Improved approximation algorithms for broadcast scheduling

We consider two scheduling problems in the broadcast setting. The first is that of minimizing the average response time of requests. For the offline version of this problem we give an algorithm with an approximation ratio of O(log2 (n)/ log log(n)), where n is the total number of pages. This substantially improves the previously best known approximation factor of O(√n) for the problem [3]. Our second result is for the profit maximization version of the broadcast scheduling problem. Here each request has a deadline and a profit which is obtained if the request is satisfied before its deadline. The goal is to maximize the total profit. We give an algorithm with an approximation ratio of 5/6, which improves the previously best known approximation guarantee of 3/4 for the problem [13].

[1]  Madhu Sudan,et al.  The minimum latency problem , 1994, STOC '94.

[2]  Jon M. Kleinberg,et al.  An improved approximation ratio for the minimum latency problem , 1996, SODA '96.

[3]  Bernard Chazelle,et al.  The discrepancy method - randomness and complexity , 2000 .

[4]  S. Muthukrishnan,et al.  Minimizing maximum response time in scheduling broadcasts , 2000, SODA '00.

[5]  Bala Kalyanasundaram,et al.  Scheduling Broadcasts in Wireless Networks , 2000, ESA.

[6]  Thomas Erlebach,et al.  NP-hardness of broadcast scheduling and inapproximability of single-source unsplittable min-cost flow , 2001 .

[7]  Rajiv Gandhi,et al.  Dependent rounding in bipartite graphs , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[8]  Kirk Pruhs,et al.  Broadcast scheduling: when fairness is fine , 2002, SODA '02.

[9]  Sudipto Guha,et al.  Throughput maximization of real-time scheduling with batching , 2002, SODA '02.

[10]  Thomas Erlebach,et al.  NP-Hardness of Broadcast Scheduling and Inapproximability of Single-Source Unsplittable Min-Cost Flow , 2002, SODA '02.

[11]  Satish Rao,et al.  Paths, trees, and minimum latency tours , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[12]  Jacques Carlier,et al.  Handbook of Scheduling - Algorithms, Models, and Performance Analysis , 2004 .

[13]  Maxim Sviridenko,et al.  Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee , 2004, J. Comb. Optim..

[14]  Samir Khuller,et al.  Equivalence of two linear programming relaxations for broadcast scheduling , 2004, Oper. Res. Lett..

[15]  Joseph Naor,et al.  Approximating the average response time in broadcast scheduling , 2005, SODA '05.

[16]  Kirk Pruhs,et al.  A maiden analysis of longest wait first , 2005, TALG.

[17]  Samir Khuller,et al.  A robust maximum completion time measure for scheduling , 2006, SODA '06.

[18]  Julien Robert,et al.  Pull-based data broadcast with dependencies: be fair to users, not to items , 2007, SODA '07.