The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Scheduling with forbidden sets
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
Reoptimization of Steiner Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Reoptimization of the Metric Deadline TSP
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Reoptimization of Steiner trees: Changing the terminal set
Theoretical Computer Science
On the hardness of reoptimization
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Approximation Algorithms
Reoptimization of minimum and maximum traveling salesman's tours
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Knowing all optimal solutions does not help for TSP reoptimization
Computation, cooperation, and life
New advances in reoptimizing the minimum steiner tree problem
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Reoptimization of maximum weight induced hereditary subgraph problems
Theoretical Computer Science
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In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-triangle inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened triangle inequality (and even in graphs where edge-costs are restricted to the values 1 and 1+γ for an arbitrary small γ0), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time (1/2+β)-approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs (β=1), none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any β