# Alternation-free Sequences and Parametric Shortest Paths

Speaker:

## Time:

Friday, 25 January 2019, 17:15 to 18:15

## Venue:

• A-201 (STCS Seminar Room)

## Organisers:

Abstract: In this talk, we will see a close connection between alternation-free sequences of words over the alphabet $\mathbb{Z}_n$ and parametric shortest paths in certain graphs. Turns out, in the case of planar graphs, these are words over the alphabet $\mathbb{Z}_2$.

Also, as an application of alternation-free sequences, we will see that thin grid graphs have small parametric complexity. This shows a dichotomy between thin grids and square grids, as square grids have large parametric complexity.

This is based on joint work with Prof. J. Radhakrishnan.