373 research outputs found
Multifractal Network Generator
We introduce a new approach to constructing networks with realistic features.
Our method, in spite of its conceptual simplicity (it has only two parameters)
is capable of generating a wide variety of network types with prescribed
statistical properties, e.g., with degree- or clustering coefficient
distributions of various, very different forms. In turn, these graphs can be
used to test hypotheses, or, as models of actual data. The method is based on a
mapping between suitably chosen singular measures defined on the unit square
and sparse infinite networks. Such a mapping has the great potential of
allowing for graph theoretical results for a variety of network topologies. The
main idea of our approach is to go to the infinite limit of the singular
measure and the size of the corresponding graph simultaneously. A very unique
feature of this construction is that the complexity of the generated network is
increasing with the size. We present analytic expressions derived from the
parameters of the -- to be iterated-- initial generating measure for such major
characteristics of graphs as their degree, clustering coefficient and
assortativity coefficient distributions. The optimal parameters of the
generating measure are determined from a simple simulated annealing process.
Thus, the present work provides a tool for researchers from a variety of fields
(such as biology, computer science, biology, or complex systems) enabling them
to create a versatile model of their network data.Comment: Preprint. Final version appeared in PNAS
Lower Bounds for On-line Interval Coloring with Vector and Cardinality Constraints
We propose two strategies for Presenter in the on-line interval graph
coloring games. Specifically, we consider a setting in which each interval is
associated with a -dimensional vector of weights and the coloring needs to
satisfy the -dimensional bandwidth constraint, and the -cardinality
constraint. Such a variant was first introduced by Epstein and Levy and it is a
natural model for resource-aware task scheduling with different shared
resources where at most tasks can be scheduled simultaneously on a single
machine.
The first strategy forces any on-line interval coloring algorithm to use at
least different colors on an -colorable set of intervals. The second strategy forces any
on-line interval coloring algorithm to use at least
different colors on an
-colorable set of unit intervals
Maximizing the Probability of Delivery of Multipoint Relay Broadcast Protocol in Wireless Ad Hoc Networks with a Realistic Physical Layer
It is now commonly accepted that the unit disk graph used to model the
physical layer in wireless networks does not reflect real radio transmissions,
and that the lognormal shadowing model better suits to experimental
simulations. Previous work on realistic scenarios focused on unicast, while
broadcast requirements are fundamentally different and cannot be derived from
unicast case. Therefore, broadcast protocols must be adapted in order to still
be efficient under realistic assumptions. In this paper, we study the
well-known multipoint relay protocol (MPR). In the latter, each node has to
choose a set of neighbors to act as relays in order to cover the whole 2-hop
neighborhood. We give experimental results showing that the original method
provided to select the set of relays does not give good results with the
realistic model. We also provide three new heuristics in replacement and their
performances which demonstrate that they better suit to the considered model.
The first one maximizes the probability of correct reception between the node
and the considered relays multiplied by their coverage in the 2-hop
neighborhood. The second one replaces the coverage by the average of the
probabilities of correct reception between the considered neighbor and the
2-hop neighbors it covers. Finally, the third heuristic keeps the same concept
as the second one, but tries to maximize the coverage level of the 2-hop
neighborhood: 2-hop neighbors are still being considered as uncovered while
their coverage level is not higher than a given coverage threshold, many
neighbors may thus be selected to cover the same 2-hop neighbors
Recommendation Subgraphs for Web Discovery
Recommendations are central to the utility of many websites including
YouTube, Quora as well as popular e-commerce stores. Such sites typically
contain a set of recommendations on every product page that enables visitors to
easily navigate the website. Choosing an appropriate set of recommendations at
each page is one of the key features of backend engines that have been deployed
at several e-commerce sites.
Specifically at BloomReach, an engine consisting of several independent
components analyzes and optimizes its clients' websites. This paper focuses on
the structure optimizer component which improves the website navigation
experience that enables the discovery of novel content.
