1,224 research outputs found
Exploiting non-constant safe memory in resilient algorithms and data structures
We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a
safe memory of arbitrary size , and we then derive tradeoffs between the
performance of resilient algorithmic techniques and the size of the safe
memory. Let and denote, respectively, the maximum amount of
faults which can happen during the execution of an algorithm and the actual
number of occurred faults, with . We propose a resilient
algorithm for sorting entries which requires time and uses safe memory words. Our
algorithm outperforms previous resilient sorting algorithms which do not
exploit the available safe memory and require time. Finally, we exploit our sorting algorithm for
deriving a resilient priority queue. Our implementation uses safe
memory words and faulty memory words for storing keys, and
requires amortized time for each insert and
deletemin operation. Our resilient priority queue improves the amortized time required by the state of the art.Comment: To appear in Theoretical Computer Science, 201
A Lower Bound Technique for Communication in BSP
Communication is a major factor determining the performance of algorithms on
current computing systems; it is therefore valuable to provide tight lower
bounds on the communication complexity of computations. This paper presents a
lower bound technique for the communication complexity in the bulk-synchronous
parallel (BSP) model of a given class of DAG computations. The derived bound is
expressed in terms of the switching potential of a DAG, that is, the number of
permutations that the DAG can realize when viewed as a switching network. The
proposed technique yields tight lower bounds for the fast Fourier transform
(FFT), and for any sorting and permutation network. A stronger bound is also
derived for the periodic balanced sorting network, by applying this technique
to suitable subnetworks. Finally, we demonstrate that the switching potential
captures communication requirements even in computational models different from
BSP, such as the I/O model and the LPRAM
Information Spreading in Stationary Markovian Evolving Graphs
Markovian evolving graphs are dynamic-graph models where the links among a
fixed set of nodes change during time according to an arbitrary Markovian rule.
They are extremely general and they can well describe important dynamic-network
scenarios.
We study the speed of information spreading in the "stationary phase" by
analyzing the completion time of the "flooding mechanism". We prove a general
theorem that establishes an upper bound on flooding time in any stationary
Markovian evolving graph in terms of its node-expansion properties.
We apply our theorem in two natural and relevant cases of such dynamic
graphs. "Geometric Markovian evolving graphs" where the Markovian behaviour is
yielded by "n" mobile radio stations, with fixed transmission radius, that
perform independent random walks over a square region of the plane.
"Edge-Markovian evolving graphs" where the probability of existence of any edge
at time "t" depends on the existence (or not) of the same edge at time "t-1".
In both cases, the obtained upper bounds hold "with high probability" and
they are nearly tight. In fact, they turn out to be tight for a large range of
the values of the input parameters. As for geometric Markovian evolving graphs,
our result represents the first analytical upper bound for flooding time on a
class of concrete mobile networks.Comment: 16 page
Una lettura delle dinamiche dellâindustria automobilistica europea in termini di Flying Geese e di Sophistication Index
This paper deals with the evolution of automobile sector during the 1990s in Central and Eastern Europe (CEE) Countries from a double point of view. At first, we wonder about the applicability to the sector of Flying Geese (FG) model, theorised by Kaname Akmatsu in the 1930s to explain export-driven development patterns in Japan, and neglected for a long time. Through the calculation of Revealed Comparative Advantage (RCA, or Balassa) index of import and export of a group of goods directly related to the automobile chain, we try to highlight the presence of sequences in the comparative industrial specialization of CEE Countries, from lower to higher sophisticated goods, connected to the European landscape, and on the consolidation of a regional hierarchy for this industrial sector. Secondly, we reframe the whole investigation to check the robustness of this hierarchy using a sophistication index approach, both in the product (PRODY) and in the country (EXPY) version Some final remarks highlights the role of Italy with respect to the hierarchy emerging both from RCA and Sophistication index analysisExport sophistication, Specialization pattern, RCA, Flying Geese
Adaptive MapReduce Similarity Joins
Similarity joins are a fundamental database operation. Given data sets S and
R, the goal of a similarity join is to find all points x in S and y in R with
distance at most r. Recent research has investigated how locality-sensitive
hashing (LSH) can be used for similarity join, and in particular two recent
lines of work have made exciting progress on LSH-based join performance. Hu,
Tao, and Yi (PODS 17) investigated joins in a massively parallel setting,
showing strong results that adapt to the size of the output. Meanwhile, Ahle,
Aum\"uller, and Pagh (SODA 17) showed a sequential algorithm that adapts to the
structure of the data, matching classic bounds in the worst case but improving
them significantly on more structured data. We show that this adaptive strategy
can be adapted to the parallel setting, combining the advantages of these
approaches. In particular, we show that a simple modification to Hu et al.'s
algorithm achieves bounds that depend on the density of points in the dataset
as well as the total outsize of the output. Our algorithm uses no extra
parameters over other LSH approaches (in particular, its execution does not
depend on the structure of the dataset), and is likely to be efficient in
practice
Locality-Sensitive Hashing of Curves
We study data structures for storing a set of polygonal curves in
such that, given a query curve, we can efficiently retrieve similar curves from
the set, where similarity is measured using the discrete Fr\'echet distance or
the dynamic time warping distance. To this end we devise the first
locality-sensitive hashing schemes for these distance measures. A major
challenge is posed by the fact that these distance measures internally optimize
the alignment between the curves. We give solutions for different types of
alignments including constrained and unconstrained versions. For unconstrained
alignments, we improve over a result by Indyk from 2002 for short curves. Let
be the number of input curves and let be the maximum complexity of a
curve in the input. In the particular case where , for some fixed , our solutions imply an approximate near-neighbor
data structure for the discrete Fr\'echet distance that uses space in
and achieves query time in and
constant approximation factor. Furthermore, our solutions provide a trade-off
between approximation quality and computational performance: for any parameter
, we can give a data structure that uses space in , answers queries in time and achieves
approximation factor in .Comment: Proc. of 33rd International Symposium on Computational Geometry
(SoCG), 201
Communication Lower Bounds for Distributed-Memory Computations
In this paper we propose a new approach to the study of the communication requirements of distributed computations, which advocates for the removal of the restrictive assumptions under which earlier results were derived. We illustrate our approach by giving tight lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast Fourier Transform. Our bounds rely only on a mild assumption on work distribution, and significantly strengthen previous results which require either the computation to be balanced among the processors, or specific initial distributions of the input data, or an upper bound on the size of processors\u27 local memories
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