The paper by Matteo Cacciari and Gavin P. Salam addresses the computational complexity of the $k_t$ jet-finder, a widely used method for identifying jets in high-energy collisions. Traditionally, the $k_t$ algorithm has been believed to scale as $N^3$, making it impractical for high-multiplicity events at colliders like the LHC and heavy-ion colliders. The authors propose a new algorithm that reduces the complexity to $N \ln N$, significantly improving its efficiency. This is achieved by reducing the computationally intensive part of the $k_t$ algorithm to finding the nearest neighbour of each particle in a dynamic set of points, a problem well-studied in computational geometry. The FastJet implementation of this algorithm is shown to run orders of magnitude faster than existing implementations, making it feasible for high-multiplicity event studies. The paper also discusses the implications of this speed improvement, including the ability to estimate jet areas more accurately and the potential for novel applications of the $k_t$ jet-finder in high-luminosity environments.The paper by Matteo Cacciari and Gavin P. Salam addresses the computational complexity of the $k_t$ jet-finder, a widely used method for identifying jets in high-energy collisions. Traditionally, the $k_t$ algorithm has been believed to scale as $N^3$, making it impractical for high-multiplicity events at colliders like the LHC and heavy-ion colliders. The authors propose a new algorithm that reduces the complexity to $N \ln N$, significantly improving its efficiency. This is achieved by reducing the computationally intensive part of the $k_t$ algorithm to finding the nearest neighbour of each particle in a dynamic set of points, a problem well-studied in computational geometry. The FastJet implementation of this algorithm is shown to run orders of magnitude faster than existing implementations, making it feasible for high-multiplicity event studies. The paper also discusses the implications of this speed improvement, including the ability to estimate jet areas more accurately and the potential for novel applications of the $k_t$ jet-finder in high-luminosity environments.