NPHardness of Broadcast Scheduling and Inapproximability of SingleSource Unsplittable MinCost Flow
 Thomas Erlebach,
 Alexander Hall
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Abstract
We consider the version of broadcast scheduling where a server can transmit W messages of a given set at each timestep, answering previously made requests for these messages. The goal is to minimize the average response time (ART) if the amount of requests is known in advance for each timestep and message. We prove that this problem is NPhard, thus answering an open question stated by Kalyanasundaram, Pruhs and Velauthapillai (Proceedings of ESA 2000, LNCS 1879, 2000, pp. 290–301). Furthermore, we present an approximation algorithm that is allowed to send several messages at once. Using six channels for transmissions, the algorithm achieves an ART that is at least as good as the optimal solution using one channel.
From the NPhardness of broadcast scheduling we derive a new inapproximability result of (2 − ε, 1) for the (congestion, cost) bicriteria version of the single source unsplittable mincost flow problem, for arbitrary ε > 0. The result holds even in the often considered case where the maximum demand is less than or equal to the minimum edge capacity (d _{max} ≤ u _{min}), a case for which an algorithm with ratio (3, 1) was presented by Skutella.
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 Title
 NPHardness of Broadcast Scheduling and Inapproximability of SingleSource Unsplittable MinCost Flow
 Journal

Journal of Scheduling
Volume 7, Issue 3 , pp 223241
 Cover Date
 20040501
 DOI
 10.1023/B:JOSH.0000019682.75022.96
 Print ISSN
 10946136
 Online ISSN
 10991425
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 NPcomplete
 broadcast scheduling
 resource augmentation
 approximation algorithm
 inapproximability
 Industry Sectors
 Authors

 Thomas Erlebach ^{(1)}
 Alexander Hall ^{(1)}
 Author Affiliations

 1. Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Gloriastrasse 35, CH8092, Zurich, Switzerland