62,247 research outputs found
On the complexity of the dual method for maximum balanced flows
AbstractIn an earlier paper we develop a quite general dual method and apply it to balanced submodular flow problems with flow values in modules. Here, we analyze that method for the particular case of balanced flows with rational or integral flow values in more detail. While, for integral flows, the general problem turns out to be NP-hard, the method is strongly polynomial for rational as well as for integral flows when applied to the motivating reliability problem given by Minoux. In that case, a maximum balanced flow is determined in O(m · M(m, n)), where M(m, n) is the complexity of some maxflow procedure for a network with n vertices and m arcs
Maximum Skew-Symmetric Flows and Matchings
The maximum integer skew-symmetric flow problem (MSFP) generalizes both the
maximum flow and maximum matching problems. It was introduced by Tutte in terms
of self-conjugate flows in antisymmetrical digraphs. He showed that for these
objects there are natural analogs of classical theoretical results on usual
network flows, such as the flow decomposition, augmenting path, and max-flow
min-cut theorems. We give unified and shorter proofs for those theoretical
results.
We then extend to MSFP the shortest augmenting path method of Edmonds and
Karp and the blocking flow method of Dinits, obtaining algorithms with similar
time bounds in general case. Moreover, in the cases of unit arc capacities and
unit ``node capacities'' the blocking skew-symmetric flow algorithm has time
bounds similar to those established in Even and Tarjan (1975) and Karzanov
(1973) for Dinits' algorithm. In particular, this implies an algorithm for
finding a maximum matching in a nonbipartite graph in time,
which matches the time bound for the algorithm of Micali and Vazirani. Finally,
extending a clique compression technique of Feder and Motwani to particular
skew-symmetric graphs, we speed up the implied maximum matching algorithm to
run in time, improving the best known bound
for dense nonbipartite graphs.
Also other theoretical and algorithmic results on skew-symmetric flows and
their applications are presented.Comment: 35 pages, 3 figures, to appear in Mathematical Programming, minor
stylistic corrections and shortenings to the original versio
Reflection methods for user-friendly submodular optimization
Recently, it has become evident that submodularity naturally captures widely
occurring concepts in machine learning, signal processing and computer vision.
Consequently, there is need for efficient optimization procedures for
submodular functions, especially for minimization problems. While general
submodular minimization is challenging, we propose a new method that exploits
existing decomposability of submodular functions. In contrast to previous
approaches, our method is neither approximate, nor impractical, nor does it
need any cumbersome parameter tuning. Moreover, it is easy to implement and
parallelize. A key component of our method is a formulation of the discrete
submodular minimization problem as a continuous best approximation problem that
is solved through a sequence of reflections, and its solution can be easily
thresholded to obtain an optimal discrete solution. This method solves both the
continuous and discrete formulations of the problem, and therefore has
applications in learning, inference, and reconstruction. In our experiments, we
illustrate the benefits of our method on two image segmentation tasks.Comment: Neural Information Processing Systems (NIPS), \'Etats-Unis (2013
Structural models and structural change: analytical principles and methodological issues
Structural analysis is the main topic of this paper and structural change is a dominant theme of the present work. The analysis of structural models and of theories of structural changes carried out in this paper has a double meaning. On the one hand, it allows to pick up several essential principles that characterize these models, on the other hand, it should allow us to reconsider some important methodological issues under a new light, such as different methods of decomposition of the productive systems, the problem of complexity and the strategies to reduce complexity. Moreover, the paper tries to compare Quesnay’s Tableau, taken as a benchmark model, with Leontief’s, von Neumann’s and Sraffa’s models to pick up the different features of these models with respect to his theoretical framework and also to identify their characteristics for structural analysis and structural change.
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Robust capacitated trees and networks with uniform demands
We are interested in the design of robust (or resilient) capacitated rooted
Steiner networks in case of terminals with uniform demands. Formally, we are
given a graph, capacity and cost functions on the edges, a root, a subset of
nodes called terminals, and a bound k on the number of edge failures. We first
study the problem where k = 1 and the network that we want to design must be a
tree covering the root and the terminals: we give complexity results and
propose models to optimize both the cost of the tree and the number of
terminals disconnected from the root in the worst case of an edge failure,
while respecting the capacity constraints on the edges. Second, we consider the
problem of computing a minimum-cost survivable network, i.e., a network that
covers the root and terminals even after the removal of any k edges, while
still respecting the capacity constraints on the edges. We also consider the
possibility of protecting a given number of edges. We propose three different
formulations: a cut-set based formulation, a flow based one, and a bilevel one
(with an attacker and a defender). We propose algorithms to solve each
formulation and compare their efficiency
Petascale turbulence simulation using a highly parallel fast multipole method on GPUs
This paper reports large-scale direct numerical simulations of
homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08
petaflop/s on gpu hardware using single precision. The simulations use a vortex
particle method to solve the Navier-Stokes equations, with a highly parallel
fast multipole method (FMM) as numerical engine, and match the current record
in mesh size for this application, a cube of 4096^3 computational points solved
with a spectral method. The standard numerical approach used in this field is
the pseudo-spectral method, relying on the FFT algorithm as numerical engine.
The particle-based simulations presented in this paper quantitatively match the
kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted
code. In terms of parallel performance, weak scaling results show the fmm-based
vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per
mpi process, 3 gpus per node of the TSUBAME-2.0 system). The FFT-based spectral
method is able to achieve just 14% parallel efficiency on the same number of
mpi processes (using only cpu cores), due to the all-to-all communication
pattern of the FFT algorithm. The calculation time for one time step was 108
seconds for the vortex method and 154 seconds for the spectral method, under
these conditions. Computing with 69 billion particles, this work exceeds by an
order of magnitude the largest vortex method calculations to date
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