Abstract
We consider scheduling of unit-length jobs with release times and deadlines, where the objective is to minimize the number of gaps in the schedule. Polynomial-time algorithms for this problem are known, yet they are rather inefficient, with the best algorithm running in time \(O(n^4)\) and requiring \(O(n^3)\) memory. We present a greedy algorithm that approximates the optimum solution within a factor of 2 and show that our analysis is tight. Our algorithm runs in time \(O(n^2 \log n)\) and needs only O(n) memory. In fact, the running time is \(O(n (g^*+1)\log n)\), where \(g^*\) is the minimum number of gaps.
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Acknowledgments
Marek Chrobak has been supported by the National Science Foundation grants CCF-1217314, CCF-1536026, and OISE-1157129. Mohammad Taghi Hajiaghayi has been supported in part by the National Science Foundation CAREER award 1053605, Office of Naval Research YIP award N000141110662, and a University of Maryland Research and Scholarship Award (RASA). Fei Li has been supported by the National Science Foundation grants CCF-0915681 and CCF-1216993.
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Chrobak, M., Feige, U., Hajiaghayi, M.T. et al. A greedy approximation algorithm for minimum-gap scheduling. J Sched 20, 279–292 (2017). https://doi.org/10.1007/s10951-016-0492-y
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DOI: https://doi.org/10.1007/s10951-016-0492-y