68,094 research outputs found
Answering Spatial Multiple-Set Intersection Queries Using 2-3 Cuckoo Hash-Filters
We show how to answer spatial multiple-set intersection queries in O(n(log
w)/w + kt) expected time, where n is the total size of the t sets involved in
the query, w is the number of bits in a memory word, k is the output size, and
c is any fixed constant. This improves the asymptotic performance over previous
solutions and is based on an interesting data structure, known as 2-3 cuckoo
hash-filters. Our results apply in the word-RAM model (or practical RAM model),
which allows for constant-time bit-parallel operations, such as bitwise AND,
OR, NOT, and MSB (most-significant 1-bit), as exist in modern CPUs and GPUs.
Our solutions apply to any multiple-set intersection queries in spatial data
sets that can be reduced to one-dimensional range queries, such as spatial join
queries for one-dimensional points or sets of points stored along space-filling
curves, which are used in GIS applications.Comment: Full version of paper from 2017 ACM SIGSPATIAL International
Conference on Advances in Geographic Information System
Parallel Sort-Based Matching for Data Distribution Management on Shared-Memory Multiprocessors
In this paper we consider the problem of identifying intersections between
two sets of d-dimensional axis-parallel rectangles. This is a common problem
that arises in many agent-based simulation studies, and is of central
importance in the context of High Level Architecture (HLA), where it is at the
core of the Data Distribution Management (DDM) service. Several realizations of
the DDM service have been proposed; however, many of them are either
inefficient or inherently sequential. These are serious limitations since
multicore processors are now ubiquitous, and DDM algorithms -- being
CPU-intensive -- could benefit from additional computing power. We propose a
parallel version of the Sort-Based Matching algorithm for shared-memory
multiprocessors. Sort-Based Matching is one of the most efficient serial
algorithms for the DDM problem, but is quite difficult to parallelize due to
data dependencies. We describe the algorithm and compute its asymptotic running
time; we complete the analysis by assessing its performance and scalability
through extensive experiments on two commodity multicore systems based on a
dual socket Intel Xeon processor, and a single socket Intel Core i7 processor.Comment: Proceedings of the 21-th ACM/IEEE International Symposium on
Distributed Simulation and Real Time Applications (DS-RT 2017). Best Paper
Award @DS-RT 201
Coloring triangle-free rectangle overlap graphs with colors
Recently, it was proved that triangle-free intersection graphs of line
segments in the plane can have chromatic number as large as . Essentially the same construction produces -chromatic
triangle-free intersection graphs of a variety of other geometric
shapes---those belonging to any class of compact arc-connected sets in
closed under horizontal scaling, vertical scaling, and
translation, except for axis-parallel rectangles. We show that this
construction is asymptotically optimal for intersection graphs of boundaries of
axis-parallel rectangles, which can be alternatively described as overlap
graphs of axis-parallel rectangles. That is, we prove that triangle-free
rectangle overlap graphs have chromatic number , improving on
the previous bound of . To this end, we exploit a relationship
between off-line coloring of rectangle overlap graphs and on-line coloring of
interval overlap graphs. Our coloring method decomposes the graph into a
bounded number of subgraphs with a tree-like structure that "encodes"
strategies of the adversary in the on-line coloring problem. Then, these
subgraphs are colored with colors using a combination of
techniques from on-line algorithms (first-fit) and data structure design
(heavy-light decomposition).Comment: Minor revisio
Subsquares Approach - Simple Scheme for Solving Overdetermined Interval Linear Systems
In this work we present a new simple but efficient scheme - Subsquares
approach - for development of algorithms for enclosing the solution set of
overdetermined interval linear systems. We are going to show two algorithms
based on this scheme and discuss their features. We start with a simple
algorithm as a motivation, then we continue with a sequential algorithm. Both
algorithms can be easily parallelized. The features of both algorithms will be
discussed and numerically tested.Comment: submitted to PPAM 201
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