The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A faster algorithm for the steiner tree problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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
Reoptimization of the Shortest Common Superstring Problem
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Reoptimization of the metric deadline TSP
Journal of Discrete Algorithms
Fast approximation in subspaces by doubling metric decomposition
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Knowing all optimal solutions does not help for TSP reoptimization
Computation, cooperation, and life
Steiner tree reoptimization in graphs with sharpened triangle inequality
Journal of Discrete Algorithms
The steiner tree reoptimization problem with sharpened triangle inequality
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Reoptimization of the maximum weighted Pk-free subgraph problem under vertex insertion
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Reoptimization of some maximum weight induced hereditary subgraph problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
On the Hardness of Reoptimization with Multiple Given Solutions
Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
Reoptimizing the strengthened metric TSP on multiple edge weight modifications
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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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Given an instance of the Steiner tree problem together with an optimal solution, we consider the scenario where this instance is modified locally by adding one of the vertices to the terminal set or removing one vertex from it. In this paper, we investigate the problem of whether the knowledge of an optimal solution to the unaltered instance can help in solving the locally modified instance. Our results are as follows: (i) We prove that these reoptimization variants of the Steiner tree problem are NP-hard, even if edge costs are restricted to values from {1,2}. (ii) We design 1.5-approximation algorithms for both variants of local modifications. This is an improvement over the currently best known approximation algorithm for the classical Steiner tree problem which achieves an approximation ratio of 1+ln(3)/2~1.55. (iii) We present a PTAS for the subproblem in which the edge costs are natural numbers {1,...,k} for some constant k.