20,161 research outputs found
Sketching Cuts in Graphs and Hypergraphs
Sketching and streaming algorithms are in the forefront of current research
directions for cut problems in graphs. In the streaming model, we show that
-approximation for Max-Cut must use space;
moreover, beating -approximation requires polynomial space. For the
sketching model, we show that -uniform hypergraphs admit a
-cut-sparsifier (i.e., a weighted subhypergraph that
approximately preserves all the cuts) with
edges. We also make first steps towards sketching general CSPs (Constraint
Satisfaction Problems)
Reducing bias and quantifying uncertainty in watershed flux estimates: the R package loadflex
Many ecological insights into the function of rivers and watersheds emerge from quantifying the flux of solutes or suspended materials in rivers. Numerous methods for flux estimation have been described, and each has its strengths and weaknesses. Currently, the largest practical challenges in flux estimation are to select among these methods and to implement or apply whichever method is chosen. To ease this process of method selection and application, we have written an R software package called loadflex that implements several of the most popular methods for flux estimation, including regressions, interpolations, and the special case of interpolation known as the period-weighted approach. Our package also implements a lesser-known and empirically promising approach called the “composite method,” to which we have added an algorithm for estimating prediction uncertainty. Here we describe the structure and key features of loadflex, with a special emphasis on the rationale and details of our composite method implementation. We then demonstrate the use of loadflex by fitting four different models to nitrate data from the Lamprey River in southeastern New Hampshire, where two large floods in 2006–2007 are hypothesized to have driven a long-term shift in nitrate concentrations and fluxes from the watershed. The models each give believable estimates, and yet they yield different answers for whether and how the floods altered nitrate loads. In general, the best modeling approach for each new dataset will depend on the specific site and solute of interest, and researchers need to make an informed choice among the many possible models. Our package addresses this need by making it simple to apply and compare multiple load estimation models, ultimately allowing researchers to estimate riverine concentrations and fluxes with greater ease and accuracy
Streaming Verification of Graph Properties
Streaming interactive proofs (SIPs) are a framework for outsourced
computation. A computationally limited streaming client (the verifier) hands
over a large data set to an untrusted server (the prover) in the cloud and the
two parties run a protocol to confirm the correctness of result with high
probability. SIPs are particularly interesting for problems that are hard to
solve (or even approximate) well in a streaming setting. The most notable of
these problems is finding maximum matchings, which has received intense
interest in recent years but has strong lower bounds even for constant factor
approximations.
In this paper, we present efficient streaming interactive proofs that can
verify maximum matchings exactly. Our results cover all flavors of matchings
(bipartite/non-bipartite and weighted). In addition, we also present streaming
verifiers for approximate metric TSP. In particular, these are the first
efficient results for weighted matchings and for metric TSP in any streaming
verification model.Comment: 26 pages, 2 figure, 1 tabl
Weighted Reservoir Sampling from Distributed Streams
We consider message-efficient continuous random sampling from a distributed
stream, where the probability of inclusion of an item in the sample is
proportional to a weight associated with the item. The unweighted version,
where all weights are equal, is well studied, and admits tight upper and lower
bounds on message complexity. For weighted sampling with replacement, there is
a simple reduction to unweighted sampling with replacement. However, in many
applications the stream has only a few heavy items which may dominate a random
sample when chosen with replacement. Weighted sampling \textit{without
replacement} (weighted SWOR) eludes this issue, since such heavy items can be
sampled at most once.
In this work, we present the first message-optimal algorithm for weighted
SWOR from a distributed stream. Our algorithm also has optimal space and time
complexity. As an application of our algorithm for weighted SWOR, we derive the
first distributed streaming algorithms for tracking \textit{heavy hitters with
residual error}. Here the goal is to identify stream items that contribute
significantly to the residual stream, once the heaviest items are removed.
Residual heavy hitters generalize the notion of heavy hitters and are
important in streams that have a skewed distribution of weights. In addition to
the upper bound, we also provide a lower bound on the message complexity that
is nearly tight up to a factor. Finally, we use our weighted
sampling algorithm to improve the message complexity of distributed
tracking, also known as count tracking, which is a widely studied problem in
distributed streaming. We also derive a tight message lower bound, which closes
the message complexity of this fundamental problem.Comment: To appear in PODS 201
Maximum Matching in Turnstile Streams
We consider the unweighted bipartite maximum matching problem in the one-pass
turnstile streaming model where the input stream consists of edge insertions
and deletions. In the insertion-only model, a one-pass -approximation
streaming algorithm can be easily obtained with space , where
denotes the number of vertices of the input graph. We show that no such result
is possible if edge deletions are allowed, even if space is
granted, for every . Specifically, for every , we show that in the one-pass turnstile streaming model, in order to compute
a -approximation, space is
required for constant error randomized algorithms, and, up to logarithmic
factors, space is sufficient. Our lower bound result is
proved in the simultaneous message model of communication and may be of
independent interest
Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging
Signals comprised of a stream of short pulses appear in many applications
including bio-imaging and radar. The recent finite rate of innovation
framework, has paved the way to low rate sampling of such pulses by noticing
that only a small number of parameters per unit time are needed to fully
describe these signals. Unfortunately, for high rates of innovation, existing
sampling schemes are numerically unstable. In this paper we propose a general
sampling approach which leads to stable recovery even in the presence of many
pulses. We begin by deriving a condition on the sampling kernel which allows
perfect reconstruction of periodic streams from the minimal number of samples.
We then design a compactly supported class of filters, satisfying this
condition. The periodic solution is extended to finite and infinite streams,
and is shown to be numerically stable even for a large number of pulses. High
noise robustness is also demonstrated when the delays are sufficiently
separated. Finally, we process ultrasound imaging data using our techniques,
and show that substantial rate reduction with respect to traditional ultrasound
sampling schemes can be achieved.Comment: 14 pages, 13 figure
AROMA: Automatic Generation of Radio Maps for Localization Systems
WLAN localization has become an active research field recently. Due to the
wide WLAN deployment, WLAN localization provides ubiquitous coverage and adds
to the value of the wireless network by providing the location of its users
without using any additional hardware. However, WLAN localization systems
usually require constructing a radio map, which is a major barrier of WLAN
localization systems' deployment. The radio map stores information about the
signal strength from different signal strength streams at selected locations in
the site of interest. Typical construction of a radio map involves measurements
and calibrations making it a tedious and time-consuming operation. In this
paper, we present the AROMA system that automatically constructs accurate
active and passive radio maps for both device-based and device-free WLAN
localization systems. AROMA has three main goals: high accuracy, low
computational requirements, and minimum user overhead. To achieve high
accuracy, AROMA uses 3D ray tracing enhanced with the uniform theory of
diffraction (UTD) to model the electric field behavior and the human shadowing
effect. AROMA also automates a number of routine tasks, such as importing
building models and automatic sampling of the area of interest, to reduce the
user's overhead. Finally, AROMA uses a number of optimization techniques to
reduce the computational requirements. We present our system architecture and
describe the details of its different components that allow AROMA to achieve
its goals. We evaluate AROMA in two different testbeds. Our experiments show
that the predicted signal strength differs from the measurements by a maximum
average absolute error of 3.18 dBm achieving a maximum localization error of
2.44m for both the device-based and device-free cases.Comment: 14 pages, 17 figure
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