Vector assignment problems: a general framework
Journal of Algorithms
On Multidimensional Packing Problems
SIAM Journal on Computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Better bounds for online load balancing on unrelated machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing a practical access point association protocol
INFOCOM'10 Proceedings of the 29th conference on Information communications
SmartAssoc: Decentralized Access Point Selection Algorithm to Improve Throughput
IEEE Transactions on Parallel and Distributed Systems
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We give a polynomial time reduction from the vector scheduling problem (VS) to the 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"l"n"("m"d") 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 elog(md), which is in O(ln(md)), so it also improves the O(ln^2d) 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.