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
Online computation and competitive analysis
Online computation and competitive analysis
Bandwidth Allocation with Preemption
SIAM Journal on Computing
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
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We consider the problem of scheduling a sequence of intervals revealed on-line one by one in the order of their release dates on a set of k identical machines. Each interval i is associated with a processing time pi and a pair of arbitrary weights (w$_{i}^{A}$,w$_{i}^{B}$) and may be scheduled on one of the k identical machines or rejected. The objective is to determine a valid schedule maximizing the sum of the weights of the scheduled intervals for each coordinate. We first propose a generic on-line algorithm based on the combination of two monocriteria on-line algorithms and we prove that it gives rise to a pair of competitive ratios that are function of the competitive ratios of the monocriteria algorithms in the input. We apply this technique to the special case where w$_{i}^{A}$=1 and w$_{i}^{B}$=pi for every interval and as a corollary we obtain a pair of constant competitive ratios.