# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, June 17, 2004, 12:15 pm

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

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

**Speaker**: Stefano Tessaro

## Fast Integer Programming in Fixed Dimension

The integer programming problem is known to be NP-hard. However, if the dimension is considered to be constant, a well known algorithm by H.W. Lenstra requires *O(m φ + φ*^{2}) arithmetic operations on rational numbers of size *O(φ)*, where φ is the facet complexity of the integer program, and m the number of constraints.

In this talk, a new algorithm by Friedrich Eisenbrand for the special case where additionally the number of constraints is also constant is presented. This algorithm performs *O(s)* arithmetic operations on rational number with size bounded by *O(s)*, where s is the size of the integer program. Moreover, even in the case where the number of constraints *m* is not a constant, this new algorithm can be used to obtain a Las Vegas algorithm for integer programming in fixed dimension which requires an expected number of *O(m + φ log m)* arithmetic operations on rational number of size *O(φ)*, outperforming Lenstra's algorithm in expectation.

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