# 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.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login