giroudeau, Rodolphe; König, Jean-Claude

doi:10.1016/j.ejor.2006.11.020

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…Thus, the dual objective in this case is at least 2 times the algorithm's cost (here we without loss of generality assume that ≤ 1/8, and we can remove this assumption easily by scaling ). Now we will show that we can divide all the dual variables by 20 2 to obtain a feasible solution to the dual. This will give an O(1/ 3 ) competitive algorithm.…”

Section: Identical Endpoints On Broomsticksmentioning

confidence: 99%

“…Addressing these scheduling issues is not new. Besides a large amount of work being done in practical scheduling literature, there has been some theoretical work done offline with the goal of minimizing makespan [8,9,16,17,20,21]. Additionally, over two decades ago Phillps, Stein and Wein [32] introduced an interesting model of network scheduling and argued its importance in practice.…”

Section: Introductionmentioning

confidence: 98%

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Scheduling in Bandwidth Constrained Tree Networks

Moseley

2015

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

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In this paper we introduce a new network scheduling model. Here jobs need to be sent via routers on a tree to machines to be scheduled, and the communication is constrained by network bandwidth. The scheduler coordinates network communication and job machine scheduling. This type of scheduler is highly desirable in practice; yet few works have considered combing networking with job processing. We consider the popular objective of total flow time in the online setting. We give a (1+ )-speed O( 1 7 )-competitive algorithm when all routers are identical and all machines are identical for any fixed > 0. Then we go on to show a (2 + )-speed O( 1 7 )-competitive algorithm when the routers are identical and the machines are unrelated. To show these results we introduce an interesting combination of potential function and dual fitting techniques as well as a reduction of general tree scheduling to a special case of trees.

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Section: Identical Endpoints On Broomsticksmentioning

confidence: 99%