Randomized algorithms
Efficient algorithms for robustness in matroid optimization
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Increasing the weight of minimum spanning trees
Journal of Algorithms
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Edge-disjoint trees containing some given vertices in a graph
Journal of Combinatorial Theory Series B
Fastest Mixing Markov Chain on a Graph
SIAM Review
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On Budgeted Optimization Problems
SIAM Journal on Discrete Mathematics
Minimizing Effective Resistance of a Graph
SIAM Review
Design is as easy as optimization
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
IEEE Transactions on Information Theory
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We consider the class of max-min and min-max optimization problems subject to a global budget constraint. We undertake a systematic algorithmic and complexity-theoretic study of such problems, which we call design problems. Every optimization problem leads to a natural design problem. Our main result uses techniques of Freund and Schapire [Games Econom. Behav., 29 (1999), pp. 79-103] from learning theory, and its generalizations, to show that for a large class of optimization problems, the design version is as easy as the optimization version. We also observe the relationship between max-min design problems and fractional packing problems. In particular, we obtain in a systematic fashion results about the fractional packing number of Steiner trees.