Algorithms For Longest Chains In Pseudo- Transitive Graphs

TL;DR

This paper introduces algorithms for finding the longest chains in pseudo-transitive directed acyclic graphs, with applications in geometry that unify and enhance previous results.

Contribution

It presents new algorithms for longest chain computation in pseudo-transitive graphs and demonstrates their geometric applications, improving upon prior results.

Findings

Algorithms efficiently compute longest chains in pseudo-transitive graphs.

Applications unify and improve previous geometric results.

Demonstrates practical relevance in geometric contexts.

Abstract

A directed acyclic graph G = (V, E) is pseudo-transitive with respect to a given subset of edges E1, if for any edge ab in E1 and any edge bc in E, we have ac in E. We give algorithms for computing longest chains and demonstrate geometric applications that unify and improves some important past results. (For specific applications see the introduction.)