236 research outputs found
A New Lower Bound for Semigroup Orthogonal Range Searching
We report the first improvement in the space-time trade-off of lower bounds
for the orthogonal range searching problem in the semigroup model, since
Chazelle's result from 1990. This is one of the very fundamental problems in
range searching with a long history. Previously, Andrew Yao's influential
result had shown that the problem is already non-trivial in one
dimension~\cite{Yao-1Dlb}: using units of space, the query time must
be where is the
inverse Ackermann's function, a very slowly growing function.
In dimensions, Bernard Chazelle~\cite{Chazelle.LB.II} proved that the
query time must be where .
Chazelle's lower bound is known to be tight for when space consumption is
`high' i.e., . We have two main results.
The first is a lower bound that shows Chazelle's lower bound was not tight for
`low space': we prove that we must have . Our lower bound does not close the gap to the existing data
structures, however, our second result is that our analysis is tight. Thus, we
believe the gap is in fact natural since lower bounds are proven for idempotent
semigroups while the data structures are built for general semigroups and thus
they cannot assume (and use) the properties of an idempotent semigroup. As a
result, we believe to close the gap one must study lower bounds for
non-idempotent semigroups or building data structures for idempotent
semigroups. We develope significantly new ideas for both of our results that
could be useful in pursuing either of these directions
On the complexity of range searching among curves
Modern tracking technology has made the collection of large numbers of
densely sampled trajectories of moving objects widely available. We consider a
fundamental problem encountered when analysing such data: Given polygonal
curves in , preprocess into a data structure that answers
queries with a query curve and radius for the curves of that
have \Frechet distance at most to .
We initiate a comprehensive analysis of the space/query-time trade-off for
this data structuring problem. Our lower bounds imply that any data structure
in the pointer model model that achieves query time, where is
the output size, has to use roughly space in
the worst case, even if queries are mere points (for the discrete \Frechet
distance) or line segments (for the continuous \Frechet distance). More
importantly, we show that more complex queries and input curves lead to
additional logarithmic factors in the lower bound. Roughly speaking, the number
of logarithmic factors added is linear in the number of edges added to the
query and input curve complexity. This means that the space/query time
trade-off worsens by an exponential factor of input and query complexity. This
behaviour addresses an open question in the range searching literature: whether
it is possible to avoid the additional logarithmic factors in the space and
query time of a multilevel partition tree. We answer this question negatively.
On the positive side, we show we can build data structures for the \Frechet
distance by using semialgebraic range searching. Our solution for the discrete
\Frechet distance is in line with the lower bound, as the number of levels in
the data structure is , where denotes the maximal number of vertices
of a curve. For the continuous \Frechet distance, the number of levels
increases to
Data Structure Lower Bounds for Document Indexing Problems
We study data structure problems related to document indexing and pattern
matching queries and our main contribution is to show that the pointer machine
model of computation can be extremely useful in proving high and unconditional
lower bounds that cannot be obtained in any other known model of computation
with the current techniques. Often our lower bounds match the known space-query
time trade-off curve and in fact for all the problems considered, there is a
very good and reasonable match between the our lower bounds and the known upper
bounds, at least for some choice of input parameters. The problems that we
consider are set intersection queries (both the reporting variant and the
semi-group counting variant), indexing a set of documents for two-pattern
queries, or forbidden- pattern queries, or queries with wild-cards, and
indexing an input set of gapped-patterns (or two-patterns) to find those
matching a document given at the query time.Comment: Full version of the conference version that appeared at ICALP 2016,
25 page
Compressed Representations of Conjunctive Query Results
Relational queries, and in particular join queries, often generate large
output results when executed over a huge dataset. In such cases, it is often
infeasible to store the whole materialized output if we plan to reuse it
further down a data processing pipeline. Motivated by this problem, we study
the construction of space-efficient compressed representations of the output of
conjunctive queries, with the goal of supporting the efficient access of the
intermediate compressed result for a given access pattern. In particular, we
initiate the study of an important tradeoff: minimizing the space necessary to
store the compressed result, versus minimizing the answer time and delay for an
access request over the result. Our main contribution is a novel parameterized
data structure, which can be tuned to trade off space for answer time. The
tradeoff allows us to control the space requirement of the data structure
precisely, and depends both on the structure of the query and the access
pattern. We show how we can use the data structure in conjunction with query
decomposition techniques, in order to efficiently represent the outputs for
several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom
A New Lower Bound for Semigroup Orthogonal Range Searching
We report the first improvement in the space-time trade-off of lower bounds for the orthogonal range searching problem in the semigroup model, since Chazelle\u27s result from 1990. This is one of the very fundamental problems in range searching with a long history. Previously, Andrew Yao\u27s influential result had shown that the problem is already non-trivial in one dimension [Yao, 1982]: using m units of space, the query time Q(n) must be Omega(alpha(m,n) + n/(m-n+1)) where alpha(*,*) is the inverse Ackermann\u27s function, a very slowly growing function. In d dimensions, Bernard Chazelle [Chazelle, 1990] proved that the query time must be Q(n) = Omega((log_beta n)^{d-1}) where beta = 2m/n. Chazelle\u27s lower bound is known to be tight for when space consumption is "high" i.e., m = Omega(n log^{d+epsilon}n).
