719,019 research outputs found
A Self-Organization Framework for Wireless Ad Hoc Networks as Small Worlds
Motivated by the benefits of small world networks, we propose a
self-organization framework for wireless ad hoc networks. We investigate the
use of directional beamforming for creating long-range short cuts between
nodes. Using simulation results for randomized beamforming as a guideline, we
identify crucial design issues for algorithm design. Our results show that,
while significant path length reduction is achievable, this is accompanied by
the problem of asymmetric paths between nodes. Subsequently, we propose a
distributed algorithm for small world creation that achieves path length
reduction while maintaining connectivity. We define a new centrality measure
that estimates the structural importance of nodes based on traffic flow in the
network, which is used to identify the optimum nodes for beamforming. We show,
using simulations, that this leads to significant reduction in path length
while maintaining connectivity.Comment: Submitted to IEEE Transactions on Vehicular Technolog
A guided Monte Carlo method for optimization problems
We introduce a new Monte Carlo method by incorporating a guided distribution
function to the conventional Monte Carlo method. In this way, the efficiency of
Monte Carlo methods is drastically improved. To further speed up the algorithm,
we include two more ingredients into the algorithm. First, we freeze the
sub-patterns that have high probability of appearance during the search for
optimal solution, resulting in a reduction of the phase space of the problem.
Second, we perform the simulation at a temperature which is within the optimal
temperature range of the optimization search in our algorithm. We use this
algorithm to search for the optimal path of the traveling salesman problem and
the ground state energy of the spin glass model and demonstrate that its
performance is comparable with more elaborate and heuristic methods.Comment: 4 pages, ReVTe
Hyper-systolic parallel computing
A new class of parallel algorithms is introduced that can achieve a complexity of O(n^3/2) with respect to the interprocessor communication, in the exact computation of systems with pairwise mutual interactions of all elements. Hitherto, conventional methods exhibit a communicational complexity of O(n^2). The amount of computation operations is not altered for the new algorithm which can be formulated as a kind of h-range problem, known from the mathematical field of Additive Number Theory. We will demonstrate the reduction in communicational expense by comparing the standard-systolic algorithm and the new algorithm on the connection machine CM5 and the CRAY T3D. The parallel method can be useful in various scientific and engineering fields like exact n-body dynamics with long range forces, polymer chains, protein folding or signal processing
FPTAS for Weighted Fibonacci Gates and Its Applications
Fibonacci gate problems have severed as computation primitives to solve other
problems by holographic algorithm and play an important role in the dichotomy
of exact counting for Holant and CSP frameworks. We generalize them to weighted
cases and allow each vertex function to have different parameters, which is a
much boarder family and #P-hard for exactly counting. We design a fully
polynomial-time approximation scheme (FPTAS) for this generalization by
correlation decay technique. This is the first deterministic FPTAS for
approximate counting in the general Holant framework without a degree bound. We
also formally introduce holographic reduction in the study of approximate
counting and these weighted Fibonacci gate problems serve as computation
primitives for approximate counting. Under holographic reduction, we obtain
FPTAS for other Holant problems and spin problems. One important application is
developing an FPTAS for a large range of ferromagnetic two-state spin systems.
This is the first deterministic FPTAS in the ferromagnetic range for two-state
spin systems without a degree bound. Besides these algorithms, we also develop
several new tools and techniques to establish the correlation decay property,
which are applicable in other problems
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