On the competitiveness of on-line real-time task scheduling
Real-Time Systems
An efficient algorithm for finding a maximum weight 2-independent set on interval graphs
Information Processing Letters
MOCA: a multiprocessor on-line competitive algorithm for real-time system scheduling
Theoretical Computer Science - Special issue on dependable parallel computing
On-line scheduling of jobs with fixed start and end times
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Bounding the Power of Preemption in Randomized Scheduling
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
A short proof that “proper = unit”
Discrete Mathematics - Special issue on partial ordered sets
Patience is a virtue: the effect of slack on competitiveness for admission control
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Online scheduling with hard deadlines
Journal of Algorithms
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
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On-demand bounded broadcast scheduling with tight deadlines
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Improved Randomized Results for That Interval Selection Problem
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved Randomized Online Scheduling of Unit Length Intervals and Jobs
Approximation and Online Algorithms
Improved randomized results for the interval selection problem
Theoretical Computer Science
Interval scheduling on related machines
Computers and Operations Research
Space-constrained interval selection
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Online interval scheduling: randomized and multiprocessor cases
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
On-demand bounded broadcast scheduling with tight deadlines
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
Online selection of intervals and t-intervals
Information and Computation
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Given a set of weighted intervals, the objective of the weighted interval selection problem (WISP) is to select a maximum-weight subset such that the selected intervals are pairwise disjoint. We consider on-line algorithms that process the intervals in order of non-decreasing left endpoints. Preemption is allowed, but rejections are irrevocable. This problem has natural applications in various scheduling problems. We study the class of monotone instances of WISP, i.e., we require that the order of right endpoints of the given intervals coincides with that of the left endpoints. This class includes the case where all intervals have the same length. For monotone instances of WISP, the best possible competitive ratio for deterministic on-line algorithms is known to be 1/4. It has long been an open question whether there exists a randomized algorithm with better competitive ratio. In this paper, we present a new randomized algorithm and prove that it achieves a better competitive ratio 1/3 for the special case of monotone WISP where the sequence of weights of the arriving intervals is non-decreasing. Thus we provide the first result towards a solution of the long-standing open question. Furthermore, we show that no randomized algorithm achieves a competitive ratio strictly larger than 4/5. This is the first non-trivial upper bound for randomized algorithms for monotone WISP.