Efficiency analysis of GREEDI algorithm under delta-matroid constraints for subset selection in distributed systems

Abstract

The subject matter of the article is the efficiency analysis of greedy optimization algorithms for subset selection in distributed systems under delta-matroid constraints. The goal is to compare the performance of the classical unconstrained greedy algorithm and the GREEDI algorithm with delta-matroid constraints in terms of solution quality, computational characteristics, and scalability. The tasks to be solved are: to implement both algorithms; to perform simulations on synthetic graph datasets with sizes ranging from 10 to 100 nodes; to benchmark computational efficiency and approximation quality; to analyze the impact of delta-matroid constraints on benefit maximization and distributed execution. The methods used are: graph-based modeling, combinatorial optimization under matroid-type constraints, approximation algorithms, and distributed processing frameworks. The following results were obtained: GREEDI consistently provided higher-benefit subsets compared to the unconstrained greedy algorithm, achieving better trade-offs between execution time and solution quality; the distributed processing framework demonstrated scalability for large datasets and supported real-time responsiveness; performance advantages were more pronounced for larger graphs and higher constraint densities. Conclusions. The scientific novelty of the results obtained is as follows: 1) an experimental validation of the GREEDI algorithm under delta-matroid constraints for distributed subset selection was carried out; 2) the influence of such constraints on approximation quality and computational characteristics was quantified; 3) a scalable real-time processing approach for large graph-structured data was proposed, enabling potential applications in sensor deployment, recommendation systems, feature selection, and cache optimization.