28 research outputs found
Distributed Community Detection via Metastability of the 2-Choices Dynamics
We investigate the behavior of a simple majority dynamics on networks of
agents whose interaction topology exhibits a community structure. By leveraging
recent advancements in the analysis of dynamics, we prove that, when the states
of the nodes are randomly initialized, the system rapidly and stably converges
to a configuration in which the communities maintain internal consensus on
different states. This is the first analytical result on the behavior of
dynamics for non-consensus problems on non-complete topologies, based on the
first symmetry-breaking analysis in such setting. Our result has several
implications in different contexts in which dynamics are adopted for
computational and biological modeling purposes. In the context of Label
Propagation Algorithms, a class of widely used heuristics for community
detection, it represents the first theoretical result on the behavior of a
distributed label propagation algorithm with quasi-linear message complexity.
In the context of evolutionary biology, dynamics such as the Moran process have
been used to model the spread of mutations in genetic populations [Lieberman,
Hauert, and Nowak 2005]; our result shows that, when the probability of
adoption of a given mutation by a node of the evolutionary graph depends
super-linearly on the frequency of the mutation in the neighborhood of the node
and the underlying evolutionary graph exhibits a community structure, there is
a non-negligible probability for species differentiation to occur.Comment: Full version of paper appeared in AAAI-1
Step-By-Step Community Detection in Volume-Regular Graphs
Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph).
Recent work (e.g., Becchetti et al., SODA 2017) suggests that observing the temporal evolution of the power method applied to an initial random vector may, at least in some cases, provide enough information on the space spanned by the first two eigenvectors, so as to allow recovery of a hidden partition without explicit eigenvector computations. While the results of Becchetti et al. apply to perfectly balanced partitions and/or graphs that exhibit very strong forms of regularity, we extend their approach to graphs containing a hidden k partition and characterized by a milder form of volume-regularity. We show that the class of k-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k "stepwise" eigenvectors (i.e., vectors that are constant over each set of the hidden partition). To obtain this result, we highlight a connection between volume regularity and lumpability of Markov chains. Moreover, we prove that if the stepwise eigenvectors are those associated to the first k eigenvalues and the gap between the k-th and the (k+1)-th eigenvalues is sufficiently large, the Averaging dynamics of Becchetti et al. recovers the underlying community structure of the graph in logarithmic time, with high probability
Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks
Consider the following process on a network: Each agent initially holds
either opinion blue or red; then, in each round, each agent looks at two random
neighbors and, if the two have the same opinion, the agent adopts it. This
process is known as the 2-Choices dynamics and is arguably the most basic
non-trivial opinion dynamics modeling voting behavior on social networks.
Despite its apparent simplicity, 2-Choices has been analytically characterized
only on networks with a strong expansion property -- under assumptions on the
initial configuration that establish it as a fast majority consensus protocol.
In this work, we aim at contributing to the understanding of the 2-Choices
dynamics by considering its behavior on a class of networks with core-periphery
structure, a well-known topological assumption in social networks. In a
nutshell, assume that a densely-connected subset of agents, the core, holds a
different opinion from the rest of the network, the periphery. Then, depending
on the strength of the cut between the core and the periphery, a
phase-transition phenomenon occurs: Either the core's opinion rapidly spreads
among the rest of the network, or a metastability phase takes place, in which
both opinions coexist in the network for superpolynomial time. The interest of
our result is twofold. On the one hand, by looking at the 2-Choices dynamics as
a simplistic model of competition among opinions in social networks, our
theorem sheds light on the influence of the core on the rest of the network, as
a function of the core's connectivity towards the latter. On the other hand, to
the best of our knowledge, we provide the first analytical result which shows a
heterogeneous behavior of a simple dynamics as a function of structural
parameters of the network. Finally, we validate our theoretical predictions
with extensive experiments on real networks
FAST Approaches to Scalable Similarity-based Test Case Prioritization
Many test case prioritization criteria have been proposed for speeding up fault detection. Among them, similarity-based approaches give priority to the test cases that are the most dissimilar from those already selected. However, the proposed criteria do not scale up to handle the many thousands or even some millions test suite sizes of modern industrial systems and simple heuristics are used instead. We introduce the FAST family of test case prioritization techniques that radically changes this landscape by borrowing algorithms commonly exploited in the big data domain to find similar items. FAST techniques provide scalable similarity-based test case prioritization in both white-box and black-box fashion. The results from experimentation on real world C and Java subjects show that the fastest members of the family outperform other black-box approaches in efficiency with no significant impact on effectiveness, and also outperform white-box approaches, including greedy ones, if preparation time is not counted. A simulation study of scalability shows that one FAST technique can prioritize a million test cases in less than 20 minutes
Biased Opinion Dynamics: When the Devil Is in the Details
We investigate opinion dynamics in multi-agent networks when a bias toward
