I/O-Efficient Algorithms for Contour Line Extraction and Planar Graph Blocking

For a polyhedral terrain C, the contour at z-coordinate h, denoted Ch, is defined to be the intersection of the plane z = h with C. In this paper, we study the contour-line extraction problem, where we want to preprocess C into a data structure so that given a query z-coordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINS). We present an I/O-optimal algorithm for this problem which stores a terrain C with N vertices using O(N/B) blocks, where B is the size of a disk block, so that for any query h, the contour ch can be computed using o(log, N + I&l/B) I/O operations, where l&l denotes the size of Ch. We also present en improved algorithm for a more general problem of blocking bounded-degree planar graphs such as TINS (i.e., storing them on disk so that any graph traversal algorithm can traverse the graph in an I/O-efficient manner), and apply it to two problms that arise in GIS

04301 Abstracts Collection -- Cache-Oblivious and Cache-Aware Algorithms

The Dagstuhl Seminar 04301 ``Cache-Oblivious and Cache-Aware Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl, from 18.07.2004 to 23.07.2004. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

External-Memory Graph Algorithms

We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we call the “proximate neighbors” problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms. Time-forward processing. We present a general technique for evaluating circuits (or “circuit-like” computations) in external memory. We also usethis in a deterministic list ranking algorithm. Deterministic 3-coloring of a cycle. We give several optimal methods for 3-coloring a cycle, which can be used as a subroutine for finding large independent sets for list ranking. Our ideas go beyond a straightforward PRAM simulation, and may be of independent interest. External depth-first search. We discuss a method for performing depth first search and solving related problems efficiently in external memory. Our technique can be used in conjunction with ideas due to Ullman and Yannakakis in order to solve graph problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold. Our techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation

Theory and Practice of I/O efficient Algorithms for Multidimensional Batched Searching Problems

Extended AbstractWe describe a powerful framework for designing efficient batch algorithms for certain large-scale dynamic problems that must be solved using external memory. The class of problems we consider, which we call colorable external decomposable problems, include rectangle intersection, orthogonal line segment intersection, range searching, and point location. We are particularly interested in these problems in two and higher dimensions. They have numerous applications in geographic information systems (GIS), spatial databases, and VLSI and CAD design. We present simplified algorithms for problems previously solved by more complicated approaches (such as rectangle intersection), and we present efficient algorithms for problems not previously solved in an efficient way (such as point location and higher dimensional versions of range searching and rectangle intersection). We give experimental results concerning the running time for our approach applied to the red-blue rectangle intersection problem, which is a key component of the extremely important database operation spatial join. Our algorithm scales well with the problem size, and for large problems sizes it greatly outperforms the well-known sweepline approach

Online Data Structures in External Memory

The original publication is available at www.springerlink.comThe data sets for many of today's computer applications are too large to t within the computer's internal memory and must instead be stored on external storage devices such as disks. A major performance bottleneck can be the input/output communication (or I/O) between the external and internal memories. In this paper we discuss a variety of online data structures for external memory, some very old and some very new, such as hashing (for dictionaries), B-trees (for dictionaries and 1-D range search), bu er trees (for batched dynamic problems), interval trees with weight-balanced B-trees (for stabbing queries), priority search trees (for 3-sided 2-D range search), and R-trees and other spatial structures. We also discuss several open problems along the way

A New Parallel Algorithm for Planarity Testing

Determining whether a graph is planar is both theoretically and practically interesting. Although several sequential algorithms have been introduced which accomplish planarity testing in O(V ) time for graphs with V vertices, very few of these have been parallelized. In a recent comparison of sequential planarity testing algorithms, the newest algorithms were found to be fastest; however, these are the ones which have not been parallelized. The goal of this thesis is to introduce a method for parallelizing one of the newest planarity testing algorithms