14,238 research outputs found
Constraint Generation Algorithm for the Minimum Connectivity Inference Problem
Given a hypergraph , the Minimum Connectivity Inference problem asks for a
graph on the same vertex set as with the minimum number of edges such that
the subgraph induced by every hyperedge of is connected. This problem has
received a lot of attention these recent years, both from a theoretical and
practical perspective, leading to several implemented approximation, greedy and
heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear
Programming (MILP) formulations have been experimented, all representing
connectivity constraints by the means of graph flows. In this work, we
investigate the efficiency of a constraint generation algorithm, where we
iteratively add cut constraints to a simple ILP until a feasible (and optimal)
solution is found. It turns out that our method is faster than the previous
best flow-based MILP algorithm on random generated instances, which suggests
that a constraint generation approach might be also useful for other
optimization problems dealing with connectivity constraints. At last, we
present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur
A knowledge-based system with learning for computer communication network design
Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay
Connectivity measures for internet topologies.
The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;
Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective
Inference and optimization of real-value edge variables in sparse graphs are
studied using the Bethe approximation and replica method of statistical
physics. Equilibrium states of general energy functions involving a large set
of real edge-variables that interact at the network nodes are obtained in
various cases. When applied to the representative problem of network resource
allocation, efficient distributed algorithms are also devised. Scaling
properties with respect to the network connectivity and the resource
availability are found, and links to probabilistic Bayesian approximation
methods are established. Different cost measures are considered and algorithmic
solutions in the various cases are devised and examined numerically. Simulation
results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated,
Figs. 1 to 3 replace
Optimisation of Mobile Communication Networks - OMCO NET
The mini conference “Optimisation of Mobile Communication Networks” focuses on advanced methods for search and optimisation applied to wireless communication networks. It is sponsored by Research & Enterprise Fund Southampton Solent University.
The conference strives to widen knowledge on advanced search methods capable of optimisation of wireless communications networks. The aim is to provide a forum for exchange of recent knowledge, new ideas and trends in this progressive and challenging area. The conference will popularise new successful approaches on resolving hard tasks such as minimisation of transmit power, cooperative and optimal routing
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