The $ k_t $ jet-finder is a widely used algorithm for identifying jets in high-energy collisions. It has been traditionally believed that its computational complexity scales as $ N^3 $, making it inefficient for high-multiplicity environments like the LHC and heavy-ion colliders. However, this paper shows that the $ k_t $ jet-finding algorithm can be implemented in $ O(N \ln N) $ time by leveraging computational geometry techniques. The key insight is that the algorithm can be reduced to finding the nearest neighbor for each particle, which can be efficiently done using Voronoi diagrams and binary trees. This approach significantly reduces the computational complexity, making the $ k_t $ jet-finder much faster than previously thought. The paper also discusses the practical implications of this improved efficiency, including the ability to handle large datasets and the potential for better jet area estimation. The results show that the $ k_t $ jet-finder is at least an order of magnitude faster than the $ N^3 $ algorithm for large $ N $, and can be used more effectively in high-multiplicity environments. The paper also introduces the Cambridge/Aachen jet-finder as an alternative that shares many of the $ k_t $ jet-finder's features and may be better suited for certain applications. Overall, the paper demonstrates that the $ k_t $ jet-finder can be implemented efficiently, opening up new possibilities for its use in high-energy physics experiments.The $ k_t $ jet-finder is a widely used algorithm for identifying jets in high-energy collisions. It has been traditionally believed that its computational complexity scales as $ N^3 $, making it inefficient for high-multiplicity environments like the LHC and heavy-ion colliders. However, this paper shows that the $ k_t $ jet-finding algorithm can be implemented in $ O(N \ln N) $ time by leveraging computational geometry techniques. The key insight is that the algorithm can be reduced to finding the nearest neighbor for each particle, which can be efficiently done using Voronoi diagrams and binary trees. This approach significantly reduces the computational complexity, making the $ k_t $ jet-finder much faster than previously thought. The paper also discusses the practical implications of this improved efficiency, including the ability to handle large datasets and the potential for better jet area estimation. The results show that the $ k_t $ jet-finder is at least an order of magnitude faster than the $ N^3 $ algorithm for large $ N $, and can be used more effectively in high-multiplicity environments. The paper also introduces the Cambridge/Aachen jet-finder as an alternative that shares many of the $ k_t $ jet-finder's features and may be better suited for certain applications. Overall, the paper demonstrates that the $ k_t $ jet-finder can be implemented efficiently, opening up new possibilities for its use in high-energy physics experiments.