We begin by formalizing the concept of recommendations used for discovery. We
formulate this as a natural graph optimization problem which in its simplest
case, reduces to a bipartite matching problem. In practice, solving these
matching problems requires superlinear time and is not scalable. Also,
implementing simple algorithms is critical in practice because they are
significantly easier to maintain in production. This motivated us to analyze
three methods for solving the problem in increasing order of sophistication: a
sampling algorithm, a greedy algorithm and a more involved partitioning based
algorithm.
We first theoretically analyze the performance of these three methods on
random graph models characterizing when each method will yield a solution of
sufficient quality and the parameter ranges when more sophistication is needed.
We complement this by providing an empirical analysis of these algorithms on
simulated and real-world production data. Our results confirm that it is not
always necessary to implement complicated algorithms in the real-world and that
very good practical results can be obtained by using heuristics that are backed
by the confidence of concrete theoretical guarantees
Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing
We consider sequences of graphs and define various notions of convergence
related to these sequences: ``left convergence'' defined in terms of the
densities of homomorphisms from small graphs into the graphs of the sequence,
and ``right convergence'' defined in terms of the densities of homomorphisms
from the graphs of the sequence into small graphs; and convergence in a
suitably defined metric.
In Part I of this series, we show that left convergence is equivalent to
convergence in metric, both for simple graphs, and for graphs with nodeweights
and edgeweights. One of the main steps here is the introduction of a
cut-distance comparing graphs, not necessarily of the same size. We also show
how these notions of convergence provide natural formulations of Szemeredi
partitions, sampling and testing of large graphs.Comment: 57 pages. See also http://research.microsoft.com/~borgs/. This
version differs from an earlier version from May 2006 in the organization of
the sections, but is otherwise almost identica
Dependence of ground state energy of classical n-vector spins on n
We study the ground state energy E_G(n) of N classical n-vector spins with
the hamiltonian H = - \sum_{i>j} J_ij S_i.S_j where S_i and S_j are n-vectors
and the coupling constants J_ij are arbitrary. We prove that E_G(n) is
independent of n for all n > n_{max}(N) = floor((sqrt(8N+1)-1) / 2) . We show
that this bound is the best possible. We also derive an upper bound for E_G(m)
in terms of E_G(n), for m<n. We obtain an upper bound on the frustration in the
system, as measured by F(n), which is defined to be (\sum_{i>j} |J_ij| +
E_G(n)) / (\sum_{i>j} |J_ij|). We describe a procedure for constructing a set
of J_ij's such that an arbitrary given state, {S_i}, is the ground state.Comment: 6 pages, 2 figures, submitted to Physical Review
A simulação do real organizacional: O método dos casos como ponte entre o conhecimento tácito e o académico
O desenvolvimento da ciência organizacional tem sido marcado pelo desdobramento de
modas e modelos nas mais diversas áreas. O presente artigo reflecte sobre o seu papel, particularmente,
por via dos estudos de caso. Sendo as escolas de negócios e de gestão um dos actores importantes
na difusão destes modismos, o método dos casos, enquanto estratégia pedagógica, é entendido
aqui como um importante veículo de coordenação entre a investigação científica organizacional e
a sua realidade. Contribui para a aproximação entre os vários intervenientes neste processo (professores,
alunos, gestores, líderes e empresários). Advoga-se a sua importância por estabelecer uma ponte
entre a academia e a o mundo organizacional, entre o conhecimento teórico dos académicos e o
conhecimento tácito dos agentes empresariais.The development of organizational science has been marked by the growth of models
and fashions in different areas. The aim of this article is about it’s role, namely, by the hand of case
studies. Business and management schools are one of important agents in models and fashions diffusion
process. The case method, while pedagogic strategy, is an important vehicle of coordination
between organizational scientific investigation and its reality. It contributes to different actors get
close of each other (teachers, students, managers, leaders, business men). We address the relevance
to build a bridge between the academic world and the organizational one, between the academic
theoretical knowledge and tacit knowledge of organizational managers
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