The steiner problem with edge lengths 1 and 2,
Information Processing Letters
SIAM Journal on Computing
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On bounded occurrence constraint satisfaction
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
Better approximation bounds for the network and Euclidean Steiner tree problems
Better approximation bounds for the network and Euclidean Steiner tree problems
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Steiner trees in uniformly quasi-bipartite graphs
Information Processing Letters
MVSink: Incrementally Building In-Network Aggregation Trees
EWSN '09 Proceedings of the 6th European Conference on Wireless Sensor Networks
Coordinated navigation for multi-robot systems with additional constraints
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
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The Steiner tree problem asks for a shortest subgraph connecting a given set of terminals in a graph. It is known to be APX-complete, which means that no polynomial time approximation scheme can exist for this problem, unless P=NP. Currently, the best approximation algorithm for the Steiner tree problem has a performance ratio of 1.55, whereas the corresponding lower bound is smaller than 1.01. In this paper, we provide for several Steiner tree approximation algorithms lower bounds on their performance ratio that are much larger. For two algorithms that solve the Steiner tree problem on quasi-bipartite instances, we even prove lower bounds that match the upper bounds. Quasi-bipartite instances are of special interest, as currently all known lower bound reductions for the Steiner tree problem in graphs produce such instances.