Improved Approximation Algorithm for the Combination of Parallel Machine Scheduling and Vertex Cover

2017 ◽  
Vol 28 (08) ◽  
pp. 977-992 ◽  
Author(s):  
Wenyi Hong ◽  
Zhenbo Wang
Keyword(s):  
Approximation Algorithm ◽  
Parallel Machines ◽  
Vertex Cover ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Combination Problem ◽  
Vertex Cover Problem ◽  
Cover Problem

This paper studies the combination problem of parallel machine scheduling and the vertex cover problem. Wang and Cui developed a [Formula: see text]-approximation algorithm for this problem [13], where [Formula: see text] is the number of parallel machines. We reduce the approximation factors from [Formula: see text] to [Formula: see text] for [Formula: see text], from [Formula: see text] to [Formula: see text] for [Formula: see text], and to [Formula: see text] for [Formula: see text].

An Optimal Preemptive Algorithm for the Single-Server Parallel-Machine Scheduling with Loading and Unloading Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450039 ◽  
Author(s):  
Yiwei Jiang ◽  
Huijuan Wang ◽  
Ping Zhou
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Solution Algorithm ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Loading And Unloading

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

An approximation algorithm for the partial vertex cover problem in hypergraphs

2014 ◽  
Vol 31 (2) ◽  
pp. 846-864 ◽  
Author(s):  
Mourad El Ouali ◽  
Helena Fohlin ◽  
Anand Srivastav
Keyword(s):  
Approximation Algorithm ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

scholarly journals A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

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