Off-line algorithms for minimizing total flow time in broadcast scheduling

We study the off-line broadcast scheduling problem to minimize total (or average) flow time. Assume the server has k pages and the requests arrive at n distinct times, we give the first algorithm to find the optimal schedule for the server with a single channel, in O(k³(n + k)^k-1) time. For m-channel case, i.e., the server can broadcast m different pages at a time where m < k, we find the optimal schedule in O(n^k-m) time when k and m are constants. In the single channel case, we also give a simple linear-time approximation algorithm to minimize average flow time, which achieves an additive (k - 1)/2-approximation.