2025/06/30 by Boris Rubinstein, Rubinstein, Boris Y.
Computer Science · Engineering · Mathematics · #11P82 #Advanced Optimization Algorithms Research #Computational Geometry and Mesh Generation #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2506.23499
openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The unbounded knapsack problem can be considered as a particular case of the double partition problem that asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. In the middle of 19th century Sylvester and Cayley suggested an approach based on the variable elimination allowing a reduction of a double partition to a sum of scalar partitions. This manuscript discusses a geometric interpretation of this method and its application to the knapsack problem.