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Examples of Combinatorial Problems
Abstract
Combinatorial problems are mathematical challenges that involve finding optimal solutions while satisfying specific constraints. The chapter explores various problems, including the Longest Common Subsequence (LCS), used in bioinformatics and text analysis, and clustering, which groups data based on similarities. It also covers the Minimum Spanning Tree (MST) problem, crucial for efficient networks, and the Traveling Salesman Problem (TSP), a classic optimization issue. Other problems discussed include the maximum flow in a graph, which is used for network and traffic optimization, and the maximum cut problem, which is applicable in social network analysis. The chapter also examines algorithms for maximum node independence in graphs, maximum coverage, stable matching (Gale-Shapley problem), and even soccer team formation strategies. Finally, it explores efficient algorithms for solving these problems, demonstrating their practical applications in various fields.
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