Algebraic and Combinatorial Algorithms for S-Packing Coloring

S -packing coloring is a generalization of proper coloring of graphs, introduced more than a decade ago. In this paper, we present algebraic and combinatorial algorithms for the problem of S -packing coloring of finite undirected and unweighted graphs. We assess the upper bounds for the complexity of our algorithms and of an existing algebraic algorithm by Maarouf [Electron. J. Combin. 2017]. We also provide a comparative evaluation of these algorithms.