Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Adaptivity and approximation for stochastic packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Resource allocation algorithms for virtualized service hosting platforms
Journal of Parallel and Distributed Computing
SIAM Journal on Computing
Mixed-criticality scheduling of sporadic task systems
ESA'11 Proceedings of the 19th European conference on Algorithms
Journal of Discrete Algorithms
Vector bin packing with multiple-choice
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Stochastic covering and adaptivity
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Vector bin packing with multiple-choice
Discrete Applied Mathematics
scc: cluster storage provisioning informed by application characteristics and SLAs
FAST'12 Proceedings of the 10th USENIX conference on File and Storage Technologies
Approximation algorithms for dynamic resource allocation
Operations Research Letters
Efficient submodular function maximization under linear packing constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating the min-max (regret) selecting items problem
Information Processing Letters
Partitioning sporadic task systems upon memory-constrained multiprocessors
ACM Transactions on Embedded Computing Systems (TECS)
A multi-resource load balancing algorithm for cloud cache systems
Proceedings of the 28th Annual ACM Symposium on Applied Computing
Tight bounds for online vector bin packing
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Scheduling jobs with multiple non-uniform tasks
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
Research note: Online vector scheduling and generalized load balancing
Journal of Parallel and Distributed Computing
Mixed-criticality scheduling on multiprocessors
Real-Time Systems
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We study the approximability of multidimensional generalizations of three classical packing problems: multiprocessor scheduling, bin packing, and the knapsack problem. Specifically, we study the vector scheduling problem, its dual problem, namely, the vector bin packing problem, and a class of packing integer programs. The vector scheduling problem is to schedule n d-dimensional tasks on m machines such that the maximum load over all dimensions and all machines is minimized. The vector bin packing problem, on the other hand, seeks to minimize the number of bins needed to schedule all n tasks such that the maximum load on any dimension across all bins is bounded by a fixed quantity, say, 1. Such problems naturally arise when scheduling tasks that have multiple resource requirements. Finally, packing integer programs capture a core problem that directly relates to both vector scheduling and vector bin packing, namely, the problem of packing a maximum number of vectors in a single bin of unit height. We obtain a variety of new algorithmic as well as inapproximability results for these three problems.