59,708 research outputs found
A Simple Linear-Space Data Structure for Constant-Time Range Minimum Query
Abstract. We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space
Exact Distance Oracles for Planar Graphs
We present new and improved data structures that answer exact node-to-node
distance queries in planar graphs. Such data structures are also known as
distance oracles. For any directed planar graph on n nodes with non-negative
lengths we obtain the following:
* Given a desired space allocation , we show how to
construct in time a data structure of size that answers
distance queries in time per query.
As a consequence, we obtain an improvement over the fastest algorithm for
k-many distances in planar graphs whenever .
* We provide a linear-space exact distance oracle for planar graphs with
query time for any constant eps>0. This is the first such data
structure with provable sublinear query time.
* For edge lengths at least one, we provide an exact distance oracle of space
such that for any pair of nodes at distance D the query time is
. Comparable query performance had been observed
experimentally but has never been explained theoretically.
Our data structures are based on the following new tool: given a
non-self-crossing cycle C with nodes, we can preprocess G in
time to produce a data structure of size that can
answer the following queries in time: for a query node u, output
the distance from u to all the nodes of C. This data structure builds on and
extends a related data structure of Klein (SODA'05), which reports distances to
the boundary of a face, rather than a cycle.
The best distance oracles for planar graphs until the current work are due to
Cabello (SODA'06), Djidjev (WG'96), and Fakcharoenphol and Rao (FOCS'01). For
and space , we essentially improve the query
time from to .Comment: To appear in the proceedings of the 23rd ACM-SIAM Symposium on
Discrete Algorithms, SODA 201
Query processing of spatial objects: Complexity versus Redundancy
The management of complex spatial objects in applications, such as geography and cartography,
imposes stringent new requirements on spatial database systems, in particular on efficient
query processing. As shown before, the performance of spatial query processing can be improved
by decomposing complex spatial objects into simple components. Up to now, only decomposition
techniques generating a linear number of very simple components, e.g. triangles or trapezoids, have
been considered. In this paper, we will investigate the natural trade-off between the complexity of
the components and the redundancy, i.e. the number of components, with respect to its effect on
efficient query processing. In particular, we present two new decomposition methods generating
a better balance between the complexity and the number of components than previously known
techniques. We compare these new decomposition methods to the traditional undecomposed representation
as well as to the well-known decomposition into convex polygons with respect to their
performance in spatial query processing. This comparison points out that for a wide range of query
selectivity the new decomposition techniques clearly outperform both the undecomposed representation
and the convex decomposition method. More important than the absolute gain in performance
by a factor of up to an order of magnitude is the robust performance of our new decomposition
techniques over the whole range of query selectivity
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