On The Diameter of Pancake Graphs

TL;DR

This paper investigates the diameter of pancake graphs, which represent permutations with prefix reversals, and introduces a graph-theoretic approach to improve upper bounds on this diameter.

Contribution

It proposes a novel graph-theoretic method to derive tighter upper bounds for the diameter of pancake graphs, moving away from algebraic techniques.

Findings

New upper bounds for the diameter of pancake graphs

Method focuses on graph theoretical concepts rather than algebra

Potential for more efficient permutation routing algorithms

Abstract

The Pancake graph($P_n$) represents the group of all permutations on n elements, namely $S_n$, with respect to the generating set containing all prefix reversals. The diameter of a graph is the maximum of all distances on the graph, where the distance between two vertices is the shortest path between them. In the case of the $P_n$, it is the maximum of the shortest generating sequence of each permutation in $S_n$. Here we propose a method to realise better upper bounds to the diameter of $P_n$ that has its focus on Graph Theoretical concepts rather than Algebra.