46,454 research outputs found
Network correlated data gathering with explicit communication: NP-completeness and algorithms
We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal
Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps
We deal with the problem of maintaining a shortest-path tree rooted at some process r in a network that may be disconnected after topological changes. The goal is then to maintain a shortest-path tree rooted at r in its connected component, V_r, and make all processes of other components detecting that r is not part of their connected component. We propose, in the composite atomicity model, a silent self-stabilizing algorithm for this problem working in semi-anonymous networks under the distributed unfair daemon (the most general daemon) without requiring any a priori knowledge about global parameters of the network. This is the first algorithm for this problem that is proven to achieve a polynomial stabilization time in steps. Namely, we exhibit a bound in O(W_{max} * n_{maxCC}^3 * n), where W_{max} is the maximum weight of an edge, n_{maxCC} is the maximum number of non-root processes in a connected component, and n is the number of processes. The stabilization time in rounds is at most 3n_{maxCC} + D, where D is the hop-diameter of V_r
Caminos Pareto-eficientes en redes: aplicaciones
The problem of finding the path in a network connecting two given nodes,
source and sink, with minimum possible cost is known in the literature as
the shortest path problem (SPP) and it is a core model that lies at the
heart of network optimization. The reason is the wide range of its practical
applications and the large amount of interesting generalizations that can be
considered, among them, the analysis of the multiobjective shortest path
problem. This last model allows us to find how to send a given product
between two specified nodes of a network as quickly, as cheaply and as reliable as possible taking into account the so-called Pareto optimal paths.
The text presented here consists of two chapters. The first one is devoted
to the introduction of some notation and properties related to networks where each arc is associated to just one cost value. The formulation of the SPP as a Mathematical Programming model is considered as well as its corresponding dual problem. The complementary slackness theorem provides us with a characterization of any basic feasible solution as a spanning tree in the original network. A sufficient optimality condition is also derived from this relation. Finally, the Dijkstra algorithm is studied as well as other specific algorithms that use special properties on acyclic networks.
The second chapter extends the hypotheses considered in the previous
one to a multiobjective context. The continuous formulation of the problem
of finding the Pareto optimal paths is compared with its discrete version
and some properties are stated. A generalization of the Dijkstra algorithm
is proposed in order to find the whole set of Pareto optimal solutions. This
procedure allows us to determine that the optimal set of paths corresponds
with a set of adjacent trees. This property is very important in order to
generate the Pareto optimal set of solutions and is the basis of a new improved algorithm that, starting with a given optimal tree, explores its adjacent trees and finds those Pareto optimal ones by using the duality conditions of the complementary slackness theorem presented in the chapter one.Universidad de Sevilla. Grado en MatemĂĄtica
A Superstabilizing -Approximation Algorithm for Dynamic Steiner Trees
In this paper we design and prove correct a fully dynamic distributed
algorithm for maintaining an approximate Steiner tree that connects via a
minimum-weight spanning tree a subset of nodes of a network (referred as
Steiner members or Steiner group) . Steiner trees are good candidates to
efficiently implement communication primitives such as publish/subscribe or
multicast, essential building blocks for the new emergent networks (e.g. P2P,
sensor or adhoc networks). The cost of the solution returned by our algorithm
is at most times the cost of an optimal solution, where is the
group of members. Our algorithm improves over existing solutions in several
ways. First, it tolerates the dynamism of both the group members and the
network. Next, our algorithm is self-stabilizing, that is, it copes with nodes
memory corruption. Last but not least, our algorithm is
\emph{superstabilizing}. That is, while converging to a correct configuration
(i.e., a Steiner tree) after a modification of the network, it keeps offering
the Steiner tree service during the stabilization time to all members that have
not been affected by this modification
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
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