22,970 research outputs found
A Model of Optimal Network Structure for Decentralized Nearest Neighbor Search
One of the approaches for the nearest neighbor search problem is to build a
network which nodes correspond to the given set of indexed objects. In this
case the search of the closest object can be thought as a search of a node in a
network. A procedure in a network is called decentralized if it uses only local
information about visited nodes and its neighbors. Networks, which structure
allows efficient performing the nearest neighbour search by a decentralised
search procedure started from any node, are of particular interest especially
for pure distributed systems. Several algorithms that construct such networks
have been proposed in literature. However, the following questions arise: "Are
there network models in which decentralised search can be performed faster?";
"What are the optimal networks for the decentralised search?"; "What are their
properties?". In this paper we partially give answers to these questions. We
propose a mathematical programming model for the problem of determining an
optimal network structure for decentralized nearest neighbor search. We have
found an exact solution for a regular lattice of size 4x4 and heuristic
solutions for sizes from 5x5 to 7x7. As a distance function we use L1 , L2 and
L_inf metrics. We hope that our results and the proposed model will initiate
study of optimal network structures for decentralised nearest neighbour search
Simplicial Homology for Future Cellular Networks
Simplicial homology is a tool that provides a mathematical way to compute the
connectivity and the coverage of a cellular network without any node location
information. In this article, we use simplicial homology in order to not only
compute the topology of a cellular network, but also to discover the clusters
of nodes still with no location information. We propose three algorithms for
the management of future cellular networks. The first one is a frequency
auto-planning algorithm for the self-configuration of future cellular networks.
It aims at minimizing the number of planned frequencies while maximizing the
usage of each one. Then, our energy conservation algorithm falls into the
self-optimization feature of future cellular networks. It optimizes the energy
consumption of the cellular network during off-peak hours while taking into
account both coverage and user traffic. Finally, we present and discuss the
performance of a disaster recovery algorithm using determinantal point
processes to patch coverage holes
An algebraic framework for the greedy algorithm with applications to the core and Weber set of cooperative games
An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in . This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory. As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model. \u
Submodular linear programs on forests
A general linear programming model for an order-theoretic analysis of both Edmonds' greedy algorithm for matroids and the NW-corner rule for transportation problems with Monge costs is introduced. This approach includes the model of Queyranne, Spieksma and Tardella (1993) as a special case. We solve the problem by optimal greedy algorithms for rooted forests as underlying structures. Other solvable cases are also discussed
Certified data-driven physics-informed greedy auto-encoder simulator
A parametric adaptive greedy Latent Space Dynamics Identification (gLaSDI)
framework is developed for accurate, efficient, and certified data-driven
physics-informed greedy auto-encoder simulators of high-dimensional nonlinear
dynamical systems. In the proposed framework, an auto-encoder and dynamics
identification models are trained interactively to discover intrinsic and
simple latent-space dynamics. To effectively explore the parameter space for
optimal model performance, an adaptive greedy sampling algorithm integrated
with a physics-informed error indicator is introduced to search for optimal
training samples on the fly, outperforming the conventional predefined uniform
sampling. Further, an efficient k-nearest neighbor convex interpolation scheme
is employed to exploit local latent-space dynamics for improved predictability.
Numerical results demonstrate that the proposed method achieves 121 to 2,658x
speed-up with 1 to 5% relative errors for radial advection and 2D Burgers
dynamical problems.Comment: arXiv admin note: substantial text overlap with arXiv:2204.1200
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