14,906 research outputs found
Globally and Locally Minimal Weight Spanning Tree Networks
The competition between local and global driving forces is significant in a
wide variety of naturally occurring branched networks. We have investigated the
impact of a global minimization criterion versus a local one on the structure
of spanning trees. To do so, we consider two spanning tree structures - the
generalized minimal spanning tree (GMST) defined by Dror et al. [1] and an
analogous structure based on the invasion percolation network, which we term
the generalized invasive spanning tree or GIST. In general, these two
structures represent extremes of global and local optimality, respectively.
Structural characteristics are compared between the GMST and GIST for a fixed
lattice. In addition, we demonstrate a method for creating a series of
structures which enable one to span the range between these two extremes. Two
structural characterizations, the occupied edge density (i.e., the fraction of
edges in the graph that are included in the tree) and the tortuosity of the
arcs in the trees, are shown to correlate well with the degree to which an
intermediate structure resembles the GMST or GIST. Both characterizations are
straightforward to determine from an image and are potentially useful tools in
the analysis of the formation of network structures.Comment: 23 pages, 5 figures, 2 tables, typographical error correcte
A multipopulation parallel genetic simulated annealing based QoS routing and wavelength assignment integration algorithm for multicast in optical networks
Copyright @ 2008 Elsevier B.V. All rights reserved.In this paper, we propose an integrated Quality of Service (QoS) routing algorithm for optical networks. Given a QoS multicast request and the delay interval specified by users, the proposed algorithm can find a flexible-QoS-based cost suboptimal routing tree. The algorithm first constructs the multicast tree based on the multipopulation parallel genetic simulated annealing algorithm, and then assigns wavelengths to the tree based on the wavelength graph. In the algorithm, routing and wavelength assignment are integrated into a single process. For routing, the objective is to find a cost suboptimal multicast tree. For wavelength assignment, the objective is to minimize the delay of the multicast tree, which is achieved by minimizing the number of wavelength conversion. Thus both the cost of multicast tree and the user QoS satisfaction degree can approach the optimal. Our algorithm also considers load balance. Simulation results show that the proposed algorithm is feasible and effective. We also discuss the practical realization mechanisms of the algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant nos. 60673159 and 70671020, the National High-Tech Research and Development Plan of China under Grant no. 2006AA01Z214, Program for New Century Excellent Talents in University, and the Key Project of Chinese Ministry of Education under Grant no. 108040
Connected Spatial Networks over Random Points and a Route-Length Statistic
We review mathematically tractable models for connected networks on random
points in the plane, emphasizing the class of proximity graphs which deserves
to be better known to applied probabilists and statisticians. We introduce and
motivate a particular statistic measuring shortness of routes in a network.
We illustrate, via Monte Carlo in part, the trade-off between normalized
network length and in a one-parameter family of proximity graphs. How close
this family comes to the optimal trade-off over all possible networks remains
an intriguing open question. The paper is a write-up of a talk developed by the
first author during 2007--2009.Comment: Published in at http://dx.doi.org/10.1214/10-STS335 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Spanning Trees in Random Satisfiability Problems
Working with tree graphs is always easier than with loopy ones and spanning
trees are the closest tree-like structures to a given graph. We find a
correspondence between the solutions of random K-satisfiability problem and
those of spanning trees in the associated factor graph. We introduce a modified
survey propagation algorithm which returns null edges of the factor graph and
helps us to find satisfiable spanning trees. This allows us to study
organization of satisfiable spanning trees in the space spanned by spanning
trees.Comment: 12 pages, 5 figures, published versio
- …