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Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the S<sc>teiner</sc> T<sc>ree</sc> problem, for example, edges must be chosen to connect terminals (clients); in V<sc>ertex</sc> C<sc>over</sc>, vertices must be chosen to cover edges(More)
We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems , and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing), and contain representatives with different approximation(More)
Real-world networks often need to be designed under uncertainty , with only partial information and predictions of demand available at the outset of the design process. The field of stochastic optimization deals with such problems where the forecasts are specified in terms of probability distributions of future data. In this paper, we broaden the set of(More)
We provide constant factor approximation algorithms for covering the nodes of a graph using trees (rooted or unrooted), under the objective function of minimizing the weight of the maximum weight tree, subject to an upper bound on the number of trees used. These problems are related to location routing and traveling salesperson problems. with the title "(More)
Consider the following classical network design problem: a set of terminals <i>T</i> &equals; &lcub;<i>t<sub>i</sub></i>&rcub; wishes to send traffic to a root <i>r</i> in an <i>n</i>-node graph <i>G</i> &equals; (<i>V</i>, <i>E</i>). Each terminal <i>t<sub>i</sub></i> sends <i>d<sub>i</sub></i> units of traffic and enough bandwidth has to be allocated on(More)
The field of stochastic optimization studies decision making under uncertainty, when only probabilistic information about the future is available. Finding approximate solutions to well-studied optimization problems (such as Steiner tree, Vertex Cover, and Facility Location, to name but a few) presents new challenges when investigated in this framework ,(More)
We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also(More)