D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), 45--58.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Network Upgrading 6. 1 Introduction Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at certain nodes or edges of the network [Ber92,Phi93,PS95,KN 96d] Consider the following scenario which best illustrates the type of problems we investigate. A large communication company is approached by a client with the requirement to interconnect a set of cities housing the client s offices (e.g. banks with high transaction rates between ....

....nice property that the running time increases only by a factor of O(log n) while the other way round we get a factor of O(log K) where K = P v2V c(v) 6. 4 Related Work The node upgrading model used in this chapter generalizes a model which was introduced in a recent paper by Paik and Sahni [PS95] In the model from [PS95] we are given a graph G = V; E) and a nonnegative delay function d on the edges of G. When a node v is upgraded, the delay of each edge incident on v decreases by a fixed factor ae, where 0 ae 1. Thus, if e = v; u) is an edge, its delay after upgrading exactly one ....

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D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), 45--58.

....from the node. In signal flow networks used in VLSI design, upgrading a node corresponds to replacing a circuit module at the node by a functionally equivalent module containing suitable drivers. Such an upgrade decreases the signal transmission delay along the wires connected to the module [PS95] Usually, there is a cost associated with upgrading a node, and this motivates the study of problems of the following type: find an upgrading set of minimum cost so that the resulting network satisfies certain performance requirements. The performance of the upgraded network can be quantified ....

....c(v) Given a set W V of vertices, denote by dW the edge weight function resulting from the upgrade of the vertices in W; that is, for an edge (u; v) 2 E dW (u; v) d i (u; v) where i = jW fu; vgj. Our model is a generalization of the node upgrade model introduced by Paik and Sahni in [PS95] In their model, the reduction in edge weight resulting from an upgrade of nodes is determined by a constant 0 ff 1 in the following way: if exactly one endpoint of an edge is upgraded, then its weight is reduced by the factor ff; if both endpoints are upgraded, the weight is reduced by the ....

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D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), 45--58.

....a computed network from scratch exceeds the cost of modifying an already installed network. There are two main models for network upgrading problems: the edge upgrading model [Ber92, Phi93, KN 96] where upgrading an edge reduces the delay on the upgraded edge, and the node upgrading model [PS95, KM 97] where upgrading a node reduces the delay on all edges incident with the upgraded node. In communication networks, upgrading a node corresponds to installing faster communication equipment at an exchange point which results in a speedup of all links leading through that node. In this ....

....hardness result within a constant factor. Our results presented in this paper generalize results provided in [KM 97] where similar problems for the special case of spanning trees were investigated. 2 Preliminaries The node based upgrading model used in this paper generalizes the model from [PS95] and was introduced in [KM 97] It can be formally described as follows. Let G = V; E) be a connected undirected graph with n : jV j vertices and m : jEj edges. For each edge e 2 E, we are given three integers d 0 (e) d 1 (e) d 2 (e) 0. The value d i (e) represents the weight or delay ....

D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), 45--58. 13

....from the node. In signal flow networks used in VLSI design, upgrading a node corresponds to replacing a circuit module at the node by a functionally equivalent module containing suitable drivers. Such an upgrade decreases the signal transmission delay along the wires connected to the module [PS95] Usually, there is a cost associated with upgrading a node, and this motivates the study of problems of the following type: find an upgrading set of minimum cost so that the resulting network satisfies certain performance requirements. The performance of the upgraded network can be quantified ....

....c(v) Given a set W V of vertices, denote by dW the edge weight function resulting from the upgrade of the vertices in W; that is, for an edge (u; v) 2 E dW (u; v) d i (u; v) where i = jW fu; vgj. Our model is a generalization of the node upgrade model introduced by Paik and Sahni in [PS95] In their model, the reduction in edge weight resulting from an upgrade of nodes is determined by a constant 0 ff 1 in the following way: if exactly one endpoint of an edge is upgraded, then its weight is reduced by the factor ff; if both endpoints are upgraded, the weight is reduced by the ....

[Article contains additional citation context not shown here]

D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), 45--58.

....Algorithms 1. Introduction and Motivation Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at certain nodes and or edges of the network [7, 19, 21, 13, 14]. Consider the following scenario which best illustrates the type of problems we investigate. A large communication company is approached by a client with the 2 requirement to interconnect a set of cities housing the client s oces (e.g. banks with high transaction rates between branches) The ....

....of bicriteria problems. Recently, there has been substantial work on nding ecient approximation algorithms for a variety of bicriteria problems (see [15, 11, 18, 25, 24, 26] and the references cited therein) Some node upgrading problems have been studied under a simpler model by Paik and Sahni [21]. In their model, upgrading a node causes the delay of each edge incident on that node to be reduced by a given constant factor 1. When both end points of an edge are upgraded, the delay of the edge is reduced by the factor 2 . It is easy to see that this model is a special case of the model ....

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D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), pp. 45-58.

....Due to space limitations, the remainder of this paper discusses mainly the algorithm mentioned in Theorem 6 above. Proofs of other results will appear in a complete version of this paper. 1. 4 Related Work Some node upgrading problems have been investigated under a simpler model by Paik and Sahni [9]. In their model, the delay of an edge is decreased by constant factors of ffi or ffi 2 , when one or two of its endpoints are upgraded, respectively. Clearly, this model is a special case of the model treated in our paper. Under their model, Paik and Sahni studied the upgrading problem for ....

D. Paik and S. Sahni, "Network Upgrading Problems," Networks, Vol. 26, 1995, pp. 45--58.

....NY 12222, USA. Email: ravi cs.albany.edu. 1 Introduction Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at some nodes of the network [24]. In communication networks, upgrading a node corresponds to installing faster communication equipment at that node. Such an upgrade reduces the communication delay along each edge emanating from the node. In signal flow networks used in VLSI design, upgrading a node corresponds to replacing a ....

....node. In signal flow networks used in VLSI design, upgrading a node corresponds to replacing a circuit module at the node by a functionally equivalent module containing suitable drivers. Such an upgrade decreases the signal transmission delay along the wires connected to the module. Paik and Sahni [24] investigate several node upgrading problems. They present complexity results for general networks and efficient algorithms for special classes of networks. In this paper we investigate the complexity and approximability of the following upgrading problem: We are given a network where nodes ....

[Article contains additional citation context not shown here]

D. Paik and S. Sahni, "Network Upgrading Problems," Networks, Vol. 26, 1995, pp. 45--58.

....Algorithms 1. Introduction and Motivation Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at certain nodes and or edges of the network [7, 19, 21, 13, 14]. Consider the following scenario which best illustrates the type of problems we investigate. A large communication company is approached by a client with the 2 requirement to interconnect a set of cities housing the client s offices (e.g. banks with high transaction rates between branches) The ....

....bicriteria problems. Recently, there has been substantial work on finding efficient approximation algorithms for a variety of bicriteria problems (see [15, 11, 18, 25, 24, 26] and the references cited therein) Some node upgrading problems have been studied under a simpler model by Paik and Sahni [21]. In their model, upgrading a node causes the delay of each edge incident on that node to be reduced by a given constant factor ffi 1. When both end points of an edge are upgraded, the delay of the edge is reduced by the factor ffi 2 . It is easy to see that this model is a special case of ....

[Article contains additional citation context not shown here]

D. Paik and S. Sahni, Network upgrading problems, Networks 26 (1995), pp. 45--58.

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