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120
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of t ..."
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Cited by 147 (12 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 134 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and finds applications in VLSI design. The group Steiner tree problem generalizes the set covering problem, and is therefore at least as had. We give a randomized O(log 3 n log k)approximation algorithm for the group Steiner tree problem on an nnode graph, where k is the number of groups. The best previous ink)v/ (Bateman, Helvig, performance guarantee was (1 +  Robins and Zelikovsky).
Nearoptimal network design with selfish agents
 IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC
, 2003
"... We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possi ..."
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Cited by 121 (21 self)
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We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possible edges in the network have costs and each agent’s goal is to pay as little as possible. Determining whether or not a Nash equilibrium exists in this game is NPcomplete. However, when the goal of each player is to connect a terminal to a common source, we prove that there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithm to find a (1 + ε)approximate Nash equilibrium that does not cost much more. For the general connection game we prove that there is a 3approximate Nash equilibrium that is as cheap as the optimal network, and give an algorithm to find a (4.65 + ε)approximate Nash equilibrium that does not cost much more.
MinimumCost Multicast over Coded Packet Networks
 IEEE TRANS. ON INF. THE
, 2006
"... We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as b ..."
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Cited by 110 (28 self)
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We consider the problem of establishing minimumcost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomialtime solvable optimization problem, ... and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimumcost multicast. By contrast, establishing minimumcost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
Achieving MinimumCost Multicast: A Decentralized Approach Based on Network Coding
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumco ..."
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Cited by 86 (14 self)
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We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumcost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixedrate multicast in networks with directed pointtopoint links, and consider the problem of minimumenergy multicast in wireless networks as well as the case of a concave utility function at the sender.
Towards Compressing Web Graphs
 In Proc. of the IEEE Data Compression Conference (DCC
, 2000
"... In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web. ..."
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Cited by 80 (1 self)
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In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web.
Approximating minimum cost connectivity problems
 58 in Approximation algorithms and Metaheuristics, Editor
, 2007
"... ..."
Network Coding with a Cost Criterion
 in Proc. 2004 International Symposium on Information Theory and its Applications (ISITA 2004
, 2004
"... We consider applying network coding in settings where there is a cost associated with network use. ..."
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Cited by 61 (16 self)
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We consider applying network coding in settings where there is a cost associated with network use.
Rounding via Trees: Deterministic Approximation Algorithms for Group Steiner Trees and kmedian
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1998
"... Most optimization problems on an undirected graph reduce in complexity when restricted to instances on a tree. A recent result [3] for probabilistically approximating graph metrics by trees such that no edge stretches (in an expected sense) by more than a factor of O(log 2 n) has resulted in several ..."
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Cited by 56 (8 self)
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Most optimization problems on an undirected graph reduce in complexity when restricted to instances on a tree. A recent result [3] for probabilistically approximating graph metrics by trees such that no edge stretches (in an expected sense) by more than a factor of O(log 2 n) has resulted in several approximation algorithms which exploit the ease of solving problems on trees. The tree construction in [3] is inherently randomized and a natural question to ask is whether approximation algorithms which use this construction can be derandomized. We present a general framework for derandomizing approximation algorithms which use the above tree construction as a primitive. Let \Pi be a graph optimization problem which can be expressed as an integer program with 01 variables ¯ x(e) for each edge and with an objective function expressible as...
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 49 (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