On the Complexity of Optimal k-Anonymity: A New Proof Based on Graph Coloring

Privacy is a complex balancing problem between risks and utility of data. K-anonymity, a fundamental model for preserving privacy, guarantees that an item cannot be differentiated from at least k-1 other items. Due to the k-anonymity is a hard problem, which means obtaining an optimal solution within a reasonable time is not possible, researchers endeavor to create near-optimal solutions. There are some researches in the literature demonstrating the NP-Hardness of achieving k-anonymity. The problems of k-dimensional perfect matching, edge partition into triangles, minimum vertex covering, and maximum k-dimensional matching with k-occurrences are some examples of NP-Complete problems commonly used for reduction to prove the NP-Hardness of k-anonymity. However, previous proofs use large alphabet size and suppress more cells causing less utility. This study presents a significant contribution by providing a new proof for the NP-Hardness of k-anonymity and enhances both the alphabet size and the number of suppressed cells. The proof is achieved by using a reduction from the graph coloring problem, which is being provided for the first time.