# Theoretical and Experimental Analysis of the Canadian Traveler Problem

## TL;DR

This paper provides a comprehensive theoretical and experimental analysis of the Canadian Traveler Problem, introducing a new variant with dependencies, and proposing an optimal algorithm that outperforms existing methods.

## Contribution

It introduces Dep-CTP with dependencies, proves its intractability, and develops Gen-PAO, an optimal algorithm for multiple CTP variants with improved performance.

## Key findings

- Dep-CTP is intractable.
- Gen-PAO solves multiple CTP variants optimally.
- Pruning methods improve search efficiency.

## Abstract

Devising an optimal strategy for navigation in a partially observable environment is one of the key objectives in AI. One of the problem in this context is the Canadian Traveler Problem (CTP). CTP is a navigation problem where an agent is tasked to travel from source to target in a partially observable weighted graph, whose edge might be blocked with a certain probability and observing such blockage occurs only when reaching upon one of the edges end points. The goal is to find a strategy that minimizes the expected travel cost. The problem is known to be P$\#$ hard. In this work we study the CTP theoretically and empirically. First, we study the Dep-CTP, a CTP variant we introduce which assumes dependencies between the edges status. We show that Dep-CTP is intractable, and further we analyze two of its subclasses on disjoint paths graph. Second, we develop a general algorithm Gen-PAO that optimally solve the CTP. Gen-PAO is capable of solving two other types of CTP called Sensing-CTP and Expensive-Edges CTP. Since the CTP is intractable, Gen-PAO use some pruning methods to reduce the space search for the optimal solution. We also define some variants of Gen-PAO, compare their performance and show some benefits of Gen-PAO over existing work.