Abstract
We consider online algorithms for pull-based broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, namely maximum response time (waiting time) and maximum delay-factor and their weighted versions. We obtain the following results in the worst-case online competitive model.
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We show that FIFO (first-in first-out) is 2-competitive even when the page sizes are different. Previously this was known only for unit-sized pages [10] via a delicate argument. Our proof differs from [10] and is perhaps more intuitive.
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We give an online algorithm for maximum delay-factor that is O(1/ε 2)-competitive with (1 + ε)-speed for unit-sized pages and with (2 + ε)-speed for different sized pages. This improves on the algorithm in [13] which required (2 + ε)-speed and (4 + ε)-speed respectively. In addition we show that the algorithm and analysis can be extended to obtain the same results for maximum weighted response time and delay factor.
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We show that a natural greedy algorithm modeled after LWF (Longest-Wait-First) is not O(1)-competitive for maximum delay factor with any constant speed even in the setting of standard scheduling with unit-sized jobs. This complements our upper bound and demonstrates the importance of the tradeoff made in our algorithm.
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Chekuri, C., Im, S., Moseley, B. (2009). Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_40
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DOI: https://doi.org/10.1007/978-3-642-04128-0_40
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