Operations Research
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Stochastic analyses for online combinatorial optimization problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A simpler and better derandomization of an approximation algorithm for single source rent-or-buy
Operations Research Letters
Algorithms for the universal and a priori TSP
Operations Research Letters
Deterministic Sampling Algorithms for Network Design
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved lower bounds for the universal and a priori TSP
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Stochastic minimum spanning trees in euclidean spaces
Proceedings of the twenty-seventh annual symposium on Computational geometry
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
One of the interesting recent developments in the design and analysis of approximation algorithms has been in the area of algorithms for discrete stochastic optimization problems. In this domain, one is given not just one input, but rather a probability distribution over inputs, and yet the aim is to design an algorithm that has provably good worst-case performance, that is, for any probability distribution over inputs, the objective function value of the solution found by the algorithm must be within a specified factor of the optimal value. The a priori traveling salesman problem is a prime example of such a stochastic optimization problem. One starts with the standard traveling salesman problem (in which one wishes to find the shortest tour through a given set of points N), and then considers the possibility that only a subset A of the entire set of points is active. The active set is given probabilistically; that is, there is a probability distribution over the subsets of N, which is given as part of the input. The aim is still to compute a tour through all points in N, but in order to evaluate its cost, we instead compute the expectation of the length of this tour after shortcutting it to include only those points in the active set A (where the expectation is computed with respect to the given probability distribution). The goal is to compute a "master tour" for which this expectation is minimized. This problem was introduced in the doctoral theses of Jaillet and Bertsimas, who gave asymptotic analyses when the distances between points in the input set are also given probabilistically. In this paper, we restrict attention to the so-called "independent activation" model in which we assume that each point j is active with a given probability pj, and that these independent random events. For this setting, we give a 8-approximation algorithm, a polynomial-time algorithm that computes a tour whose a priori TSP objective function value is guaranteed to be within a factor of 8 of optimal (and a randomized 4-approximation algorithm, which produces a tour of expected cost within a factor of 4 of optimal). This is the first constant approximation algorithm for this model.