1,573 research outputs found
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
A Time-Space Tradeoff for Triangulations of Points in the Plane
In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Capacitated Vehicle Routing with Non-Uniform Speeds
The capacitated vehicle routing problem (CVRP) involves distributing
(identical) items from a depot to a set of demand locations, using a single
capacitated vehicle. We study a generalization of this problem to the setting
of multiple vehicles having non-uniform speeds (that we call Heterogenous
CVRP), and present a constant-factor approximation algorithm.
The technical heart of our result lies in achieving a constant approximation
to the following TSP variant (called Heterogenous TSP). Given a metric denoting
distances between vertices, a depot r containing k vehicles with possibly
different speeds, the goal is to find a tour for each vehicle (starting and
ending at r), so that every vertex is covered in some tour and the maximum
completion time is minimized. This problem is precisely Heterogenous CVRP when
vehicles are uncapacitated.
The presence of non-uniform speeds introduces difficulties for employing
standard tour-splitting techniques. In order to get a better understanding of
this technique in our context, we appeal to ideas from the 2-approximation for
scheduling in parallel machine of Lenstra et al.. This motivates the
introduction of a new approximate MST construction called Level-Prim, which is
related to Light Approximate Shortest-path Trees. The last component of our
algorithm involves partitioning the Level-Prim tree and matching the resulting
parts to vehicles. This decomposition is more subtle than usual since now we
need to enforce correlation between the size of the parts and their distances
to the depot
Matroid and Knapsack Center Problems
In the classic -center problem, we are given a metric graph, and the
objective is to open nodes as centers such that the maximum distance from
any vertex to its closest center is minimized. In this paper, we consider two
important generalizations of -center, the matroid center problem and the
knapsack center problem. Both problems are motivated by recent content
distribution network applications. Our contributions can be summarized as
follows:
1. We consider the matroid center problem in which the centers are required
to form an independent set of a given matroid. We show this problem is NP-hard
even on a line. We present a 3-approximation algorithm for the problem on
general metrics. We also consider the outlier version of the problem where a
given number of vertices can be excluded as the outliers from the solution. We
present a 7-approximation for the outlier version.
2. We consider the (multi-)knapsack center problem in which the centers are
required to satisfy one (or more) knapsack constraint(s). It is known that the
knapsack center problem with a single knapsack constraint admits a
3-approximation. However, when there are at least two knapsack constraints, we
show this problem is not approximable at all. To complement the hardness
result, we present a polynomial time algorithm that gives a 3-approximate
solution such that one knapsack constraint is satisfied and the others may be
violated by at most a factor of . We also obtain a 3-approximation
for the outlier version that may violate the knapsack constraint by
.Comment: A preliminary version of this paper is accepted to IPCO 201
Selection from read-only memory with limited workspace
Given an unordered array of elements drawn from a totally ordered set and
an integer in the range from to , in the classic selection problem
the task is to find the -th smallest element in the array. We study the
complexity of this problem in the space-restricted random-access model: The
input array is stored on read-only memory, and the algorithm has access to a
limited amount of workspace. We prove that the linear-time prune-and-search
algorithm---presented in most textbooks on algorithms---can be modified to use
bits instead of words of extra space. Prior to our
work, the best known algorithm by Frederickson could perform the task with
bits of extra space in time. Our result separates
the space-restricted random-access model and the multi-pass streaming model,
since we can surpass the lower bound known for the latter
model. We also generalize our algorithm for the case when the size of the
workspace is bits, where . The running time
of our generalized algorithm is ,
slightly improving over the
bound of Frederickson's algorithm. To obtain the improvements mentioned above,
we developed a new data structure, called the wavelet stack, that we use for
repeated pruning. We expect the wavelet stack to be a useful tool in other
applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201
Assessing direct contributions of morphological awareness and prosodic sensitivity to children’s word reading and reading comprehension
We examined the independent contributions of prosodic sensitivity and morphological awareness to word reading, text reading accuracy, and reading comprehension. We did so in a longitudinal study of English-speaking children (N = 70). At 5 to 7 years of age, children completed the metalinguistic measures along with control measures of phonological awareness and vocabulary. Children completed the reading measures two years later. Morphological awareness, but not prosodic sensitivity made a significant independent contribution to word reading, text reading accuracy and reading comprehension. The effects of morphological awareness on reading comprehension remained after controls for word reading. These results suggest that morphological awareness needs to be considered seriously in models of reading development and that prosodic sensitivity might have primarily indirect relations to reading outcomes.
Keywords: Morphological Awareness; Prosody; Word Reading; Reading Comprehension
Development and Validation of an Anodic Stripping Voltammetric Method for Determination of Zn2+ Ions in Brain Microdialysate Samples
An easy, rapid, and sensitive anodic stripping voltammetric method with a controlled growth mercury drop electrode has been developed and validated for the determination of Zn2+ ions in brain microdialysate samples obtained from rats. The considered level of the zinc concentration in the dialysate was 0.5–6 ppb. In the investigated method, the stripping step was carried out by using a differential pulse potential-time voltammetric excitation signal. The optimal experimental conditions as well as the instrumental and accumulation parameters and supporting electrolyte composition were investigated. The optimized method was validated for precision, linearity, and accuracy. Mean recovery 82–110% was achieved, the precision expressed by CV not greater than 7.6% and the linearity given by correlation coefficient not lower than 0.9988. The limit of detection was 0.1 ppb. No interferences were observed. Due to high linearity, precision, and sensitivity, the developed method may be successfully applied in the determination of zinc ions in microdialysate brain samples. The results obtained for the first time demonstrate detailed characteristics of the determination of zinc in the brain microdialysate fluid by the ASV method. It may be applied in a wide range of physiological and pharmacological studies which focus on very low zinc concentration/alteration in various compartments of the organisms
Electoral and political changes: the impact on political bureaucratic relationships in Scottish Local Government
Transient Increase in Zn2+ in Hippocampal CA1 Pyramidal Neurons Causes Reversible Memory Deficit
The translocation of synaptic Zn2+ to the cytosolic compartment has been studied to understand Zn2+ neurotoxicity in neurological diseases. However, it is unknown whether the moderate increase in Zn2+ in the cytosolic compartment affects memory processing in the hippocampus. In the present study, the moderate increase in cytosolic Zn2+ in the hippocampus was induced with clioquinol (CQ), a zinc ionophore. Zn2+ delivery by Zn-CQ transiently attenuated CA1 long-term potentiation (LTP) in hippocampal slices prepared 2 h after i.p. injection of Zn-CQ into rats, when intracellular Zn2+ levels was transiently increased in the CA1 pyramidal cell layer, followed by object recognition memory deficit. Object recognition memory was transiently impaired 30 min after injection of ZnCl2 into the CA1, but not after injection into the dentate gyrus that did not significantly increase intracellular Zn2+ in the granule cell layer of the dentate gyrus. Object recognition memory deficit may be linked to the preferential increase in Zn2+ and/or the preferential vulnerability to Zn2+ in CA1 pyramidal neurons. In the case of the cytosolic increase in endogenous Zn2+ in the CA1 induced by 100 mM KCl, furthermore, object recognition memory was also transiently impaired, while ameliorated by co-injection of CaEDTA to block the increase in cytosolic Zn2+. The present study indicates that the transient increase in cytosolic Zn2+ in CA1 pyramidal neurons reversibly impairs object recognition memory
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