When trees collide: an approximation algorithm for the generalized Steiner problem on networks
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Steiner points in tree metrics don't (really) help
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The k-traveling repairman problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Orienteering and Discounted-Reward TSP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate k-Steiner forests via the Lagrangian relaxation technique with internal preprocessing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
On the k-edge-incident subgraph problem and its variants
Discrete Applied Mathematics
| Hi-index | 0.00 |
The k-forest problem is a common generalization of both the k-MST and the dense-k-subgraph problems. Formally, given a metric space on n vertices V, with m demand pairs ⊆ V × V and a “target” k≤ m, the goal is to find a minimum cost subgraph that connects at least k pairs. In this paper, we give an O(min{&sqrt;n⋅log k,&sqrt;k})-approximation algorithm for k-forest, improving on the previous best ratio of O(min {n2/3,&sqrt;m}log n) by Segev and Segev. We then apply our algsorithm for k-forest to obtain approximation algorithms for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the following: given an n point metric space with m objects each with its own source and destination, and a vehicle capable of carrying at most k objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We want that the tour be non-preemptive: that is, each object, once picked up at its source, is dropped only at its destination. We prove that an α-approximation algorithm for the k-forest problem implies an O(α⋅log2n)-approximation algorithm for Dial-a-Ride. Using our results for k-forest, we get an O(min{&sqrt;n,&sqrt;k}⋅log2 n)-approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an O(&sqrt;klog n)-approximation by Charikar and Raghavachari; our results give a different proof of a similar approximation guarantee—in fact, when the vehicle capacity k is large, we give a slight improvement on their results. The reduction from Dial-a-Ride to the k-forest problem is fairly robust, and allows us to obtain approximation algorithms (with the same guarantee) for some interesting generalizations of Dial-a-Ride.