Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bicriteria network design problems
Journal of Algorithms
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Generalized submodular cover problems and applications
Theoretical Computer Science
A deterministic algorithm for the cost-distance problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for constrained for constrained node weighted steiner tree problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A constant factor approximation for the single sink edge installation problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximating the Single-Sink Link-Installation Problem in Network Design
SIAM Journal on Optimization
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Minimum Restricted Diameter Spanning Trees
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
On non-uniform multicommodity buy-at-bulk network design
Proceedings of the thirty-seventh 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
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Some Network Design Problems with Node Costs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
Approximating some network design problems with node costs
Theoretical Computer Science
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We study two related network design problems with two cost functions. In the buy-at-bulk k-Steiner tree problem we are given a graph G(V,E) with a set of terminals T⊆V including a particular vertex s called the root, and an integer k ≤|T|. There are two cost functions on the edges of G, a buy cost $b:E\longrightarrow {\mathbb{R}}^+$ and a distance cost $r:E\longrightarrow {\mathbb{R}}^+$. The goal is to find a subtree H of G rooted at s with at least k terminals so that the cost ∑$_{e\in{\it H}}$b(e)+∑$_{t\in{\it T}-{\it s}}$dist(t,s) is minimize, where dist(t,s) is the distance from t to s in H with respect to the r cost. We present an O(log4n)-approximation for the buy-at-bulk k-Steiner tree problem. The second and closely related one is bicriteria approximation algorithm for Shallow-light k-Steiner trees. In the shallow-light k-Steiner tree problem we are given a graph G with edge costs b(e) and distance costs r(e) over the edges, and an integer k. Our goal is to find a minimum cost (under b-cost) k-Steiner tree such that the diameter under r-cost is at most some given bound D. We develop an (O(logn),O(log3n))-approximation algorithm for a relaxed version of Shallow-light k-Steiner tree where the solution has at least $\frac{k}{8}$ terminals. Using this we obtain an (O(log2n),O(log4n))-approximation for the shallow-light k-Steiner tree and an O(log4n)-approximation for the buy-at-bulk k-Steiner tree problem.