We have two main results. The first is a lower bound that shows Chazelle\u27s lower bound was not tight for "low space": we prove that we must have m Q(n) = Omega(n (log n log log n)^{d-1}). Our lower bound does not close the gap to the existing data structures, however, our second result is that our analysis is tight. Thus, we believe the gap is in fact natural since lower bounds are proven for idempotent semigroups while the data structures are built for general semigroups and thus they cannot assume (and use) the properties of an idempotent semigroup. As a result, we believe to close the gap one must study lower bounds for non-idempotent semigroups or building data structures for idempotent semigroups. We develope significantly new ideas for both of our results that could be useful in pursuing either of these directions
Laser Vaporization Methods for the Synthesis of Metal and Semiconductor Nanoparticles; Graphene, Doped Graphene and Nanoparticles Supported on Graphene
The major objective of the research described in this dissertation is the development of new laser vaporization methods for the synthesis of metal and semiconductor nanoparticles, graphene, B- and N-doped graphene, and metal and semiconductor nanoparticles supported on graphene. These methods include the Laser Vaporization Controlled Condensation (LVCC) approach, which has been used in this work for the synthesis of: (1) gold nanoparticles supported on ceria and zirconia nanoparticles for the low temperature oxidation of carbon monoxide, and (2) graphene, boron- and nitrogen-doped graphene, hydrogen-terminated graphene (HTG), metal nanoparticles supported on graphene, and graphene quantum dots. The gold nanoparticles supported on ceria prepared by the LVCC method exhibit high activity for CO oxidation with a 100% conversion of CO to CO2 at about 60 °C. The first application of the LVCC method for the synthesis of these graphene and graphene-based nanomaterials is reported in this dissertation. Complete characterizations of the graphene-based nanomaterials using a variety of techniques including spectroscopic, X-ray diffraction, mass spectrometric and microscopic methods such as Raman, FTIR, UV-Vis, PL, XRD, XPS, TOF-MS, and TEM. The application of B- and N-doped graphene as catalysts for the oxygen reduction reaction in fuel cell applications is reported. The application of Pd nanoparticles supported on graphene for the Suzuki carbon-carbon cross-coupling reaction is reported. A new method is described for the synthesis of graphene quantum dots based on the combination of the LVCC method with oxidation/reduction sequences in solution. The N-doped graphene quantum dots emit strong blue luminescence, which can be tuned to produce different emission colors that could be used in biomedical imagining and other optoelectronic applications. The second method used in the research described in this dissertation is based on the Laser Vaporization Solvent Capturing (LVSC) approach, which has been introduced and developed, for the first time, for the synthesis of solvent-capped semiconductor and metal oxide nanoparticles. The method has been demonstrated for the synthesis of V, Mo, and W oxide nanoparticles capped by different solvent molecules such as acetonitrile and methanol. The LVSC method has also been applied for the synthesis of Si nanocrystals capped by acetonitrile clusters. The acetonitrile-capped Si nanocrystals exhibit strong emissions, which depend on the excitation wavelength and indicate the presence of Si quantum dots with different sizes. The Si and the metal oxide nanoparticles prepared by the LVSC method have been incorporated into graphene in order to synthesize graphene nanosheets with tunable properties depending on graphene-nanoparticle interactions
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