1 research outputs found
Achieving Optimal Backlog in the Vanilla Multi-Processor Cup Game
In each step of the -processor cup game on cups, a filler distributes
up to units of water among the cups, subject only to the constraint that no
cup receives more than unit of water; an emptier then removes up to
unit of water from each of cups. Designing strategies for the emptier that
minimize backlog (i.e., the height of the fullest cup) is important for
applications in processor scheduling, buffer management in networks, quality of
service guarantees, and deamortization. We prove that the greedy algorithm
(i.e., the empty-from-fullest-cups algorithm) achieves backlog for
any . This resolves a long-standing open problem for , and is
asymptotically optimal as long as . If the filler is an oblivious
adversary, then we prove that there is a randomized emptying algorithm that
achieve backlog with probability for steps. This
is known to be asymptotically optimal when is sufficiently large relative
to . The analysis of the randomized algorithm can also be reinterpreted as a
smoothed analysis of the deterministic greedy algorithm. Previously, the only
known bound on backlog for , and the only known randomized guarantees
for any (including when ), required the use of resource
augmentation, meaning that the filler can only distribute at most units of water in each step, and that the emptier is then permitted
to remove units of water from each of cups, for some