Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
On-line scheduling of jobs with fixed start and end times
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Note on scheduling intervals on-line
Discrete Applied Mathematics
On the k-coloring of intervals
Discrete Applied Mathematics
Bounding the Power of Preemption in Randomized Scheduling
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
An optimal real-time algorithm for planar convex hulls
Communications of the ACM
An Improved Randomized On-Line Algorithm for a Weighted Interval Selection Problem
Journal of Scheduling
Randomized online interval scheduling
Operations Research Letters
On-line scheduling of equal-length intervals on parallel machines
Information Processing Letters
Online optimization of busy time on parallel machines
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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We consider the problem of scheduling n intervals (jobs with fixed starting times) on m machines with different speeds with the objective to maximize the number of accepted intervals. We prove that the offline version of the problem is strongly NP-hard to solve. For the online version, we show a lower bound of 53 on the competitive ratio of any deterministic online algorithm for the problem. Moreover, we present two simple greedy rules for online algorithms and show that any online algorithm using these rules is 2-competitive. One of these 2-competitive algorithms is shown to run in O(nlogm) time. Additionally, we prove that our greedy rules impose no loss in the sense that every online algorithm for the problem can be modified to use the rules without reducing the number of accepted intervals on any instance.