A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
On the minimum diameter spanning tree problem
Information Processing Letters
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
On finding a cycle basis with a shortest maximal cycle
Information Processing Letters
SIAM Journal on Discrete Mathematics
A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees
SIAM Journal on Computing
Approximation algorithms for the shortest total path length spanning tree problem
Discrete Applied Mathematics
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
Tree spanners in planar graphs
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum Restricted Diameter Spanning Trees
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Low Stretch Spanning Trees for Planar Graphs,
Low Stretch Spanning Trees for Planar Graphs,
MAD Trees and distance-hereditary graphs
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
On finding cycle bases and fundamental cycle bases with a shortest maximal cycle
Information Processing Letters
SIAM Journal on Discrete Mathematics
Tree spanners on chordal graphs: complexity and algorithms
Theoretical Computer Science
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Brief Annoucement: Distributed Swap Edges Computation for Minimum Routing Cost Spanning Trees
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Minimum cut bases in undirected networks
Discrete Applied Mathematics
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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Tree spanner problems have important applications in network design, e.g. in the telecommunications industry. Mathematically, there have been considered quite a number of max-stretch tree spanner problems and of average stretch tree spanner problems. We propose a unified notation for 20 tree spanner problems, which we investigate for graphs with general positive weights, with metric weights, and with unit weights. This covers several prominent problems of combinatorial optimization. Having this notation at hand, we can clearly identify which problems coincide. In the case of unweighted graphs, the formally 20 problems collapse to only five different problems. Moreover, our systematic notation for tree spanner problems enables us to identify a tree spanner problem whose complexity status has not been solved so far. We are able to provide an NP-hardness proof. Furthermore, due to our new notation of tree spanner problems, we are able to detect that an inapproximability result that is due to Galbiati [On min-max cycle bases, in: P. Eades, T. Takaoka (Eds.), ISAAC, Lecture Notes in Computer Science, vol. 2223, Springer, Berlin, 2001, pp. 116-123; On finding cycle bases and fundamental cycle bases with a shortest maximal cycle, Inform. Process. Lett. 88(4) (2003) 155-159] in fact applies to the classical max-stretch tree spanner problem. We conclude that the inapproximability factor for this problem thus is 2-@?, instead of only 1+52~1.618 according to Peleg and Reshef [A variant of the arrow distributed directory with low average complexity, in: J. Wiedermann, P. van Emde Boas, M. Nielsen (Eds.), ICALP, Lecture Notes in Computer Science, vol. 1644, Springer, Berlin, 1999, pp. 615-624].