22,604 research outputs found
Tight and simple Web graph compression
Analysing Web graphs has applications in determining page ranks, fighting Web
spam, detecting communities and mirror sites, and more. This study is however
hampered by the necessity of storing a major part of huge graphs in the
external memory, which prevents efficient random access to edge (hyperlink)
lists. A number of algorithms involving compression techniques have thus been
presented, to represent Web graphs succinctly but also providing random access.
Those techniques are usually based on differential encodings of the adjacency
lists, finding repeating nodes or node regions in the successive lists, more
general grammar-based transformations or 2-dimensional representations of the
binary matrix of the graph. In this paper we present two Web graph compression
algorithms. The first can be seen as engineering of the Boldi and Vigna (2004)
method. We extend the notion of similarity between link lists, and use a more
compact encoding of residuals. The algorithm works on blocks of varying size
(in the number of input lines) and sacrifices access time for better
compression ratio, achieving more succinct graph representation than other
algorithms reported in the literature. The second algorithm works on blocks of
the same size, in the number of input lines, and its key mechanism is merging
the block into a single ordered list. This method achieves much more attractive
space-time tradeoffs.Comment: 15 page
Entanglement and coherence in quantum state merging
Understanding the resource consumption in distributed scenarios is one of the
main goals of quantum information theory. A prominent example for such a
scenario is the task of quantum state merging where two parties aim to merge
their parts of a tripartite quantum state. In standard quantum state merging,
entanglement is considered as an expensive resource, while local quantum
operations can be performed at no additional cost. However, recent developments
show that some local operations could be more expensive than others: it is
reasonable to distinguish between local incoherent operations and local
operations which can create coherence. This idea leads us to the task of
incoherent quantum state merging, where one of the parties has free access to
local incoherent operations only. In this case the resources of the process are
quantified by pairs of entanglement and coherence. Here, we develop tools for
studying this process, and apply them to several relevant scenarios. While
quantum state merging can lead to a gain of entanglement, our results imply
that no merging procedure can gain entanglement and coherence at the same time.
We also provide a general lower bound on the entanglement-coherence sum, and
show that the bound is tight for all pure states. Our results also lead to an
incoherent version of Schumacher compression: in this case the compression rate
is equal to the von Neumann entropy of the diagonal elements of the
corresponding quantum state.Comment: 9 pages, 1 figure. Lemma 5 in Appendix D of the previous version was
not correct. This did not affect the results of the main tex
A multiscale Molecular Dynamics approach to Contact Mechanics
The friction and adhesion between elastic bodies are strongly influenced by
the roughness of the surfaces in contact. Here we develop a multiscale
molecular dynamics approach to contact mechanics, which can be used also when
the surfaces have roughness on many different length-scales, e.g., for self
affine fractal surfaces. As an illustration we consider the contact between
randomly rough surfaces, and show that the contact area varies linearly with
the load for small load. We also analyze the contact morphology and the
pressure distribution at different magnification, both with and without
adhesion. The calculations are compared with analytical contact mechanics
models based on continuum mechanics.Comment: Format Revtex4, two columns, 13 pages, 19 pictures. Submitted for
publication in the European Physical Journal E. Third revision with minimal
changes: Corrected a few mistypin
Information-Preserving Markov Aggregation
We present a sufficient condition for a non-injective function of a Markov
chain to be a second-order Markov chain with the same entropy rate as the
original chain. This permits an information-preserving state space reduction by
merging states or, equivalently, lossless compression of a Markov source on a
sample-by-sample basis. The cardinality of the reduced state space is bounded
from below by the node degrees of the transition graph associated with the
original Markov chain.
We also present an algorithm listing all possible information-preserving
state space reductions, for a given transition graph. We illustrate our results
by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table
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