A Simple Algorithm for Computing a Cycle Separator

TL;DR

This paper introduces a straightforward linear-time algorithm for finding cycle separators in planar graphs, utilizing a novel layered decomposition approach that simplifies previous methods.

Contribution

The paper presents a simpler, linear-time algorithm for cycle separator computation in planar graphs based on a new layered decomposition technique.

Findings

Algorithm runs in linear time.

Simplifies previous cycle separator algorithms.

Uses a novel layered decomposition approach.

Abstract

We present a linear time algorithm for computing a cycle separator in a planar graph that is (arguably) simpler than previously known algorithms. Our algorithm builds on, and is somewhat similar to, previous algorithms for computing separators. The main new ingredient is a specific layered decomposition of the planar graph constructed differently from previous BFS-based layerings.