On-line algorithms for the dynamic traveling repair problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Reducing truth-telling online mechanisms to online optimization
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Local search algorithms for the k-cardinality tree problem
Discrete Applied Mathematics
On-Line Algorithms for the Dynamic Traveling Repair Problem
Journal of Scheduling
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithms for the on-line quota traveling salesman problem
Information Processing Letters
An online throughput-competitive algorithm for multicast routing and admission control
Journal of Algorithms
A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem
Computers and Operations Research
Near-optimal sensor placements: maximizing information while minimizing communication cost
Proceedings of the 5th international conference on Information processing in sensor networks
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
A stabilized column generation scheme for the traveling salesman subtour problem
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The online Prize-Collecting Traveling Salesman Problem
Information Processing Letters
A Constant Factor Approximation for Minimum λ-Edge-Connected k-Subgraph with Metric Costs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Networks of polynomial pieces with application to the analysis of point clouds and images
Journal of Approximation Theory
A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem
Computers and Operations Research
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Antourage: mining distance-constrained trips from flickr
Proceedings of the 19th international conference on World wide web
To fill or not to fill: the gas station problem
ESA'07 Proceedings of the 15th annual European conference on Algorithms
The k-Cardinality Tree Problem: Reformulations and Lagrangian Relaxation
Discrete Applied Mathematics
Robust sensor placements at informative and communication-efficient locations
ACM Transactions on Sensor Networks (TOSN)
To fill or not to fill: The gas station problem
ACM Transactions on Algorithms (TALG)
Exploring and triangulating a region by a swarm of robots
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Improved algorithms for orienteering and related problems
ACM Transactions on Algorithms (TALG)
Physical search problems with probabilistic knowledge
Artificial Intelligence
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We consider a formalization of the following problem. A salesperson must sell some quota of brushes in order to win a trip to Hawaii. This salesperson has a map (a weighted graph) in which each city has an attached demand specifying the number of brushes that can be sold in that city. What is the best route to take to sell the quota while traveling the least distance possible? Notice that unlike the standard traveling salesman problem, not only do we need to figure out the order in which to visit the cities, but we must decide the more fundamental question: which cities do we want to visit?In this paper we give the first approximation algorithm having a polylogarithmic performance guarantee for this problem, as well as for the slightly more general "prize-collecting traveling salesman problem" (PCTSP) of Balas, and a variation we call the "bank robber problem" (also called the "orienteering problem" by Golden, Levi, and Vohra). We do this by providing an O(log2 k) approximation to the somewhat cleaner k-MST problem which is defined as follows. Given an undirected graph on n nodes with nonnegative edge weights and an integer $k \leq n$, find the tree of least weight that spans k vertices. (If desired, one may specify in the problem a "root vertex" that must be in the tree as well.) Our result improves on the previous best bound of $O(\sqrt{k})$ of Ravi et al.