**Preprint series:**
08-07 , Reports on Computer Science

**MSC:**- 90C27 Combinatorial optimization
- 68W25 Approximation algorithms
- 90C35 Programming involving graphs or networks [See also 90C27]

**Abstract:** We consider the following optimization problem: Given an instance of an optimization problem and some optimum solution for this instance, we want to find a good solution for a slightly modified instance. Additionally, the scenario is adressed where the solution for the original instance is not an arbitrary optimum solution, but is chosen among all optimum solutions in a most helpful way. In this context, we examine reoptimization of the travelling salesperson problem (MinTSP and MaxTSP as well as their metric versions) and the Steiner tree problem (MinST). We study the case where the weight of a single edge is modified. Our main results are the following: existence of a 4/3-approximation for the metric MinTSP, a 5/4-approximation for MaxTSP, and a PTAS for the metric version of MaxTSP. Regarding the problem MinST, we give similar positive results and show nonexistence of an FPTAS.

**Keywords:** *reoptimization, TSP, Steiner tree, innapproximability*

**Upload:** 2008-07-31

The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.