Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

TL;DR

This paper introduces space-efficient algorithms for identifying cut vertices, biconnected components, and recognizing outerplanar graphs in linear or near-linear time with minimal memory usage.

Contribution

It presents novel space-efficient algorithms for graph connectivity and outerplanar graph recognition, optimizing both time and space complexity.

Findings

Linear time computation of cut vertices with minimal space

Space-efficient biconnected components algorithm

Fast recognition of outerplanar graphs using limited memory

Abstract

We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in $O(n\log \log n)$ time using $O(n)$ bits.