17,699 research outputs found
A dandelion-encoded evolutionary algorithm for the delay-constrained capacitated minimum spanning tree problem
This paper proposes an evolutionary algorithm with Dandelion-encoding to tackle the Delay-Constrained Capacitated Minimum Spanning Tree (DC-CMST) problem. This problem has been recently proposed, and consists of finding several broadcast trees from a source node, jointly considering traffic and delay constraints in trees. A version of the problem in which the source node is also included in the optimization process is considered as well in the paper. The Dandelion code used in the proposed evolutionary algorithm has been recently proposed as an effective way of encoding trees in evolutionary algorithms. Good properties of locality has been reported on this encoding, which makes it very effective to solve problems in which the solutions can be expressed in form of trees. In the paper we describe the main characteristics of the algorithm, the implementation of the Dandelion-encoding to tackled the DC-CMST problem and a modification needed to include the source node in the optimization. In the experimental section of this article we compare the results obtained by our evolutionary with that of a recently proposed heuristic for the DC-CMST. the Least Cost (LC) algorithm. We show that our Dandelion-encoded evolutionary algorithm is able to obtain better results that the LC in all the instances tackled. (C) 2008 Elsevier B.V. All rights reserved
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Improving spanning trees by upgrading nodes
We study budget constrained optimal network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. A general problem in this setting is the following. We are given an edge weighted graph G = (V, E) where nodes represent processors and edges represent bidirectional communication links. The processor at a node v {element_of} V can be upgraded at a cost of c(v). Such an upgrade reduces the delay of each link emanating from v. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has the best performance with respect to some measure. We consider the problem under two measures, namely, the weight of a minimum spanning tree and the bottleneck weight of a minimum bottleneck spanning tree. We present approximation and hardness results for the problem. Our results are tight to within constant factors. We also show that these approximation algorithms can be used to construct good approximation algorithms for the dual versions of the problems where there is a budget constraint on the upgrading cost and the objectives are minimum weight spanning tree and minimum bottleneck weight spanning tree respectively
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Low Cost Quality of Service Multicast Routing in High Speed Networks
Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.
A Hybrid Approach to Quality of Service Multicast Routing
Several multicast routing heuristics have been proposed to support multimedia services, both interactive and distribution, in high speed networks such as B-ISDN/ATM. Since such services may have large numbers of members and have real-time constraints, the objective of the heuristics is to minimise the multicast tree cost while maintaining a bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. We present a detailed analysis and evaluation of some of these heuristics which illustrate that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast/network combination. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the specific efficiency of a heuristics solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our proposal is supported by our evaluation results. We conclude by discussing the types of networks for which this method is most appropriate and identifying further work
Throughput-Optimal Multihop Broadcast on Directed Acyclic Wireless Networks
We study the problem of efficiently broadcasting packets in multi-hop
wireless networks. At each time slot the network controller activates a set of
non-interfering links and forwards selected copies of packets on each activated
link. A packet is considered jointly received only when all nodes in the
network have obtained a copy of it. The maximum rate of jointly received
packets is referred to as the broadcast capacity of the network. Existing
policies achieve the broadcast capacity by balancing traffic over a set of
spanning trees, which are difficult to maintain in a large and time-varying
wireless network. We propose a new dynamic algorithm that achieves the
broadcast capacity when the underlying network topology is a directed acyclic
graph (DAG). This algorithm is decentralized, utilizes local queue-length
information only and does not require the use of global topological structures
such as spanning trees. The principal technical challenge inherent in the
problem is the absence of work-conservation principle due to the duplication of
packets, which renders traditional queuing modelling inapplicable. We overcome
this difficulty by studying relative packet deficits and imposing in-order
delivery constraints to every node in the network. Although in-order packet
delivery, in general, leads to degraded throughput in graphs with cycles, we
show that it is throughput optimal in DAGs and can be exploited to simplify the
design and analysis of optimal algorithms. Our characterization leads to a
polynomial time algorithm for computing the broadcast capacity of any wireless
DAG under the primary interference constraints. Additionally, we propose an
extension of our algorithm which can be effectively used for broadcasting in
any network with arbitrary topology
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