When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Approximation algorithms
Primal-dual approaches to the Steiner problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Primal-Dual-Based Algorithms for a Directed Network Design Problem
INFORMS Journal on Computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Multicast routing in multi-radio multi-channel wireless mesh networks
IEEE Transactions on Wireless Communications
Fast object detection using steiner tree
Machine Graphics & Vision International Journal
A primal-dual approximation algorithm for the vertex cover P3 problem
Theoretical Computer Science
Fast semantic object search and detection for vegetable trading information using Steiner tree
Artificial Intelligence Review
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We present new primal-dual algorithms for several network design problems. The problems considered are the generalized Steiner tree problem (GST), the directed Steiner tree problem (DST), and the set cover problem (SC) which is a subcase of DST. All our problems are NP-hard; so we are interested in their approximation algorithms. First, we give an algorithm for DST which is based on the traditional approach of designing primal-dual approximation algorithms. We show that the approximation factor of the algorithm is k, where k is the number of terminals, in the case when the problem is restricted to quasi-bipartite graphs. We also give pathologically bad examples for the algorithm performance. To overcome the problems exposed by the bad examples, we design a new framework for primal-dual algorithms which can be applied to all of our problems. The main feature of the new approach is that, unlike the traditional primal-dual algorithms, it keeps the dual solution in the interior of the dual feasible region. The new approach allows us to avoid including too many arcs in the solution, and thus achieves a smaller-cost solution. Our computational results show that the interior-point version of the primal-dual most of the time performs better than the original primal-dual method.