Note on scheduling intervals on-line
Ulrich Faigle,Willem M. Nawijn +1 more
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TLDR
An optimal on-line algorithm is presented for the following optimization problem, which constitutes the special case of the k-track assignment problem with identical time windows, and performs as well as the optimal greedy k-coloring algorithm due to Faigle and Nawijn and, independently, to Carlisle and Lloyd for the same problem under full a priori information.About:
This article is published in Discrete Applied Mathematics.The article was published on 1995-03-10 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Interval scheduling & Greedy algorithm.read more
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Book ChapterDOI
On-line Scheduling
TL;DR: On-line scheduling illustrates many general aspects of competitive analysis, especially in the setting and numerical results, but also in the techniques used.
Journal ArticleDOI
Interval scheduling: A survey
TL;DR: This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time and investigates the complexity and approximability of different variants of interval schedules.
Journal ArticleDOI
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
Amotz Bar-Noy,Sudipto Guha +1 more
TL;DR: This work considers the following fundamental scheduling problem, and gives constant factor approximation algorithms for four variants of the problem, depending on the type of the machines and the weight of the jobs (identical vs. arbitrary).
Journal ArticleDOI
Fixed interval scheduling: Models, applications, computational complexity and algorithms
TL;DR: A general formulation of the interval scheduling problem is presented, its relations to cognate problems in graph theory are shown, and existing models, results on computational complexity and solution algorithms are surveyed.
Journal ArticleDOI
On the approximability of an interval scheduling problem
TL;DR: In this article, the authors consider a general interval scheduling problem and show that unless =, this maximization problem cannot be approximated in polynomial time within arbitrarily good precision, and present a simple greedy algorithm that delivers a solution with a value of at least 1/2 times the value of an optimal solution.
References
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Proceedings ArticleDOI
Online interval scheduling
TL;DR: The online interval scheduling problem, in which a set of intervals of the positive real line is presented to a scheduling algorithm in order of start time, is introduced and an algorithm with competitive factor O((log A)l+E), and it is shown that no O(logA)-competitive algorithm can exist.
Journal ArticleDOI
On chain and antichain families of a partially ordered set
TL;DR: A common generalization of the theorems of Greene and Greene and Kleitman yields some insight into the relation of optimal chain and antichain families of a partially ordered set.
Book ChapterDOI
On the k-Coloring of Intervals
TL;DR: An O(k+n) time algorithm is provided for k-coloring a maximum cardinality subset of the intervals of k colors, which provides improved solutions to problems of local register allocation, task scheduling, and the routing of nets on a chip.
Journal ArticleDOI
The k-track assignment problem
Peter Brucker,L. Nordmann +1 more
TL;DR: It is shown that the more general problem, in which for each track only a given set of jobs can be scheduled on that track, can be solved inO(nkk!kk)-time.