At SIGMOD 2015, an article was presented with the title “DBSCAN Revisited: Mis-Claim, Un-Fixability, and Approximation” that won the conference’s best paper award. In this technical correspondence, we want to point out some inaccuracies in the way DBSCAN was represented, and why the criticism should have been directed at the assumption about the performance of spatial index structures such as R-trees and not at an algorithm that can use such indexes. We will also discuss the relationship of DBSCAN performance and the indexability of the dataset, and discuss some heuristics for choosing appropriate DBSCAN parameters. Some indicators of bad parameters will be proposed to help guide future users of this algorithm in choosing parameters such as to obtain both meaningful results and good performance. In new experiments, we show that the new SIGMOD 2015 methods do not appear to offer practical benefits if the DBSCAN parameters are well chosen and thus they are primarily of theoretical interest. In conclusion, the original DBSCAN algorithm with effective indexes and reasonably chosen parameter values performs competitively compared to the method proposed by Gan and Tao.

DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN

Data sets in large applications are often too massive to fit completely inside the computers internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. In this article we survey the state of the art in the design and analysis of external memory (or EM) algorithms and data structures, where the goal is to exploit locality in order to reduce the I/O costs. We consider a variety of EM paradigms for solving batched and online problems efficiently in external memory. For the batched problem of sorting and related problems such as permuting and fast Fourier transform, the key paradigms include distribution and merging. The paradigm of disk striping offers an elegant way to use multiple disks in parallel. For sorting, however, disk striping can be nonoptimal with respect to I/O, so to gain further improvements we discuss distribution and merging techniques for using the disks independently. We also consider useful techniques for batched EM problems involving matrices (such as matrix multiplication and transposition), geometric data (such as finding intersections and constructing convex hulls), and graphs (such as list ranking, connected components, topological sorting, and shortest paths). In the online domain, canonical EM applications include dictionary lookup and range searching. The two important classes of indexed data structures are based upon extendible hashing and B-trees. The paradigms of filtering and bootstrapping provide a convenient means in online data structures to make effective use of the data accessed from disk. We also reexamine some of the above EM problems in slightly different settings, such as when the data items are moving, when the data items are variable-length (e.g., text strings), or when the allocated amount of internal memory can change dynamically. Programming tools and environments are available for simplifying the EM programming task. During the course of the survey, we report on some experiments in the domain of spatial databases using the TPIE system (transparent parallel I/O programming environment). The newly developed EM algorithms and data structures that incorporate the paradigms we discuss are significantly faster than methods currently used in practice.

https://users.cs.duke.edu/~reif/courses/alglectures/vitter.papers/Vit.IO_survey.pdf

External memory algorithms and data structures: dealing with massive data

Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is well investigated, collision detection for deformable objects introduces additional challenging problems. This paper focuses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields and spatial partitioning are discussed. In addition, image-space techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.

/pdf/collision-detection-for-deformable-objects-5cs8iwp1ey.pdf

Collision Detection for Deformable Objects

DORIN GHISA Riemann Zeta function is one of the most studied transcendental functions, having in view its many applications in number theory,algebra, complex analysis, statistics, as well as in physics. Another reason why this function has drawn so much attention is the celebrated Riemann conjecture regarding its non trivial zeros, which resisted proof or disproof until now. There has been lately a lot of progress in the sense of proving its truthfulness.

/pdf/the-riemann-zeta-function-3l59kypwcz.pdf

The Riemann zeta function

Computational geometry.

The query efficiency of a data structure that stores a set of objects, can normally be assessed by analysing the number of objects, pointers etc. looked at when answering a query. However, if the data structure is too big to fit in main memory, data may need to be fetched from disk. In that case, the query efficiency is easily dominated by moving the disk head to the correct locations, rather than by reading the data itself.

To reduce the number of disk accesses, once can group the data into blocks, and strive to bound the number of different blocks accessed rather than the number of individual data objects read. An R-tree is a general-purpose data structur that stores a hierarchical grouping of geometric objects into blocks. Many heuristics have been designed to determine which objects should be grouped together, but none of these heuristics could give a guarantee on the resulting worst-case query time.

We present the Priority R-tree, or PR-tree, which is the first R-tree variant that always answers a window query by accessing $O((N/B)^{1-1/d} + T/B)$ blocks, where $N$ is the number of $d$-dimensional objects stored, $B$ is the number of objects per block, and $T$ is the number of objects whose bounding boxes intersect the query window. This is provably asymptotically optimal. Experiments show that the PR-tree performs similar to the best known heuristics on real-life and relatively nicely distributed data, but outperforms them significantly on more extreme data.

The Priority R-Tree: A Practically Efficient and Worst-Case-Optimal R-Tree

We present the Priority R-tree, or PR-tree, which is the first R-tree variant that always answers a window query using O((N/B)11/d + T/B) I/Os, where N is the number of d-dimensional (hyper-) rectangles stored in the R-tree, B is the disk block size, and T is the output size. This is provably asymptotically optimal and significantly better than other R-tree variants, where a query may visit all N/B leaves in the tree even when T = 0. We also present an extensive experimental study of the practical performance of the PR-tree using both real-life and synthetic data. This study shows that the PR-tree performs similar to the best known R-tree variants on real-life and relatively nicely distributed data, but outperforms them significantly on more extreme data.

/pdf/the-priority-r-tree-a-practically-efficient-and-worst-case-1ajy6wpr66.pdf

The Priority R-tree: a practically efficient and worst-case optimal R-tree

We present the priority R-tree, or PR-tree, which is the first R-tree variant that always answers a window query using O((N/B)1−1/dpT/B) I/Os, where N is the number of d-dimensional (hyper-) rectangles stored in the R-tree, B is the disk block size, and T is the output size. This is provably asymptotically optimal and significantly better than other R-tree variants, where a query may visit all N/B leaves in the tree even when T = 0. We also present an extensive experimental study of the practical performance of the PR-tree using both real-life and synthetic data. This study shows that the PR-tree performs similarly to the best-known R-tree variants on real-life and relatively nicely distributed data, but outperforms them significantly on more extreme data.

The priority R-tree: A practically efficient and worst-case optimal R-tree

A box-tree is a \ifasci so-called \emph{bounding-volume hierarchy} \else bounding-volume hierarchy \fi that uses axis-aligned boxes as bounding volumes The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity

/pdf/box-trees-and-r-trees-with-near-optimal-query-time-1h3qkwsar7.pdf

Box-trees and R-trees with near-optimal query time

Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different space-filling curves are for this purpose. We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large class of space-filling curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and the bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with relatively bad locality by Gotsman and Lindenbaum's measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality.

Herman Haverkort

Papers

The Priority R-Tree: A Practically Efficient and Worst-Case-Optimal R-Tree

The Priority R-tree: a practically efficient and worst-case optimal R-tree

The priority R-tree: A practically efficient and worst-case optimal R-tree

Box-trees and R-trees with near-optimal query time

Locality and bounding-box quality of two-dimensional space-filling curves