An approximation algorithm for the covering Steiner problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
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
Service-constrained network design problems
Nordic Journal of Computing
Local search algorithms for the k-cardinality tree problem
Discrete Applied Mathematics
The complexity of minimizing certain cost metrics for k-source spanning trees
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
The non-approximability of bicriteria network design problems
Journal of Discrete Algorithms
Multi-source spanning trees: algorithms for minimizing source eccentricities
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
On network design problems: fixed cost flows and the covering steiner problem
ACM Transactions on Algorithms (TALG)
A new hybrid evolutionary algorithm for the huge k-cardinality tree problem
Proceedings of the 8th annual conference on Genetic and evolutionary computation
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)
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
The complexity of minimizing certain cost metrics for k-source spanning trees
Discrete Applied Mathematics
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)
Approximation algorithms for 2-source minimum routing cost k-tree problems
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
The k-Cardinality Tree Problem: Reformulations and Lagrangian Relaxation
Discrete Applied Mathematics
An approximate solution method based on tabu search for k-minimum spanning tree problems
International Journal of Knowledge Engineering and Soft Data Paradigms
Algorithms and theory of computation handbook
A General Approach for Incremental Approximation and Hierarchical Clustering
SIAM Journal on Computing
Expert Systems with Applications: An International Journal
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Multi-source trees: algorithms for minimizing eccentricity cost metrics
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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 approximations for buy-at-bulk and shallow-light k-steiner trees and (k,2)-subgraph
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Operations Research Letters
Improved approximation algorithms for (budgeted) node-weighted steiner problems
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The density maximization problem in graphs
Journal of Combinatorial Optimization
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We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of treewidth-bounded graphs, which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees and, more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.