Abstract
We study the problem of (off-line) broadcast scheduling in minimizing total flow time and propose a dynamic programming approach to compute an optimal broadcast schedule. Suppose the broadcast server has k pages and the last page request arrives at time n. The optimal schedule can be computed in O(k3(n+k)k−1) time for the case that the server has a single broadcast channel. For m channels case, i.e., the server can broadcast m different pages at a time where m < k, the optimal schedule can be computed in O(nk−m) time when k and m are constants. Note that this broadcast scheduling problem is NP-hard when k is a variable and will take O(nk−m+1) time when k is fixed and m ≥ 1 with the straightforward implementation of the dynamic programming approach.
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The preliminary version of this paper appeared in Proceedings of the 11th Annual International Computing and Combinatorics Conference as “Off-line Algorithms for Minimizing the Total Flow Time in Broadcast Scheduling”.
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Chan, WT., Chin, F.Y.L., Zhang, Y. et al. A dynamic programming approach of finding an optimal broadcast schedule in minimizing total flow time. J Comb Optim 11, 177–187 (2006). https://doi.org/10.1007/s10878-006-7128-7
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DOI: https://doi.org/10.1007/s10878-006-7128-7