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The triangle scheduling problem. (English) Zbl 1406.90040

Summary: This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio. It is shown that the greedy algorithm solves the problem to optimality when the binary tree ratio of the input instance is at most 2. We also show that the problem is unary NP-hard for instances with binary tree ratio strictly larger than 2 and provide a quasi-polynomial time approximation scheme. The approximation ratio of Greedy on general instances is shown to be between 1.5 and 1.05.

MSC:

90B35 Deterministic scheduling theory in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90C59 Approximation methods and heuristics in mathematical programming
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References:

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