Extremal behavior of the Greedy algorithm for a triangle scheduling problem

We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr et al. (2018), the problem can be treated as a specific 1-dimensional triangle scheduling problem. In that paper a new Greedy algorithm was de...

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Vydáno v:Computers & operations research Ročník 169; s. 106718
Hlavní autoři: Balogh, János, Békési, József, Büki, Nóra, Dósa, György, Tuza, Zsolt
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.09.2024
Témata:
Algorithm analysis
Mixed-criticality scheduling
Triangle scheduling
Mixed-criticality scheduling
Algorithm analysis
Triangle scheduling
ISSN:0305-0548, 1873-765X
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Shrnutí:We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr et al. (2018), the problem can be treated as a specific 1-dimensional triangle scheduling problem. In that paper a new Greedy algorithm was defined, and the authors proved that its approximation ratio lies between 1.05 and 3/2. In this paper we present a quadratic integer programming model, which can be used to computationally analyze the algorithm for inputs with small sizes. The model simulates the behavior of the algorithm and it compares the makespan with the optimal one. Using this model, we found sequences extendable to longer series, giving a lower bound of 1.27 for the Greedy algorithm. Also, the optimum on problem instances consisting of intervals of natural numbers is analyzed and a closed formula is determined. In this way, we detected two input classes where, in one of them, Greedy is far from optimal (we think that this could be the worst case), and in the other one it is optimal. •A quadratic integer programming model for the analysis of a Greedy algorithm for triangle scheduling.•A new lower bound for the approximation ratio of the Greedy algorithm.•Analysis of the Greedy algorithm for instances consisting of intervals of natural numbers.
ISSN:0305-0548
1873-765X
DOI:10.1016/j.cor.2024.106718