77 research outputs found
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
Communication tree problems
In this paper, we consider random communication
requirements and several cost
measures for a particular model of tree routing on a
complete network. First
we show that a random tree does not give any approximation.
Then give
approximation algorithms for the case for two random models
of requirements.Postprint (published version
Distributed Approximation of Minimum Routing Cost Trees
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning
Tree in the message passing model with limited bandwidth (CONGEST model). In
this problem one tries to find a spanning tree of a graph over nodes
that minimizes the sum of distances between all pairs of nodes. In the
considered model every node can transmit a different (but short) message to
each of its neighbors in each synchronous round. We provide a randomized
-approximation with runtime for
unweighted graphs. Here, is the diameter of . This improves over both,
the (expected) approximation factor and the runtime
of the best previously known algorithm.
Due to stating our results in a very general way, we also derive an (optimal)
runtime of when considering -approximations as done by the
best previously known algorithm. In addition we derive a deterministic
-approximation
A note on the data-driven capacity of P2P networks
We consider two capacity problems in P2P networks. In the first one, the
nodes have an infinite amount of data to send and the goal is to optimally
allocate their uplink bandwidths such that the demands of every peer in terms
of receiving data rate are met. We solve this problem through a mapping from a
node-weighted graph featuring two labels per node to a max flow problem on an
edge-weighted bipartite graph. In the second problem under consideration, the
resource allocation is driven by the availability of the data resource that the
peers are interested in sharing. That is a node cannot allocate its uplink
resources unless it has data to transmit first. The problem of uplink bandwidth
allocation is then equivalent to constructing a set of directed trees in the
overlay such that the number of nodes receiving the data is maximized while the
uplink capacities of the peers are not exceeded. We show that the problem is
NP-complete, and provide a linear programming decomposition decoupling it into
a master problem and multiple slave subproblems that can be resolved in
polynomial time. We also design a heuristic algorithm in order to compute a
suboptimal solution in a reasonable time. This algorithm requires only a local
knowledge from nodes, so it should support distributed implementations.
We analyze both problems through a series of simulation experiments featuring
different network sizes and network densities. On large networks, we compare
our heuristic and its variants with a genetic algorithm and show that our
heuristic computes the better resource allocation. On smaller networks, we
contrast these performances to that of the exact algorithm and show that
resource allocation fulfilling a large part of the peer can be found, even for
hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio
Spanning trees short or small
We study the problem of finding small trees. Classical network design
problems are considered with the additional constraint that only a specified
number of nodes are required to be connected in the solution. A
prototypical example is the MST problem in which we require a tree of
minimum weight spanning at least nodes in an edge-weighted graph. We show
that the MST problem is NP-hard even for points in the Euclidean plane. We
provide approximation algorithms with performance ratio for the
general edge-weighted case and for the case of points in the
plane. Polynomial-time exact solutions are also presented for the class of
decomposable graphs which includes trees, series-parallel graphs, and bounded
bandwidth graphs, and for points on the boundary of a convex region in the
Euclidean plane. We also investigate the problem of finding short trees, and
more generally, that of finding networks with minimum diameter. A simple
technique is used to provide a polynomial-time solution for finding -trees
of minimum diameter. We identify easy and hard problems arising in finding
short networks using a framework due to T. C. Hu.Comment: 27 page
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