Approximating the throughput of multiple machines under real-time scheduling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improvements in throughout maximization for real-time scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A unified approach to approximating resource allocation and scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Efficient Web Searching Using Temporal Factors
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximating an Interval Scheduling Problem
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
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Certain tasks, like accessing pages on the World Wide Web, require duration that varies over time. This poses the following Variable Length Sequencing Problem, or VLSP-L. Let [i, j) denote {i, i+1, ..., j- 1}. The problem is given by a set of jobs J and the time-dependent length function λ : J ×[0, n) → L. A sequencing function σ :J →[0, n) assigns to each job j a time interval Τσ(j) when this job is executed; if σ(j) = t then Τσ(j) = [t, t+λ(j, t)). The sequencing is valid if these time intervals are disjoint. Our objective is to minimize the makespan, i. e. the maximum ending of an assign time interval. Recently it was shown VLSP-[0, n) is NP-hard and that VLSP-{1, 2} can be solved efficiently. For a more general case of VLSP-{1, k} an 2 - 1/k approximation was shown. This paper shows that for k ≥ 3 VLSP-{1, k} is MAX-SNP hard, and that we can approximate it with ratio 2 - 4/(k + 3).