113,821 research outputs found
Parameterized TSP: Beating the Average
In the Travelling Salesman Problem (TSP), we are given a complete graph
together with an integer weighting on the edges of , and we are asked
to find a Hamilton cycle of of minimum weight. Let denote the
average weight of a Hamilton cycle of for the weighting . Vizing
(1973) asked whether there is a polynomial-time algorithm which always finds a
Hamilton cycle of weight at most . He answered this question in the
affirmative and subsequently Rublineckii (1973) and others described several
other TSP heuristics satisfying this property. In this paper, we prove a
considerable generalisation of Vizing's result: for each fixed , we give an
algorithm that decides whether, for any input edge weighting of ,
there is a Hamilton cycle of of weight at most (and constructs
such a cycle if it exists). For fixed, the running time of the algorithm is
polynomial in , where the degree of the polynomial does not depend on
(i.e., the generalised Vizing problem is fixed-parameter tractable with respect
to the parameter )
Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm
The identification of different homogeneous groups of observations and their
appropriate analysis in PLS-SEM has become a critical issue in many appli-
cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all
units on which the model is estimated, and approaches of segmentation present
in literature, consist in estimating separate models for each segments of
statistical units, which have been obtained either by assigning the units to
segments a priori defined. However, these approaches are not fully accept- able
because no causal structure among the variables is postulated. In other words,
a modeling approach should be used, where the obtained clusters are homogeneous
with respect to the structural causal relationships. In this paper, a new
methodology for simultaneous non-hierarchical clus- tering and PLS-SEM is
proposed. This methodology is motivated by the fact that the sequential
approach of applying first SEM or PLS-SEM and second the clustering algorithm
such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the
correct clustering structure existing in the data. A simulation study and an
application on real data are included to evaluate the performance of the
proposed methodology
Scaling Algorithms for Unbalanced Transport Problems
This article introduces a new class of fast algorithms to approximate
variational problems involving unbalanced optimal transport. While classical
optimal transport considers only normalized probability distributions, it is
important for many applications to be able to compute some sort of relaxed
transportation between arbitrary positive measures. A generic class of such
"unbalanced" optimal transport problems has been recently proposed by several
authors. In this paper, we show how to extend the, now classical, entropic
regularization scheme to these unbalanced problems. This gives rise to fast,
highly parallelizable algorithms that operate by performing only diagonal
scaling (i.e. pointwise multiplications) of the transportation couplings. They
are generalizations of the celebrated Sinkhorn algorithm. We show how these
methods can be used to solve unbalanced transport, unbalanced gradient flows,
and to compute unbalanced barycenters. We showcase applications to 2-D shape
modification, color transfer, and growth models
Varieties of Limited Access Orders: The nexus between politics and economics in hybrid regimes
This article advances our understanding of differences in hybrid stability by going beyond existing regime typologies that separate the study of political institutions from the study of economic institutions. It combines the work of Douglass North, John Wallis, and Barry Weingast (NWW) on varieties of social orders with the literature on political and economic regime typologies and dynamics to understand hybrid regimes as Limited Access Orders (LAOs) that differ in the way dominant elites limit access to political and economic resources. Based on a measurement of political and economic access applied to seven post‐Soviet states, the article identifies four types of LAOs. Challenging NWW's claim, it shows that hybrid regimes can combine different degrees of political and economic access to sustain stability. Our typology allows to form theoretical expectations about the kinds of political and/or economic changes that will move different types of LAOs toward more openness or closure
Efficient Computation of Sensitivity Coefficients of Node Voltages and Line Currents in Unbalanced Radial Electrical Distribution Networks
The problem of optimal control of power distribution systems is becoming
increasingly compelling due to the progressive penetration of distributed
energy resources in this specific layer of the electrical infrastructure.
Distribution systems are, indeed, experiencing significant changes in terms of
operation philosophies that are often based on optimal control strategies
relying on the computation of linearized dependencies between controlled (e.g.
voltages, frequency in case of islanding operation) and control variables (e.g.
power injections, transformers tap positions). As the implementation of these
strategies in real-time controllers imposes stringent time constraints, the
derivation of analytical dependency between controlled and control variables
becomes a non-trivial task to be solved. With reference to optimal voltage and
power flow controls, this paper aims at providing an analytical derivation of
node voltage and line current flows as a function of the nodal power injections
and transformers tap-changers positions. Compared to other approaches presented
in the literature, the one proposed here is based on the use of the [Y]
compound matrix of a generic multi-phase radial unbalanced network. In order to
estimate the computational benefits of the proposed approach, the relevant
improvements are also quantified versus traditional methods. The validation of
the proposed method is carried out by using both IEEE 13 and 34 node test
feeders. The paper finally shows the use of the proposed method for the problem
of optimal voltage control applied to the IEEE 34 node test feeder.Comment: accepted for publication to IEEE Transactions on Smart Gri
- …