Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Wheel inequalities for stable set polytopes
Mathematical Programming: Series A and B
Problems of discrete optimization: Challenges and main approaches to solve them
Cybernetics and Systems Analysis
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Upper bounds for the weighted stability number of a graph are considered that are based on the approximation of its stable set polytope by linear inequalities for odd cycles and p-wheels in the graph. Algorithms are developed for finding upper bounds on the basis of solution of LP problems with a finite number of inequalities produced by the shortest path algorithm for a special graph. The results of test experiments are given for graphs with several hundred or thousand vertices.