New approximations for broadcast scheduling via variants of α-point rounding

Abstract

We revisit the pull-based broadcast scheduling model. In this model, there are n unit-sized pages of information available at the server. Clients send their requests to the server over time asking for specific pages. The server can transmit only one page at each time. When the server transmits a page, all outstanding requests for the page are simultaneously satisfied, and this is what distinguishes broadcast scheduling from the standard scheduling setting where each job must be processed separately by the server. Broadcast scheduling has received a considerable amount of attention due to the algorithmic challenges that it gives in addition to its applications in multicast systems and wireless and LAN networks. In this paper, we give the following new approximation results for two popular objectives: For the objective of minimizing the maximum flow time, we give the first PTAS. Previously, it was known that the algorithm First-In-First-Out (FIFO) is a 2-approximation, and it is tight [14, 16]. It has been suggested as an open problem to obtain a better approximation f 14, 4, 25, 31]. For the objective of maximizing the throughput, we give a 0.7759-approximation which improves upon the previous best known 0.75-approximation [23]. Our key techniques for these improvements are novel variants of α-point rounding that can effectively reduce congestion in schedule which is often the main hurdle in designing scheduling algorithms based on linear programming. We believe that our new rounding schemes could be of potential use for other scheduling problems.