Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
An accelerated sequential algorithm for producing D-optimal designs
SIAM Journal on Scientific and Statistical Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
NetQuest: a flexible framework for large-scale network measurement
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
D-optimal design of a monitoring network for parameter estimation of distributed systems
Journal of Global Optimization
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Improving updating rules in multiplicative algorithms for computing D-optimal designs
Computational Statistics & Data Analysis
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Majorization and Matrix Monotone Functions in Wireless Communications
Majorization and Matrix Monotone Functions in Wireless Communications
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
Computing efficient exact designs of experiments using integer quadratic programming
Computational Statistics & Data Analysis
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We study a family of combinatorial optimization problems defined by a parameter p@?[0,1], which involves spectral functions applied to positive semidefinite matrices, and has some application in the theory of optimal experimental design. This family of problems tends to a generalization of the classical maximum coverage problem as p goes to 0, and to a trivial instance of the knapsack problem as p goes to 1. In this article, we establish a matrix inequality which shows that the objective function is submodular for all p@?[0,1], from which it follows that the greedy approach, which has often been used for this problem, always gives a design within 1-1/e of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors. We prove an inequality which generalizes a classical result from the theory of optimal designs, and allows us to give a rounding procedure with an approximation factor which tends to 1 as p goes to 1.