External Memory Planar Point Location with Fast Updates

We study dynamic planar point location in the External Memory Model or Disk Access Model (DAM). Previous work in this model achieves polylog query and polylog amortized update time. We present a data structure with O(log_B^2 N) query time and O(1/B^(1-epsilon) log_B N) amortized update time, where N is the number of segments, B the block size and epsilon is a small positive constant, under the assumption that all faces have constant size. This is a B^(1-epsilon) factor faster for updates than the fastest previous structure, and brings the cost of insertion and deletion down to subconstant amortized time for reasonable choices of N and B. Our structure solves the problem of vertical ray-shooting queries among a dynamic set of interior-disjoint line segments; this is well-known to solve dynamic planar point location for a connected subdivision of the plane with faces of constant size

Dynamic Planar Point Location in External Memory

In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in O(log_B n(log log_B n)^3)) I/Os and updates in O(log_B n(log log_B n)^2)) amortized I/Os, where n is the number of segments in the subdivision and B is the block size. This is the first dynamic data structure with almost-optimal query cost. For comparison all previously known results for this problem require O(log_B^2 n) I/Os to answer queries. Our result almost matches the best known upper bound in the internal-memory model

Dynamic Planar Orthogonal Point Location in Sublogarithmic Time

We study a longstanding problem in computational geometry: dynamic 2-d orthogonal point location, i.e., vertical ray shooting among n horizontal line segments. We present a data structure achieving O(log n / log log n) optimal expected query time and O(log^{1/2+epsilon} n) update time (amortized) in the word-RAM model for any constant epsilon>0, under the assumption that the x-coordinates are integers bounded polynomially in n. This substantially improves previous results of Giyora and Kaplan [SODA 2007] and Blelloch [SODA 2008] with O(log n) query and update time, and of Nekrich (2010) with O(log n / log log n) query time and O(log^{1+epsilon} n) update time. Our result matches the best known upper bound for simpler problems such as dynamic 2-d dominance range searching. We also obtain similar bounds for orthogonal line segment intersection reporting queries, vertical ray stabbing, and vertical stabbing-max, improving previous bounds, respectively, of Blelloch [SODA 2008] and Mortensen [SODA 2003], of Tao (2014), and of Agarwal, Arge, and Yi [SODA 2005] and Nekrich [ISAAC 2011]

Parallel Write-Efficient Algorithms and Data Structures for Computational Geometry

In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being close to that of random access memory but writes being significantly more expensive in terms of energy and latency. We design algorithms for planar Delaunay triangulation, $k$-d trees, and static and dynamic augmented trees. Our algorithms are designed in the recently introduced Asymmetric Nested-Parallel Model, which captures the parallel setting in which there is a small symmetric memory where reads and writes are unit cost as well as a large asymmetric memory where writes are $\omega$ times more expensive than reads. In designing these algorithms, we introduce several techniques for obtaining write-efficiency, including DAG tracing, prefix doubling, reconstruction-based rebalancing and $\alpha$-labeling, which we believe will be useful for designing other parallel write-efficient algorithms

08081 Abstracts Collection -- Data Structures

From February 17th to 22nd 2008, the Dagstuhl Seminar 08081 ``Data Structures\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. It brought together 49 researchers from four continents to discuss recent developments concerning data structures in terms of research but also in terms of new technologies that impact how data can be stored, updated, and retrieved. During the seminar a fair number of participants presented their current research. There was discussion of ongoing work, and in addition an open problem session was held. This paper first describes the seminar topics and goals in general, then gives the minutes of the open problem session, and concludes with abstracts of the presentations given during the seminar. Where appropriate and available, links to extended abstracts or full papers are provided

External-Memory Computational Geometry

(c) 1993 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper we give new techniques for designing e cient algorithms for computational geometry prob- lems that are too large to be solved in internal mem- ory. We use these techniques to develop optimal and practical algorithms for a number of important large- scale problems. We discuss our algorithms primarily in the context of single processor/single disk machines, a domain in which they are not only the rst known optimal results but also of tremendous practical value. Our methods also produce the rst known optimal al- gorithms for a wide range of two-level and hierarchical multilevel memory models, including parallel models. The algorithms are optimal both in terms of I/O cost and internal computation