The paper "Distance Browsing in Spatial Databases" by Gísli R. Hjaltason and Hanan Samet compares two techniques for browsing spatial objects stored in an R-tree: the conventional $k$-nearest neighbor algorithm and an incremental approach. The $k$-nearest neighbor algorithm reinvokes the algorithm for $m$ neighbors if $m > k$, potentially leading to redundant computations. In contrast, the incremental approach efficiently finds the $k+1$st neighbor without recalculating the $k$-nearest neighbors, making it useful for complex queries involving spatial proximity. The authors present a general incremental nearest neighbor algorithm applicable to hierarchical spatial data structures and adapt it to the R-tree. They compare its performance to the existing $k$-nearest neighbor algorithm for R-trees, showing that the incremental algorithm significantly outperforms the $k$-nearest neighbor algorithm for distance browsing queries. The incremental algorithm also outperforms the $k$-nearest neighbor algorithm for the R-tree in the $k$-nearest neighbor problem, although the improvement is less significant. The paper discusses the theoretical analysis of the incremental algorithm, its variants, and extensions, including the ability to find the farthest object and combine it with other spatial queries.The paper "Distance Browsing in Spatial Databases" by Gísli R. Hjaltason and Hanan Samet compares two techniques for browsing spatial objects stored in an R-tree: the conventional $k$-nearest neighbor algorithm and an incremental approach. The $k$-nearest neighbor algorithm reinvokes the algorithm for $m$ neighbors if $m > k$, potentially leading to redundant computations. In contrast, the incremental approach efficiently finds the $k+1$st neighbor without recalculating the $k$-nearest neighbors, making it useful for complex queries involving spatial proximity. The authors present a general incremental nearest neighbor algorithm applicable to hierarchical spatial data structures and adapt it to the R-tree. They compare its performance to the existing $k$-nearest neighbor algorithm for R-trees, showing that the incremental algorithm significantly outperforms the $k$-nearest neighbor algorithm for distance browsing queries. The incremental algorithm also outperforms the $k$-nearest neighbor algorithm for the R-tree in the $k$-nearest neighbor problem, although the improvement is less significant. The paper discusses the theoretical analysis of the incremental algorithm, its variants, and extensions, including the ability to find the farthest object and combine it with other spatial queries.