# Difference between revisions of "Applied Algebra Seminar Spring 2020"

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'''Short simplex paths in lattice polytopes | '''Short simplex paths in lattice polytopes |

## Revision as of 17:13, 5 February 2020

## Contents

## Spring 2020 Schedule

date | speaker | title | host(s) |
---|---|---|---|

February 20 | Carla Michini (UW Madison) | Short simplex paths in lattice polytopes | Local |

February 27 |

## Abstracts

### Carla Michini

**Short simplex paths in lattice polytopes**

We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The length of this path is independent on m and is the best possible up to a polynomial function, since it is only polynomially far from the worst case diameter. The number of arithmetic operations needed to compute the next vertex in the path is polynomial in n, m and log k. If k is polynomially bounded by n and m, the algorithm runs in strongly polynomial time. This is a joint work with Alberto Del Pia.

## Other events to note

### Carla Michini

**Short simplex paths in lattice polytopes**

We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The length of this path is independent on m and is the best possible up to a polynomial function, since it is only polynomially far from the worst case diameter. The number of arithmetic operations needed to compute the next vertex in the path is polynomial in n, m and log k. If k is polynomially bounded by n and m, the algorithm runs in strongly polynomial time. This is a joint work with Alberto Del Pia.