2,916 research outputs found
Coloring random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters and where the
proliferation of metastable states is responsible for the onset of complexity
in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR
Cluster Dynamics for Randomly Frustrated Systems with Finite Connectivity
In simulations of some infinite range spin glass systems with finite
connectivity, it is found that for any resonable computational time, the
saturatedenergy per spin that is achieved by a cluster algorithm is lowered in
comparison to that achieved by Metropolis dynamics.The gap between the average
energies obtained from these two dynamics is robust with respect to variations
of the annealing schedule. For some probability distribution of the
interactions the ground state energy is calculated analytically within the
replica symmetry assumptionand is found to be saturated by a cluster algorithm.Comment: Revtex, 4 pages with 3 figure
Mean Field Behavior of Cluster Dynamics
The dynamic behavior of cluster algorithms is analyzed in the classical mean
field limit. Rigorous analytical results below establish that the dynamic
exponent has the value for the Swendsen-Wang algorithm and
for the Wolff algorithm.
An efficient Monte Carlo implementation is introduced, adapted for using
these algorithms for fully connected graphs. Extensive simulations both above
and below demonstrate scaling and evaluate the finite-size scaling
function by means of a rather impressive collapse of the data.Comment: Revtex, 9 pages with 7 figure
Partitioning and modularity of graphs with arbitrary degree distribution
We solve the graph bi-partitioning problem in dense graphs with arbitrary
degree distribution using the replica method. We find the cut-size to scale
universally with . In contrast, earlier results studying the problem in
graphs with a Poissonian degree distribution had found a scaling with ^1/2
[Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also
generalize to the problem of q-partitioning. They can be used to find the
expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random
graphs and allow for the assessment of statistical significance of the output
of community detection algorithms.Comment: Revised version including new plots and improved discussion of some
mathematical detail
Polynomial iterative algorithms for coloring and analyzing random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters. Furthermore, we
extended our considerations to the case of single instances showing consistent
results. This lead us to propose a new algorithm able to color in polynomial
time random graphs in the hard but colorable region, i.e when .Comment: 23 pages, 10 eps figure
Exact solutions for diluted spin glasses and optimization problems
We study the low temperature properties of p-spin glass models with finite
connectivity and of some optimization problems. Using a one-step functional
replica symmetry breaking Ansatz we can solve exactly the saddle-point
equations for graphs with uniform connectivity. The resulting ground state
energy is in perfect agreement with numerical simulations. For fluctuating
connectivity graphs, the same Ansatz can be used in a variational way: For
p-spin models (known as p-XOR-SAT in computer science) it provides the exact
configurational entropy together with the dynamical and static critical
connectivities (for p=3, \gamma_d=0.818 and \gamma_s=0.918 resp.), whereas for
hard optimization problems like 3-SAT or Bicoloring it provides new upper
bounds for their critical thresholds (\gamma_c^{var}=4.396 and
\gamma_c^{var}=2.149 resp.).Comment: 4 pages, 1 figure, accepted for publication in PR
A constructively critical review of change and innovation-related concepts: Towards conceptual and operational clarity
The aim of this paper is to examine and clarify the nomological network of change and innovation (CI)-related constructs. A literature review in this field revealed a number of interrelated constructs that have emerged over the last decades. We examine several such constructsâinnovation, creativity, proactive behaviours, job crafting, voice, taking charge, personal initiative, submitting suggestions, and extra-role behaviours. Our conceptual analysis suggests each one of these constructs represents a specific component of CI-related behaviours. However, we also found that on occasion these concepts have been dysfunctionally operationalized with evidence of three dysfunctional effects: (a) construct confusion, (b) construct drift, and (c) construct contamination. Challenges for future research to enhance conceptual and operational clarity are discussed.This paper was supported by the British Academy: [Grant number SG110409] awarded to the first author and by UK Leverhulme Trust: [Grant number IN-2012-095] awarded to the second author
The most creative organization in the world? The BBC, 'creativity' and managerial style
The managerial styles of two BBC directors-general, John Birt and Greg Dyke, have often been contrasted but not so far analysed from the perspective of their different views of 'creative management'. This article first addresses the orthodox reading of 'Birtism'; second, it locates Dyke's 'creative' turn in the wider context of fashionable neo-management theory and UK government creative industries policy; third, it details Dyke's drive to change the BBC's culture; and finally, it concludes with some reflections on the uncertainties inherent in managing a creative organisation
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