# Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, December 18, 2008, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Zhen Hao (Univ. Heidelberg, Research Group Combinatorial Optimization)

## Construction of a PTAS for the Steiner tree problem with neighborhoods in the plane

To find a shortest Steiner tree S* (with length L*) which connects a given set R of mutually
disjoint, connected polygons is an NP-hard problem, called the geometric SMTN problem.

We show that we can construct a "near-optimal" Steiner tree S in polynomial running time:
for a given ε > 0 we construct a PTAS (polynomial-time approximation scheme) which
computes a Steiner tree S, where S connects R and has length L <= (1 + ε)L*.

The algorithm is based on a subdivision method called m-guillotine method, originally
developed by J.S.B. Mitchell in 1996.

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