Interleaved prefetching

We consider the problem of interleaving sequences of positive and negative numbers in order to maximize the minimum, over all prefixes p of the interleaved sequence, of the sum of the numbers in p. A simple and efficient offline solution is given. We also consider an online version of the problem. Under a cost model suitable for the prefetching application that motivates the problem, a strongly competitive online algorithm is given. These problems abstract two practical problems of scheduling data prefetches in a multiprogrammed or multithreaded computing environment.