Results 1  10
of
64
A quantitative comparison of graphbased models for internet topology
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and ..."
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Cited by 226 (3 self)
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Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly generated topologies. While many researchers rely upon graphs for analytic and simulation studies, there has been little analysis of the implications of using a particular model, or how the graph generation method may a ect the results of such studies. Further, the selection of one generation method over another is often arbitrary, since the differences and similarities between methods are not well understood. This paper considers the problem of generating and selecting graph models that reflect the properties of real internetworks. We review generation methods in common use, and also propose several new methods. We consider a set of metrics that characterize the graphs produced by a method, and we quantify similarities and differences amongst several generation methods with respect to these metrics. We also consider the effect of the graph model in the context of a speciffic problem, namely multicast routing.
Simultaneous Optimization for Concave Costs: Single Sink Aggregation or Single Source BuyatBulk
 In Proc. of the 14 th Symposium on Discrete Algorithms (SODA
, 2003
"... We consider the problem of finding efficient trees to send information from k sources to a single sink in a network where information can be aggregated at intermediate nodes in the tree. Specifically, we assume that if information from j sources is traveling over a link, the total information tha ..."
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Cited by 103 (3 self)
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We consider the problem of finding efficient trees to send information from k sources to a single sink in a network where information can be aggregated at intermediate nodes in the tree. Specifically, we assume that if information from j sources is traveling over a link, the total information that needs to be transmitted is f(j). One natural and important (though not necessarily comprehensive) class of functions is those which are concave, nondecreasing, and satisfy f(0) = 0. Our goal is to find a tree which is a good approximation simultaneously to the optimum trees for all such functions. This problem is motivated by aggregation in sensor networks, as well as by buyatbulk network design.
On Network Correlated Data Gathering
 IN IEEE INFOCOM
, 2004
"... We consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a SlepianWolf ..."
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Cited by 100 (9 self)
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We consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a SlepianWolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. This problem requires a joint optimization of the rate allocation at the nodes and of the transmission structure. For the SlepianWolf setting, we derive a closed form solution and an efficient distributed approximation algorithm with a good performance. For the explicit communication case, we prove that building an optimal data gathering tree is NPcomplete and we propose various distributed approximation algorithms.
Bicriteria network design problems
 In Proc. 22nd Int. Colloquium on Automata, Languages and Programming
, 1995
"... 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 subgraphclass that minimizes ..."
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Cited by 75 (13 self)
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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 subgraphclass 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 polynomialtime 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 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 clusterbased approach to devise a approximation algorithms — the solutions output violate
CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Cited by 60 (7 self)
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
A constant factor approximation for the single sink edge installation problems
 In Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing (STOC
, 2001
"... We present the first constant approximation to the single sink buyatbulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a ..."
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Cited by 59 (1 self)
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We present the first constant approximation to the single sink buyatbulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(log R), where R is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant load balanced facility location, and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor.
NearOptimal Critical Sink Routing Tree Constructions
, 1995
"... We present criticalsink routing tree (CSRT) constructions which exploit available criticalpath information to yield highperformance routing trees. Our CSSteiner and "Global Slack Removal" algorithms together modify traditional Steiner tree constructions to optimize signal delay at id ..."
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Cited by 52 (13 self)
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We present criticalsink routing tree (CSRT) constructions which exploit available criticalpath information to yield highperformance routing trees. Our CSSteiner and "Global Slack Removal" algorithms together modify traditional Steiner tree constructions to optimize signal delay at identified critical sinks. We further propose an iterative Elmore routing tree (ERT) construction which optimizes Elmore delay directly, as opposed to heuristically abstracting linear or Elmore delay as in previous approaches. Extensive timing simulations on industry IC and MCM interconnect parameters show that our methods yield trees that significantly improve (by averages of up to 67%) over minimum Steiner routings in terms of delays to identified critical sinks. ERTs also serve as generic highperformance routing trees when no critical sink is specified: for 8sink nets in standard IC (MCM) technology, we improve average sink delay by 19% (62%) and maximum sink delay by 22% (52%) over the mini...
Many birds with one stone: Multiobjective approximation algorithms
, 1992
"... We study networkdesign problems with multiple design objectives. In particular, we look at two cost measures to be minimized simultaneously: the total cost of the network and the maximum degree of any node in the network. Our main result can be roughly stated as follows: given an integer b, we p ..."
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Cited by 52 (12 self)
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We study networkdesign problems with multiple design objectives. In particular, we look at two cost measures to be minimized simultaneously: the total cost of the network and the maximum degree of any node in the network. Our main result can be roughly stated as follows: given an integer b, we present approximation algorithms for a variety of networkdesign problems on an n node graph in which the degree of the output network is O(b log( n b )) and the cost of this network is O(log n) times that of the minimumcost degreebbounded network. These algorithms can handle costs on nodes as well as edges. Moreover, we can construct such networks so as to satisfy a variety of connectivity specifications including spanning trees, Steiner trees and generalized Steiner forests. The performance guarantee on the cost of the output network is nearly bestpossible unless NP = ~ P . We also address the special case in which the costs obey the triangle inequality. In this case, we obtai...
Designing Networks with Bounded Pairwise Distance
"... We study the following network design problem: Given a communication network, find a minimum cost subset of missing links such that adding these links to the network makes every pair of points within distance at most d from each other. Theproblemhasbeenstudied earlier[17]undertheassumptionthatallli ..."
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Cited by 48 (0 self)
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We study the following network design problem: Given a communication network, find a minimum cost subset of missing links such that adding these links to the network makes every pair of points within distance at most d from each other. Theproblemhasbeenstudied earlier[17]undertheassumptionthatalllinkcostsas wellaslinklengthsareidentical,andwasshowntobe (logn)hardforeveryd4. Wepresentanovellinearprogrammingbasedapproachtoobtainan O(lognlogd)approximationalgorithmforthecaseofuniform linklengthsandcosts. We alsoextendthe(logn)hardnesstod2f2;3g. On the otherhand,iflinkcostscanvary, weshowthattheproblemis(2log1�n)hardford3. Thisversionofour problemcanbeviewedasaspecialcaseoftheminimum cost dspannerproblemandthusourhardnessresultappliesthereaswell. Ford=2,however,weshowthatthe problemcontinuestobeO(logn)approximablebygivingan O(logn)approximationtothemoregeneralminimumcost2spannerproblem.An(2log1�n)hardness resultalsoholdswhenalllinkcostsareidenticalbutlink lengthsmayvary(appliesevenwhenalllengthsare1or