Generalized Whac-a-Mole

We consider online competitive algorithms for the problem of collecting weighted items froma dynamic set S, when items are added to or deleted from S over time. The objective isto maximize the total weight of collected items. We study the general version, as well asvariants with various restrictions, including the following: the uniform case, when all itemshave the same weight, the decremental sets, when all items are present at the beginning andonly deletion operations are allowed, and dynamic queues, where the dynamic set is ordered andonly its prefixes can be deleted (with no restriction on insertions). The dynamic queue case is ageneralization of bounded-delay packet scheduling (also referred to as buffer management). Wepresent several upper and lower bounds on the competitive ratio for these variants.