NDLI: Scheduling with conflicts: online and offline algorithms

Content Provider	Springer Nature Link
Author	Even, Guy Halldórsson, Magnús M. Kaplan, Lotem Ron, Dana
Copyright Year	2008
Abstract	We consider the following problem of scheduling with conflicts (swc): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs.Our first main positive result is an exact algorithm for two machines and job sizes in {1,2}. For jobs sizes in {1,2,3}, we can obtain a $\frac{4}{3}$ -approximation, which improves on the $\frac{3}{2}$ -approximation that was previously known for this case. Our main negative result is that for jobs sizes in {1,2,3,4}, the problem is APX-hard.Our second contribution is the initiation of the study of an online model for swc, where we present the first results in this model. Specifically, we prove a lower bound of $2-\frac{1}{m}$ on the competitive ratio of any deterministic online algorithm for m machines and unit jobs, and an upper bound of 2 when the algorithm is not restricted computationally. For three machines we can show that an efficient greedy algorithm achieves this bound. For two machines we present a more complex algorithm that achieves a competitive ratio of $2-\frac{1}{7}$ when the number of jobs is known in advance to the algorithm.
Starting Page	199
Ending Page	224
Page Count	26
File Format	PDF
ISSN	10946136
Journal	Journal of Scheduling
Volume Number	12
Issue Number	2
e-ISSN	10991425
Language	English
Publisher	Springer US
Publisher Date	2008-10-28
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Scheduling with conflicts Mutual exclusion scheduling Approximation algorithms Online algorithms Production/Logistics Artificial Intelligence (incl. Robotics) Optimization Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Management Science and Operations Research Engineering Software

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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