Shortest Paths with Ordinal Weights

TL;DR

This paper studies shortest path problems in acyclic graphs with ordinal weights, introducing concepts of dominance and efficiency, and provides a polynomial-time algorithm to find all non-dominated paths.

Contribution

It defines ordinal dominance and efficiency, proves polynomial bounds on non-dominated paths, and develops a polynomial-time algorithm for finding these paths.

Findings

Number of non-dominated paths is polynomially bounded.

Proposed a polynomial-time labeling algorithm.

Established concepts of ordinal dominance and efficiency.

Abstract

We investigate the single-source-single-destination "shortest" paths problem in acyclic graphs with ordinal weighted arc costs. We define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels, respectively. Further, we show that the number of ordinally non-dominated paths vectors from the source node to every other node in the graph is polynomially bounded and we propose a polynomial time labeling algorithm for solving the problem of finding the set of ordinally non-dominated paths vectors from source to sink.