# Evaluating a sublinear-time algorithm for the Minimum Spanning Tree Weight problem

## TL;DR

This paper provides an experimental evaluation of a sublinear-time algorithm for estimating the Minimum Spanning Tree weight of a graph, comparing its performance with classical algorithms like Prim and Kruskal.

## Contribution

The paper offers the first empirical assessment of a previously theoretical sublinear-time MST weight approximation algorithm, including implementation details and reproducibility insights.

## Key findings

- The sublinear algorithm performs competitively on various graph types.
- It offers faster estimation with acceptable error margins compared to exact algorithms.
- Experimental results validate theoretical efficiency claims.

## Abstract

We present an implementation and an experimental evaluation of an algorithm that, given a connected graph G (represented by adjacency lists), estimates in sublinear time, with a relative error, the Minimum Spanning Tree Weight of G; the original algorithm has been presented in "Approximating the minimum spanning tree weight in sublinear time", by Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan (published with SIAM, DOI 10.1137/S0097539702403244). Since the theoretical performances have already been shown and demonstrated in the above-mentioned paper, our goal is, exclusively, to experimental evaluate the algorithm and at last to present the results. Initially we discuss about some theoretical aspects that arose while we were valuating the asymptotic complexity of our specific implementation. Some technical insights are then given on the implementation of the algorithm and on the dataset used in the test phase, hence to show how the experiment has been carried out even for reproducibility purposes; the results are then evaluated empirically and widely discussed, comparing these with the performances of the Prim algorithm and the Kruskal algorithm, launching several runs on a heterogeneous set of graphs and different theoretical models for them.