one of two possible opinions exists; for example, reflecting a status quo vs a
superior alternative. Starting with all agents sharing an initial opinion
representing the status quo, the system evolves in steps. In each step, one
agent selected uniformly at random adopts the superior opinion with some
probability , and with probability it follows an
underlying update rule to revise its opinion on the basis of those held by its
neighbors. We analyze convergence of the resulting process under two well-known
update rules, namely majority and voter. The framework we propose exhibits a
rich structure, with a non-obvious interplay between topology and underlying
update rule. For example, for the voter rule we show that the speed of
convergence bears no significant dependence on the underlying topology, whereas
the picture changes completely under the majority rule, where network density
negatively affects convergence. We believe that the model we propose is at the
same time simple, rich, and modular, affording mathematical characterization of
the interplay between bias, underlying opinion dynamics, and social structure
in a unified setting.Comment: The paper has appeared in the Proceedings of the Twenty-Ninth
International Joint Conference on Artificial Intelligence. The SOLE copyright
holder is IJCAI (International Joint Conferences on Artificial Intelligence),
all rights reserved. Link to the proceedings:
https://www.ijcai.org/Proceedings/2020/
Dynamic algorithms for k-center on graphs
In this paper we give the first efficient algorithms for the -center
problem on dynamic graphs undergoing edge updates. In this problem, the goal is
to partition the input into sets by choosing centers such that the
maximum distance from any data point to the closest center is minimized. It is
known that it is NP-hard to get a better than approximation for this
problem.
While in many applications the input may naturally be modeled as a graph, all
prior works on -center problem in dynamic settings are on metrics. In this
paper, we give a deterministic decremental -approximation
algorithm and a randomized incremental -approximation algorithm,
both with amortized update time for weighted graphs. Moreover, we
show a reduction that leads to a fully dynamic -approximation
algorithm for the -center problem, with worst-case update time that is
within a factor of the state-of-the-art upper bound for maintaining
-approximate single-source distances in graphs. Matching this
bound is a natural goalpost because the approximate distances of each vertex to
its center can be used to maintain a -approximation of the graph
diameter and the fastest known algorithms for such a diameter approximation
also rely on maintaining approximate single-source distances
Step-by-step community detection in volume-regular graphs
International audienceSpectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usuallythe Laplacian matrix of the graph).Recent work (e.g., Becchetti et al., SODA 2017) suggests that observing the temporal evolutionof the power method applied to an initial random vector may, at least in some cases, provide enoughinformation on the space spanned by the first two eigenvectors, so as to allow recovery of a hiddenpartition without explicit eigenvector computations. While the results of Becchetti et al. applyto perfectly balanced partitions and/or graphs that exhibit very strong forms of regularity, weextend their approach to graphs containing a hiddenkpartition and characterized by a milderform of volume-regularity. We show that the class ofk-volume regulargraphs is the largest class ofundirected (possibly weighted) graphs whose transition matrix admitsk“stepwise” eigenvectors (i.e.,vectors that are constant over each set of the hidden partition). To obtain this result, we highlight aconnection between volume regularity and lumpability of Markov chains. Moreover, we prove that ifthe stepwise eigenvectors are those associated to the firstkeigenvalues and the gap between thek-th and the (k+1)-th eigenvalues is sufficiently large, theAveragingdynamics of Becchetti et al.recovers the underlying community structure of the graph in logarithmic time, with high probabi
JTeC: A Large Collection of Java Test Classes for Test Code Analysis and Processing
International audienceThe recent push towards test automation and test-driven development continues to scale up the dimensions of test code that needs to be maintained, analysed, and processed side-by-side with production code. As a consequence, on the one side regression testing techniques, e.g., for test suite prioritization or test case selection, capable to handle such large-scale test suites become indispensable; on the other side, as test code exposes own characteristics, specific techniques for its analysis and refactoring are actively sought. We present JTeC, a large-scale dataset of test cases that researchers can use for benchmarking the above techniques or any other type of tool expressly targeting test code. JTeC collects more than 2.5M test classes belonging to 31K+ GitHub projects and summing up to more than 430 Million SLOCs of ready-to-use real-world test code
Network alignment and similarity reveal atlas-based topological differences in structural connectomes
The interactions between different brain regions can be modeled as a graph, called connectome, whose nodes correspond to parcels from a predefined brain atlas. The edges of the graph encode the strength of the axonal connectivity between regions of the atlas which can be estimated via diffusion Magnetic Resonance Imaging (MRI) tractography. Herein, we aim at providing a novel perspective on the problem of choosing a suitable atlas for structural connectivity studies by assessing how robustly an atlas captures the network topology across different subjects in a homogeneous cohort. We measure this robustness by assessing the alignability of the connectomes, namely the possibility to retrieve graph matchings that provide highly similar graphs. We introduce two novel concepts. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Lehman (WL) graph-isomorphism test.We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available