Minimizing Flow-Time on Unrelated Machines

Bansal, Nikhil; Kulkarni, Janardhan

doi:10.1145/2746539.2746601

Cited by 22 publications

(37 citation statements)

References 30 publications

(60 reference statements)

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“…Finally, our work is related to approximation algorithms of classical optimization problems for minimizing the weighted sum of completion times and flow times [18,9,2,5], none of which present an approximation algorithm for the problem minimizing average completion time in routing over a tree.…”

Section: Our Contributions and Techniquesmentioning

confidence: 99%

Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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Abstract. While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first coordination mechanisms with provable price of anarchy for this problem. Interestingly, we achieve our price of anarchy results using simple and strongly local policies such as Shortest Job First and the Smith's Rule (also called HDF). In particular, for the case of unweighted jobs, we design a coordination mechanism with polylogarithmic price of anarchy. For weighted jobs, on the other hand, we show that price of anarchy is a function of the depth of the tree and accompany this result by a lower bound for the price of anarchy for the Smith Rule policy and other common strongly local scheduling policies. Our price of anarchy results also imply improved approximation algorithms for the underlying optimization problem of routing over a tree. This problem is well motivated from applications of routing in supercomputers and data center networks where average sojourn time is an important metric.

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Section: Our Contributions and Techniquesmentioning

confidence: 99%

Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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“…For R||( j (C j ) k ) 1/k , see [6,27]. For R|r j | j (C j − r j ), a poly-logarithmic approximation is known [7]. For the special case of R|r j , p ij ∈ {p j , ∞}| j (C j − r j ), see [20,21].…”

Section: Other Related Workmentioning

confidence: 99%

“…Note that Eqn. (7), (8), (9) have no dependency on κ. Eqn. (7) is for event (i ← 1 j∧i ← 1 j ′ ) since…”

Section: Proof Outlinementioning

confidence: 99%

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Weighted Completion Time Minimization for Unrelated Machines via Iterative Fair Contention Resolution

Shadloo

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We give a 1.488-approximation for the classic scheduling problem of minimizing total weighted completion time on unrelated machines. This is a considerable improvement on the recent breakthrough of (1.5−10 −7 )-approximation (STOC 2016, Bansal-Srinivasan-Svensson) and the follow-up result of (1.5 − 1/6000)-approximation (FOCS 2017, Li). Bansal et al. introduced a novel rounding scheme yielding strong negative correlations for the first time and applied it to the scheduling problem to obtain their breakthrough, which resolved the open problem if one can beat out the long-standing 1.5-approximation barrier based on independent rounding. Our key technical contribution is in achieving significantly stronger negative correlations via iterative fair contention resolution, which is of independent interest. Previously, Bansal et al. obtained strong negative correlations via a variant of pipage type rounding and Li used it as a black box.

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“…Similar techniques have been used to develop algorithms for both problems [18,5,4,3,20]. This is natural as the objectives behave similarly mathematically.…”

Section: Introductionmentioning

confidence: 99%

Fair Scheduling via Iterative Quasi-Uniform Sampling

Im¹,

Moseley²

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the paper we consider minimizing the k -norms of flow time on a single machine offline using a preemptive scheduler for k ≥ 1. We show the first O(1)-approximation for the problem, improving upon the previous best O(log log P )-approximation by Bansal and Pruhs (FOCS 09 and SICOMP 14) where P is the ratio of the maximum job size to the minimum. Our main technical ingredient is a novel combination of quasi-uniform sampling and iterative rounding, which is of interest in its own right.

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Minimizing Flow-Time on Unrelated Machines

Cited by 22 publications

References 30 publications

Coordination Mechanisms for Selfish Routing over Time on a Tree

Coordination Mechanisms for Selfish Routing over Time on a Tree

Weighted Completion Time Minimization for Unrelated Machines via Iterative Fair Contention Resolution

Fair Scheduling via Iterative Quasi-Uniform Sampling

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