Amortized $\tilde{O}(|V|)$-Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

TL;DR

This paper introduces an efficient amortized algorithm with near-linear delay for listing all chordless cycles and paths in undirected graphs, significantly improving previous methods.

Contribution

The paper presents a novel amortized $ ilde{O}(|V|)$-delay algorithm for listing chordless cycles and paths, reducing complexity from quadratic to near-linear time.

Findings

Achieves $ ilde{O}(|E| + |V| imes C)$ time complexity

Provides a method for listing all chordless $st$-paths efficiently

Improves upon the classical cycle listing algorithms

Abstract

Chordless cycles are very natural structures in undirected graphs, with an important history and distinguished role in graph theory. Motivated also by previous work on the classical problem of listing cycles, we study how to list chordless cycles. The best known solution to list all the $C$ chordless cycles contained in an undirected graph $G = (V,E)$ takes $O(|E|^2 +|E|\cdot C)$ time. In this paper we provide an algorithm taking $\tilde{O}(|E| + |V |\cdot C)$ time. We also show how to obtain the same complexity for listing all the $P$ chordless $st$-paths in $G$ (where $C$ is replaced by $P$ ).