Reverse Line Graph Construction: The Matrix Relabeling Algorithm MARINLINGA Versus Roussopoulos's Algorithm

TL;DR

This paper introduces MARINLINGA, a new, simpler algorithm for reconstructing original graphs from line graphs, which is more time-efficient than existing methods and does not depend on Whitney's theorem.

Contribution

MARINLINGA is a novel algorithm that simplifies reverse line graph construction and improves efficiency over previous algorithms like Roussopoulos's.

Findings

MARINLINGA has a worst-case complexity of O(N^2).

MARINLINGA outperforms Roussopoulos's algorithm in time efficiency.

The algorithm does not rely on Whitney's theorem, simplifying the process.

Abstract

We propose a new algorithm MARINLINGA for reverse line graph computation, i.e., constructing the original graph from a given line graph. Based on the completely new and simpler principle of link relabeling and endnode recognition, MARINLINGA does not rely on Whitney's theorem while all previous algorithms do. MARINLINGA has a worst case complexity of O(N^2), where N denotes the number of nodes of the line graph. We demonstrate that MARINLINGA is more time-efficient compared to Roussopoulos's algorithm, which is well-known for its efficiency.