Space-Efficient Hierholzer for Undirected Graphs

2026-08-19

AI Summary

本文提出了一种线性时间算法，使用O(n)空间解决了无向多重图中欧拉回路的高效输出问题，填补了之前方法在无向图上的空白。

Abstract

We present a simple linear-time algorithm that outputs an Eulerian tour of an undirected multigraph with $n$ vertices and $m$ edges, if one exists, in $O(m)$ time and using $O(n)$ words of working memory. The input is given as read-only adjacency lists, and the output is written to an append-only stream in traversal order. Our algorithm first finds a sparse spanning circuit (a skeleton), then traverses the circuit step-by-step, repeatedly outputting further circuits rooted at the current vertex. This solves a problem left open by Ismaili Alaoui, Plump, and Wild (SOSA 2026): their space-efficient variant of Hierholzer's algorithm handles general directed multigraphs, but it is unclear how to generalize it to general undirected multigraphs. Our result completes the picture in the read-only model for space-efficient output of Eulerian tours.

Problem

• Eulerian tour
• undirected multigraphs
• space-efficient

Innovation

• Eulerian tour
• space-efficient
• undirected multigraphs
• sparse spanning circuit