18,005 research outputs found
Graph Matching via Sequential Monte Carlo
International audienceGraph matching is a powerful tool for computer vision and machine learning. In this paper, a novel approach to graph matching is developed based on the sequential Monte Carlo framework. By constructing a sequence of intermediate target distributions, the proposed algorithm sequentially performs a sampling and importance resampling to maximize the graph matching objective. Through the sequential sampling procedure, the algorithm effectively collects potential matches under one-to-one matching constraints to avoid the adverse effect of outliers and deformation. Experimental evaluations on synthetic graphs and real images demonstrate its higher robustness to deformation and outliers
Approximating the monomer-dimer constants through matrix permanent
The monomer-dimer model is fundamental in statistical mechanics. However, it
is #P-complete in computation, even for two dimensional problems. A
formulation in matrix permanent for the partition function of the monomer-dimer
model is proposed in this paper, by transforming the number of all matchings of
a bipartite graph into the number of perfect matchings of an extended bipartite
graph, which can be given by a matrix permanent. Sequential importance sampling
algorithm is applied to compute the permanents. For two-dimensional lattice
with periodic condition, we obtain , where the exact value is
. For three-dimensional lattice with periodic condition,
our numerical result is , {which agrees with the best known
bound .}Comment: 6 pages, 2 figure
Forest resampling for distributed sequential Monte Carlo
This paper brings explicit considerations of distributed computing
architectures and data structures into the rigorous design of Sequential Monte
Carlo (SMC) methods. A theoretical result established recently by the authors
shows that adapting interaction between particles to suitably control the
Effective Sample Size (ESS) is sufficient to guarantee stability of SMC
algorithms. Our objective is to leverage this result and devise algorithms
which are thus guaranteed to work well in a distributed setting. We make three
main contributions to achieve this. Firstly, we study mathematical properties
of the ESS as a function of matrices and graphs that parameterize the
interaction amongst particles. Secondly, we show how these graphs can be
induced by tree data structures which model the logical network topology of an
abstract distributed computing environment. Thirdly, we present efficient
distributed algorithms that achieve the desired ESS control, perform resampling
and operate on forests associated with these trees
Parameterized Distributed Algorithms
In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds.
Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2
On Designing Multicore-aware Simulators for Biological Systems
The stochastic simulation of biological systems is an increasingly popular
technique in bioinformatics. It often is an enlightening technique, which may
however result in being computational expensive. We discuss the main
opportunities to speed it up on multi-core platforms, which pose new challenges
for parallelisation techniques. These opportunities are developed in two
general families of solutions involving both the single simulation and a bulk
of independent simulations (either replicas of derived from parameter sweep).
Proposed solutions are tested on the parallelisation of the CWC simulator
(Calculus of Wrapped Compartments) that is carried out according to proposed
solutions by way of the FastFlow programming framework making possible fast
development and efficient execution on multi-cores.Comment: 19 pages + cover pag
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