Online Vector Scheduling and Generalized Load Balancing

Abstract

We give a polynomial time reduction from vector scheduling problem (VS) to generalized load balancing problem (GLB). This reduction gives the first non-trivial online algorithm for VS where vectors come in an online fashion. The online algorithm is very simple in that each vector only needs to minimize the $L_{\ln (md)}$ norm of the resulting load when it comes, where $m$ is the number of partitions and $d$ is the dimension of vectors. It has an approximation bound of $e\log (md)$, which is in $O(\ln (md))$, so it also improves the $O({\ln }^{2}d)$ bound of the existing polynomial time algorithm for VS. Additionally, the reduction shows that GLB does not have constant approximation algorithms that run in polynomial time unless $P=NP$.

arXiv commentThis work has been accepted to JPDC. Please refer to http://dx.doi.org/10.1016/j.jpdc.2013.12.006

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• Online Vector Scheduling and Generalized Load Balancing