2,290 research outputs found
On trip planning queries in spatial databases
In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks
On the positive and negative inertia of weighted graphs
The number of the positive, negative and zero eigenvalues in the spectrum of
the (edge)-weighted graph are called positive inertia index, negative
inertia index and nullity of the weighted graph , and denoted by ,
, , respectively. In this paper, the positive and negative
inertia index of weighted trees, weighted unicyclic graphs and weighted
bicyclic graphs are discussed, the methods of calculating them are obtained.Comment: 12. arXiv admin note: text overlap with arXiv:1107.0400 by other
author
On trip planning queries in spatial databases
In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks
Building Wavelet Histograms on Large Data in MapReduce
MapReduce is becoming the de facto framework for storing and processing
massive data, due to its excellent scalability, reliability, and elasticity. In
many MapReduce applications, obtaining a compact accurate summary of data is
essential. Among various data summarization tools, histograms have proven to be
particularly important and useful for summarizing data, and the wavelet
histogram is one of the most widely used histograms. In this paper, we
investigate the problem of building wavelet histograms efficiently on large
datasets in MapReduce. We measure the efficiency of the algorithms by both
end-to-end running time and communication cost. We demonstrate straightforward
adaptations of existing exact and approximate methods for building wavelet
histograms to MapReduce clusters are highly inefficient. To that end, we design
new algorithms for computing exact and approximate wavelet histograms and
discuss their implementation in MapReduce. We illustrate our techniques in
Hadoop, and compare to baseline solutions with extensive experiments performed
in a heterogeneous Hadoop cluster of 16 nodes, using large real and synthetic
datasets, up to hundreds of gigabytes. The results suggest significant (often
orders of magnitude) performance improvement achieved by our new algorithms.Comment: VLDB201
The extremal problems on the inertia of weighted bicyclic graphs
Let be a weighted graph. The number of the positive, negative and zero
eigenvalues in the spectrum of are called positive inertia index,
negative inertia index and nullity of , and denoted by ,
, , respectively. In this paper, sharp lower bound on
the positive (resp. negative) inertia index of weighted bicyclic graphs of
order with pendant vertices is obtained. Moreover, all the weighted
bicyclic graphs of order with at most two positive, two negative and at
least zero eigenvalues are identified, respectively.Comment: 12 pages, 5 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1307.0059 by other author
The Weyl-Wigner-Moyal Formalism for Spin
The Weyl-Wigner-Moyal formalism is developed for spin by means of a
correspondence between spherical harmonics and spherical harmonic tensor
operators. The analogue of the Moyal expansion is developed for the Weyl symbol
of the product of two operators in terms of the symbols for the individual
operators, and it is shown that in the classical limit, the Weyl symbol for a
commutator equals times the Poisson bracket of the corresponding Weyl
symbols. It is also found that, to the same order, there is no correction in
the symbol for the anticommutator
Spin current and rectification in one-dimensional electronic systems
Spin and charge currents can be generated by an ac voltage through a
one-channel quantum wire with strong electron interactions in a static uniform
magnetic field. In a certain range of low voltages, the spin current can grow
as a negative power of the voltage bias as the voltage decreases. The spin
current expressed in units of hbar/2 per second can become much larger than the
charge current in units of the electron charge per second. The system requires
neither spin-polarized particle injection nor time-dependent magnetic fields.Comment: 5 pages, 2 figure
GreedyDual-Join: Locality-Aware Buffer Management for Approximate Join Processing Over Data Streams
We investigate adaptive buffer management techniques for approximate evaluation of sliding window joins over multiple data streams. In many applications, data stream processing systems have limited memory or have to deal with very high speed data streams. In both cases, computing the exact results of joins between these streams may not be feasible, mainly because the buffers used to compute the joins contain much smaller number of tuples than the tuples contained in the sliding windows. Therefore, a stream buffer management policy is needed in that case. We show that the buffer replacement policy is an important determinant of the quality of the produced results. To that end, we propose GreedyDual-Join (GDJ) an adaptive and locality-aware buffering technique for managing these buffers. GDJ exploits the temporal correlations (at both long and short time scales), which we found to be prevalent in many real data streams. We note that our algorithm is readily applicable to multiple data streams and multiple joins and requires almost no additional system resources. We report results of an experimental study using both synthetic and real-world data sets. Our results demonstrate the superiority and flexibility of our approach when contrasted to other recently proposed techniques
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