Efficient Approximation Algorithms for Scheduling Coflows With Precedence Constraints in Identical Parallel Networks to Minimize Weighted Completion Time

This article focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, a well-known <inline-formula><tex-math notation="LaTeX">\mathcal {NP}</tex-math> <mml:math><mml:mi mathvariant="script">NP</mml:mi...

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Bibliographic Details
Published in:IEEE transactions on services computing Vol. 17; no. 5; pp. 2349 - 2364
Main Author: Chen, Chi-Yeh
Format: Journal Article
Language:English
Published: IEEE 01.09.2024
Subjects:
Approximation algorithms
coflow
Data centers
datacenter network
identical parallel network
Job shop scheduling
Linear programming
Optimal scheduling
precedence constraints
Processor scheduling
scheduling algorithms
Servers
ISSN:1939-1374, 2372-0204
Online Access:Get full text
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Summary:This article focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, a well-known <inline-formula><tex-math notation="LaTeX">\mathcal {NP}</tex-math> <mml:math><mml:mi mathvariant="script">NP</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq1-3344481.gif"/> </inline-formula>-hard problem. Coflow is a relatively new network abstraction that characterizes communication patterns in data centers. When considering workload sizes and weights that are dependent on the network topology in the input instances, the proposed algorithm for the flow-level scheduling problem achieves an approximation ratio of <inline-formula><tex-math notation="LaTeX">O(\chi)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>χ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq2-3344481.gif"/> </inline-formula> where <inline-formula><tex-math notation="LaTeX">\chi</tex-math> <mml:math><mml:mi>χ</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq3-3344481.gif"/> </inline-formula> is the coflow number of the longest path in the directed acyclic graph (DAG). Additionally, when taking into account topology-dependent workload sizes, the algorithm achieves an approximation ratio of <inline-formula><tex-math notation="LaTeX">O(R\chi)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mi>χ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq4-3344481.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">R</tex-math> <mml:math><mml:mi>R</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq5-3344481.gif"/> </inline-formula> represents the ratio of maximum weight to minimum weight. For the coflow-level scheduling problem, the proposed algorithm achieves an approximation ratio of <inline-formula><tex-math notation="LaTeX">O(m\chi)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mi>χ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq6-3344481.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">m</tex-math> <mml:math><mml:mi>m</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq7-3344481.gif"/> </inline-formula> is the number of network cores when considering workload sizes and weights that are topology-dependent. Moreover, when considering topology-dependent workload sizes, the algorithm achieves an approximation ratio of <inline-formula><tex-math notation="LaTeX">O(Rm\chi)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mi>m</mml:mi><mml:mi>χ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq8-3344481.gif"/> </inline-formula>. In the coflows of multi-stage job scheduling problem, the proposed algorithm achieves an approximation ratio of <inline-formula><tex-math notation="LaTeX">O(\chi)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>χ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq9-3344481.gif"/> </inline-formula>. Although our theoretical results are based on a limited set of input instances, experimental findings show that the results for general input instances outperform the theoretical results.
ISSN:1939-1374
2372-0204
DOI:10.1109/TSC.2023.3344481