63,875 research outputs found
VoG: Summarizing and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple
sentences? How can we measure the "importance" of a set of discovered subgraphs
in a large graph? These are exactly the problems we focus on. Our main ideas
are to construct a "vocabulary" of subgraph-types that often occur in real
graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the
most succinct description of a graph in terms of this vocabulary. We measure
success in a well-founded way by means of the Minimum Description Length (MDL)
principle: a subgraph is included in the summary if it decreases the total
description length of the graph.
Our contributions are three-fold: (a) formulation: we provide a principled
encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop
\method, an efficient method to minimize the description cost, and (c)
applicability: we report experimental results on multi-million-edge real
graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201
{VoG}: {Summarizing} and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph
Codeword stabilized quantum codes: algorithm and structure
The codeword stabilized ("CWS") quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021). This formalism reduces the problem of constructing such
quantum codes to finding a binary classical code correcting an error pattern
induced by a graph state. Finding such a classical code can be very difficult.
Here, we consider an algorithm which maps the search for CWS codes to a problem
of identifying maximum cliques in a graph. While solving this problem is in
general very hard, we prove three structure theorems which reduce the search
space, specifying certain admissible and optimal ((n,K,d)) additive codes. In
particular, we find there does not exist any ((7,3,3)) CWS code though the
linear programming bound does not rule it out. The complexity of the CWS search
algorithm is compared with the contrasting method introduced by Aggarwal and
Calderbank (arXiv:cs/0610159).Comment: 11 pages, 1 figur
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
A comparative analysis of web-based GIS applications using usability metrics
With the rapid expansion of the internet, Web-based Geographic Information System (WGIS) applications have gained popularity, despite the interface of the WGIS application being difficult to learn and understand because special functions are needed to manipulate the maps. Hence, it is essential to evaluate the usability of WGIS applications. Usability is an important factor in ensuring the development of quality, usable software products. On the other hand, there are a number of standards and models in the literature, each of which describes usability in terms of various set of attributes. These models are vague and difficult to understand. Therefore, the primary purpose of this study is to compare five common usability models (Shackel, Nielsen, ISO 9241 P-11, ISO 9126-1 and QUIM) to identify usability metrics that have most frequently used in the previous models. The questionnaire method and the automated usability evaluation method by using Loop11 tool were used, in order to evaluate the usability metrics for three case studies of commonly used WGIS applications as Google maps, Yahoo maps, and MapQuest. Finally, those case studies were compared and analysed based on usability metrics that have been identified. Based on a comparative study, four usability metrics (Effectiveness, Efficiency, Satisfaction and Learnability) were identified. Those usability metrics were characterized by consistent, comprehensive, not vaguely and proper to evaluate the usability of WGIS applications. In addition, there was a positive correlation between these usability metrics. The comparative analysis indicates that Effectiveness, Satisfaction and Learnability were higher, and the Efficiency was lesser by using the Loop11 tool compared to questionnaire method for the three case studies. In addition, Yahoo Maps and MapQuest have usability metrics rate lesser than Google Maps by applying two methods. Therefore, Google Maps is more usable compared to Yahoo Maps and MapQuest
Decoding communities in networks
According to a recent information-theoretical proposal, the problem of
defining and identifying communities in networks can be interpreted as a
classical communication task over a noisy channel: memberships of nodes are
information bits erased by the channel, edges and non-edges in the network are
parity bits introduced by the encoder but degraded through the channel, and a
community identification algorithm is a decoder. The interpretation is
perfectly equivalent to the one at the basis of well-known statistical
inference algorithms for community detection. The only difference in the
interpretation is that a noisy channel replaces a stochastic network model.
However, the different perspective gives the opportunity to take advantage of
the rich set of tools of coding theory to generate novel insights on the
problem of community detection. In this paper, we illustrate two main
applications of standard coding-theoretical methods to community detection.
First, we leverage a state-of-the-art decoding technique to generate a family
of quasi-optimal community detection algorithms. Second and more important, we
show that the Shannon's noisy-channel coding theorem can be invoked to
establish a lower bound, here named as decodability bound, for the maximum
amount of noise tolerable by an ideal decoder to achieve perfect detection of
communities. When computed for well-established synthetic benchmarks, the
decodability bound explains accurately the performance achieved by the best
community detection algorithms existing on the market, telling us that only
little room for their improvement is still potentially left.Comment: 9 pages, 5 figures + Appendi
Physical-depth architectural requirements for generating universal photonic cluster states
Most leading proposals for linear-optical quantum computing (LOQC) use
cluster states, which act as a universal resource for measurement-based
(one-way) quantum computation (MBQC). In ballistic approaches to LOQC, cluster
states are generated passively from small entangled resource states using
so-called fusion operations. Results from percolation theory have previously
been used to argue that universal cluster states can be generated in the
ballistic approach using schemes which exceed the critical threshold for
percolation, but these results consider cluster states with unbounded size.
Here we consider how successful percolation can be maintained using a physical
architecture with fixed physical depth, assuming that the cluster state is
continuously generated and measured, and therefore that only a finite portion
of it is visible at any one point in time. We show that universal LOQC can be
implemented using a constant-size device with modest physical depth, and that
percolation can be exploited using simple pathfinding strategies without the
need for high-complexity algorithms.Comment: 18 pages, 10 figure
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