Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.

/pdf/multidimensional-access-methods-4jxurm5el0.pdf

Multidimensional access methods

The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R*-tree based indexing technique that supports the efficient querying of the current and projected future positions of such moving objects. The technique is capable of indexing objects moving in one-, two-, and three-dimensional space. Update algorithms enable the index to accommodate a dynamic data set, where objects may appear and disappear, and where changes occur in the anticipated positions of existing objects. A comprehensive performance study is reported.

/pdf/indexing-the-positions-of-continuously-moving-objects-3eaflrmi98.pdf

Indexing the positions of continuously moving objects

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

Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz' Focussed Dynamic A/sup */ (D/sup */) is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan faster than planning from scratch since it modifies its previous search results locally. Consequently, it has been extensively used in mobile robotics. In this article, we introduce an alternative to D/sup */ that determines the same paths and thus moves the robot in the same way but is algorithmically different. D/sup */ Lite is simple, can be rigorously analyzed, extendible in multiple ways, and is at least as efficient as D/sup */. We believe that our results will make D/sup */-like replanning methods even more popular and enable robotics researchers to adapt them to additional applications.

Fast replanning for navigation in unknown terrain

Lifelong planning A

The purpose of this paper is twofold. First, we review several basic combinatorial problems that have been stated in terms of directed hypergraphs and have been studied in the literature in the framework of different application domains. Among them, transitive closure, transitive reduction, flow and cut problems, and minimum weight traversal problems. For such problems we illustrate some of the most important algorithmic results in the context of both static and dynamic applications. Second, we address a specific dynamic problem which finds several interesting applications, especially in the framework of knowledge representation: the maintenance of minimum weight hyperpaths under hyperarc weight increases and hyperarc deletions. For such problem we provide a new efficient algorithm applicable for a wide class of hyperpath weight measures.

Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach

We show how to preprocess a set S of points in Rd into an external memory data structure that efficiently supports linear-constraint queries. Each query is in the form of a linear constraint xd?a0+?d?1i=1aixi; the data structure must report all the points of S that satisfy the constraint. This problem is called halfspace range searching in the computational geometry literature. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d=2, we present the first data structure that uses linear space and answers linear-constraint queries using an optimal number of I/Os in the worst case. For d=3, we present a near-linear-size data structure that answers queries using an optimal number of I/Os on the average. We present linear-size data structures that can answer d-dimensional linear-constraint queries (and even more general d-dimensional simplex queries) efficiently in the worst case. For the d=3 case, we also show how to obtain trade-offs between space and query time.

/pdf/efficient-searching-with-linear-constraints-3fsj4ij70s.pdf

Efficient searching with linear constraints

We show how to maintain a shortest path tree of a general directed graph G with unit edge weights and n vertices, during a sequence of edge deletions or a sequence of edge insertions, in O(n) amortized time per operation using linear space Distance queries can be answered in constant time, while shortest path queries can be answered in time linear in the length of the retrieved path These results are extended to the case of integer edge weights in [1,C], with a bound of O(Cn) amortized time per operation

Semi-Dynamic Shortest Paths and Breadth-First Search in Digraphs

The incremental maintenance of a depth-first-search tree in directed acyclic graphs

We look at the problem: Given a set $M$ of $n$ $d$-dimensional intervals, find two $d$-dimensional intervals $S$, $T$, such that all intervals in $M$ are enclosed by $S$ or by $T$, the distribution is balanced and the intervals $S$ and $T$ fulfill a geometric criterion, eg like minimum area sum Up to now no polynomial time algorithm was known for that problem We present an $O(dn\log n) + d^2 n^{2d-1})$ algorithm for finding an optimal solution

Paolo Giulio Franciosa

Papers

Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach

Efficient searching with linear constraints

Semi-Dynamic Shortest Paths and Breadth-First Search in Digraphs

The incremental maintenance of a depth-first-search tree in directed acyclic graphs

Enclosing Many Boxes by an Optimal Pair of Boxes