Polynomially Correlated Knapsack is NP-complete
Chinmay Karande
TL;DR
This paper proves that the 0-1 Knapsack problem remains NP-complete even when weights and values are polynomially correlated, specifically when values are integral powers of weights, highlighting the problem's computational difficulty under these conditions.
Contribution
It establishes NP-completeness of 0-1 Knapsack under new polynomial correlation constraints between weights and values.
Findings
NP-completeness holds with weights and values as powers of each other
The problem remains computationally hard under these specific conditions
Extends understanding of complexity in constrained knapsack variants
Abstract
0-1 Knapsack is a fundamental NP-complete problem. In this article we prove that it remains NP-complete even when the weights of the objects in the packing constraints and their values in the objective function satisfy specific stringent conditions: the values are integral powers of the weights of the objects.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression