Greedy MAXCUT Algorithms and their Information Content

TL;DR

This paper investigates the robustness of greedy MAXCUT algorithms to noise in input data by measuring their information content using approximation set coding, providing insights for algorithm design in noisy environments.

Contribution

It introduces a novel method to exactly measure the information content of greedy MAXCUT algorithms under noise, enhancing understanding of their robustness and guiding future algorithm development.

Findings

Greedy MAXCUT algorithms exhibit varying robustness to noise.

Approximation set cardinality correlates with algorithm robustness.

Insights can inform the design of more noise-resilient algorithms.

Abstract

MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning, computer vision and statistical physics. Greedy algorithms to approximately solve MAXCUT rely on greedy vertex labelling or on an edge contraction strategy. These algorithms have been studied by measuring their approximation ratios in the worst case setting but very little is known to characterize their robustness to noise contaminations of the input data in the average case. Adapting the framework of Approximation Set Coding, we present a method to exactly measure the cardinality of the algorithmic approximation sets of five greedy MAXCUT algorithms. Their information contents are explored for graph instances generated by two different noise models: the edge reversal model and Gaussian edge weights model. The results provide insights into the robustness of different greedy heuristics and techniques for MAXCUT, which can be used for algorithm design of general USM problems.