On Approximating a Scheduling Problem
 Pierluigi Crescenzi,
 Xiaotie Deng,
 Christos H. Papadimitriou
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Given a set of communication tasks (best described in terms of a weighted bipartite graph where one set of nodes denotes the senders, the other set the receivers, edges are communication tasks, and the weight of an edge is the time required for transmission), we wish to minimize the total time required for the completion of all communication tasks assuming that tasks can be preempted (that is, each edge can be subdivided into many edges with weights adding up to the edge's original weight) and that preemption comes with a cost. In this paper, we first prove that one cannot approximate this problem within a factor smaller than \(\frac{7}{6}\) unless P=NP. It is known that a simple approximation algorithm achieves within a ratio of two (H. Choi and S.L. Hakimi, Algorithmica, vol. 3, pp. 223–245, 1988). However, our experimental results show that its performance is worse than the originally proposed heuristic algorithm (I.S. Gopal and C.K. Wong, IEEE Transactions on Communications, vol. 33, pp. 497–501, 1985). We devise a more sophisticated algorithm, called the potential function algorithm which, on the one hand, achieves a provable approximation ratio of two, and on the other hand, shows very good experimental performance. Moreover, the way in which our more sophisticated algorithm derives from the simple one, suggests a hierarchy of algorithms, all of which have a worstcase performance at most two, but which we suspect to have increasingly better performance, both in worst case and with actual instances.
 Title
 On Approximating a Scheduling Problem
 Journal

Journal of Combinatorial Optimization
Volume 5, Issue 3 , pp 287297
 Cover Date
 200109
 DOI
 10.1023/A:1011441109660
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 parallel computation
 communication
 bipartite graph
 edge coloring
 Industry Sectors
 Authors

 Pierluigi Crescenzi ^{(1)}
 Xiaotie Deng ^{(2)}
 Christos H. Papadimitriou ^{(3)}
 Author Affiliations

 1. Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Via C. Lombroso 6/17, 50134, Firenze, Italy
 2. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong SAR, China
 3. Computer Science Division, University of California at Berkeley, Soda Hall 689, Berkeley, CA, 94720, USA