We reinterpret some online greedy algorithms for a class of nonlinear "load-balancing" problems as solving a mathematical program online. For example, we consider the problem of assigning jobs to (unrelated) machines to minimize the sum of the α th -powers of the loads plus assignment costs (the online Generalized Assignment Problem); or choosing paths to connect terminal pairs to minimize the α th -powers of the edge loads (i.e., online routing with speed-scalable routers). We give analyses of these online algorithms using the dual of the primal program as a lower bound for the optimal algorithm, much in the spirit of online primal-dual results for linear problems. We then observe that a wide class of uni-processor speed scaling problems (with essentially arbitrary scheduling objectives) can be viewed as such load balancing problems with linear assignment costs. This connection gives new algorithms for problems that had resisted solutions using the dominant potential function approaches used in the speed scaling literature, as well as alternate, cleaner proofs for other known results.
Gupta et al. REF gave a primal-dual algorithm for a general class of scheduling problems with cost function f (z) = z α .
Online Primal-Dual For Non-linear Optimization with Applications to Speed Scaling
ArXiv
ArXiv
Mathematics Computer Science