The steiner problem with edge lengths 1 and 2,
Information Processing Letters
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
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
On-line algorithms for Steiner tree problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
On the approximability of the Steiner tree problem
Theoretical Computer Science - Mathematical foundations of computer science
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The greedy, the naive, and the optimal multicast routing: from theory to internet protocols
The greedy, the naive, and the optimal multicast routing: from theory to internet protocols
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs
Information and Computation
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In this paper we study a variant of the Node-Weighted Steiner Tree problem in which the weights (costs) of vertices are restricted, in the sense that the ratio of the maximum node weight to the minimum node weight is bounded by a quantity α. This problem has applications in multicast routing where the cost of participating routers must be taken into consideration and the network is relatively homogenous in terms of the cost of the routers We consider both online and offline versions of the problem. For the offline version we show an upper bound of O( min {logα, logk}) on the approximation ratio of deterministic algorithms (where k is the number of terminals). We also prove that the bound is tight unless P=NP. For the online version we show a tight bound of Θ( max { min {α, k}, logk }), which applies to both deterministic and randomized algorithms. We also show how to apply (and extend to node-weighted graphs) recent work of Alon et al. so as to obtain a randomized online algorithm with competitive ratio O(logm logk), where m is the number of the edges in the graph, independently of the value of α. All our bounds also hold for the Generalized Node-Weighted Steiner Problem, in which only connectivity between pairs of vertices must be guaranteed