Modelling the Eulerian Path Problem using a String Matching Framework

TL;DR

This paper models the Eulerian path problem within a string matching framework and introduces a polynomial-time algorithm for a generalized variant, expanding understanding of related computational problems.

Contribution

It presents the first polynomial-time algorithm for the (2,1)-STRING-MATCH problem, a generalization of the Eulerian path problem, with bounds of Omega(n) and O(n^2).

Findings

Polynomial-time algorithm for (2,1)-STRING-MATCH problem

Lower bound of Omega(n) established

Upper bound of O(n^2) established

Abstract

The well-known Eulerian path problem can be solved in polynomial time (more exactly, there exists a linear time algorithm for this problem). In this paper, we model the problem using a string matching framework, and then initiate an algorithmic study on a variant of this problem, called the (2,1)-STRING-MATCH problem (which is actually a generalization of the Eulerian path problem). Then, we present a polynomial-time algorithm for the (2,1)-STRING-MATCH problem, which is the most important result of this paper. Specifically, we get a lower bound of Omega(n), and an upper bound of O(n^{2}).