Two Algorithms for Finding $k$ Shortest Paths of a Weighted Pushdown Automaton

TL;DR

This paper presents two efficient algorithms for computing the top k shortest paths in a weighted pushdown automaton, enhancing parsing and translation tasks with minimal additional computational cost.

Contribution

It introduces two novel algorithms based on a unified deductive logic framework for WPDA pathfinding, demonstrating their efficiency and scalability.

Findings

Algorithm 2 incurs minimal overhead compared to the single shortest path algorithm

Both algorithms perform well even with large k values

Experimental results validate the efficiency of the proposed methods

Abstract

We introduce efficient algorithms for finding the $k$ shortest paths of a weighted pushdown automaton (WPDA), a compact representation of a weighted set of strings with potential applications in parsing and machine translation. Both of our algorithms are derived from the same weighted deductive logic description of the execution of a WPDA using different search strategies. Experimental results show our Algorithm 2 adds very little overhead vs. the single shortest path algorithm, even with a large $k$.