Exploring mazes at random

TL;DR

This paper analyzes a probabilistic depth-first search algorithm on mazes with two exits, demonstrating that it has an equal chance of finding either exit through a combinatorial proof.

Contribution

It introduces a probabilistic variant of depth-first search for mazes and provides a combinatorial proof of its symmetry in exit discovery.

Findings

The algorithm has equal probability of finding either exit.

A combinatorial involution proves the symmetry property.

The approach offers insights into probabilistic maze exploration.

Abstract

We consider a probabilistic version of the depth-first search on mazes with two exits, and show that this algorithm has equal probability of finding either exit. The proof is combinatorial and uses an explicit involution.