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143
Online Steiner Trees in the Euclidean Plane
 Discrete and Computational Geometry
, 1993
"... Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, online, a connected graph that connects all of them, trying to minimize the total sum of lengths of its edges. The points appear one at a time, and at each step the online algorithm must construc ..."
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Cited by 50 (4 self)
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Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, online, a connected graph that connects all of them, trying to minimize the total sum of lengths of its edges. The points appear one at a time, and at each step the online algorithm must construct a connected graph that contains all current points by connecting the new point to the previously constructed graph. This can be done by joining the new point (not necessarily by a straight line) to any point of the previous graph, (not necessarily one of the given points). The performance of our algorithm is measured by its competitive ratio: the supremum, over all sequences of points, of the ratio between the total length of the graph constructed by our algorithm and the total length of the best Steiner tree that connects all the points. There are known online algorithms whose competitive ratio is O(log n) even for all metric spaces, but the only lower bound known is of [IW] for some con...
Online Generalized Steiner Problem
, 1996
"... The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with nonnegative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Offline generalized Steiner problem ap ..."
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Cited by 41 (5 self)
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The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with nonnegative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Offline generalized Steiner problem approximation algorithms were given in [AKR91, GW92]. We consider the online generalized Steiner problem, in which pairs of vertices arrive online and are needed to be connected immediately. We give a simple O(log² n) competitive deterministic online algorithm. The previous best algorithm was O( p n log n) competitive [WY93]. We also consider the network connectivity leasing problem which is a generalization of the GSP. Here edges of the graph can be either bought or leased for different costs. We provide simple randomized O(log² n) competitive algorithm based on the online generalized Steiner problem result.
Distributed Algorithms for Multicast Path Setup in Data Networks
 IEEE/ACM Transactions on Networking
, 1995
"... Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, can be modeled as the NPcomplete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in pointtopoint data networks. ..."
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Cited by 40 (2 self)
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Establishing a multicast tree in a pointtopoint network of switch nodes, such as a widearea ATM network, can be modeled as the NPcomplete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in pointtopoint data networks. These algorithms are based on the centralized Steiner heuristics, the shortest path heuristic (SPH) and the Kruskalbased shortest path heuristic (KSPH), and have the advantage that only the multicast members and nodes in the neighborhood of the multicast tree need to participate in the execution of the algorithm. We compare our algorithms by simulation against a baseline algorithm, the pruned minimum spanningtree heuristic, which is the basis of many previously published algorithms for finding multicast trees. Our results show that the competitiveness (the ratio of the sum of the heuristic tree's edge weights to that of the best solution found) of both of our algorithms was on the average ...
A general approach to online network optimization problems
 ACM Transactions on Algorithms
, 2004
"... ..."
Informationdirected routing in ad hoc sensor networks
 IEEE Journal on Selected Areas in Communications
, 2005
"... In a sensor network, data routing is tightly coupled to the needs of a sensing task, and hence the application semantics. This paper introduces the novel idea of informationdirected routing, in which routing is formulated as a joint optimization of data transport and information aggregation. The ro ..."
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Cited by 37 (2 self)
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In a sensor network, data routing is tightly coupled to the needs of a sensing task, and hence the application semantics. This paper introduces the novel idea of informationdirected routing, in which routing is formulated as a joint optimization of data transport and information aggregation. The routing objective is to minimize communication cost while maximizing information gain, differing from routing considerations for more general ad hoc networks. The paper uses the concrete problem of locating and tracking possibly moving signal sources as an example of information generation processes, and considers two common information extraction patterns in a sensor network:routing a user query from an arbitrary entry node to the vicinity of signal sources and back, or to a prespecified exit node, maximizing information accumulated along the path. We derive information constraints from realistic signal models, and present several routing algorithms that find nearoptimal solutions for the joint optimization problem. Simulation results have demonstrated that informationdirected routing is a significant improvement over a previously reported greedy algorithm, as measured by sensing quality such as localization and tracking accuracy and communication quality such as success rate in routing around sensor holes.
NonCooperative Multicast and Facility Location Games
"... We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in ..."
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Cited by 35 (2 self)
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We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NPhard. We focus on the price of anarchy of a Nash equilibrium resulting from the bestresponse dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O ( √ n log 2 n) on the price of anarchy, and a lower bound of Ω(log n/log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.
Resource Optimization in QoS Multicast Routing of RealTime Multimedia
, 2000
"... We consider a network design problem, where applications require various levels of QualityofService (QoS) while connections have limited performance. Suppose that a source needs to send a message to a heterogeneous set of receivers. The objective is to design a low cost multicast tree from the sou ..."
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Cited by 33 (0 self)
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We consider a network design problem, where applications require various levels of QualityofService (QoS) while connections have limited performance. Suppose that a source needs to send a message to a heterogeneous set of receivers. The objective is to design a low cost multicast tree from the source that would provide the QoS levels (e.g., bandwidth) requested by the receivers. We assume that the QoS level required on a link is the maximum among the QoS levels of the receivers that are connected to the source through the link. In accordance, we define the cost of a link to be a function of the QoS level that it provides. This definition of cost makes this optimization problem more general than the classical Steiner tree problem. We consider several variants of this problem all of which are proved to be NPhard. For the variant where QoS levels of a link can vary arbitrarily and the cost function is linear in its QoS level, we give a heuristic that achieves a multicast tree with cost ...
An edge in time saves nine: LP rounding approximation algorithms for stochastic network design
 in FOCS, 2004
"... Realworld networks often need to be designed under uncertainty, with only partial information and predictions of demand available at the outset of the design process. The field of stochastic optimization deals with such problems where the forecasts are specified in terms of probability distribution ..."
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Cited by 33 (10 self)
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Realworld networks often need to be designed under uncertainty, with only partial information and predictions of demand available at the outset of the design process. The field of stochastic optimization deals with such problems where the forecasts are specified in terms of probability distributions of future data. In this paper, we broaden the set of models as well as the techniques being considered for approximating stochastic optimization problems. For example, we look at stochastic models where the cost of the elements is correlated to the set of realized demands, and riskaverse models where upper bounds are placed on the amount spent in each of the stages. These generalized models require new techniques, and our solutions are based on a novel combination of the primaldual method truncated based on optimal LP relaxation values, followed by a treerounding stage. We use these to give constantfactor approximation algorithms for the stochastic Steiner tree and single sink network design problems in these generalized models. 1.
Oblivious network design
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... Consider the following network design problem: given a network G = (V, E), sourcesink pairs {si, ti} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from all the terminal pairs), the cost is given by ∑ e ℓ(fe), wher ..."
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Cited by 32 (8 self)
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Consider the following network design problem: given a network G = (V, E), sourcesink pairs {si, ti} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from all the terminal pairs), the cost is given by ∑ e ℓ(fe), where ℓ is some concave cost function; the goal is to minimize the total cost incurred. However, we want the routing to be oblivious: when terminal pair {si, ti} makes its routing decisions, it does not know the current flow on the edges of the network, nor the identity of the other pairs in the system. Moreover, it does not even know the identity of the function ℓ, merely knowing that ℓ is a concave function of the total flow on the edge. How should it (obliviously) route its one unit of flow?
Designing networks with good equilibria
 In SODA ’08
, 2007
"... In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network co ..."
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Cited by 32 (4 self)
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In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, different classes of costsharing methods, and different measures of the inefficiency of equilibria. One of our main technical tools is a complete characterization of the uniform costsharing protocols—protocols that are designed without foreknowledge of or assumptions on the network in which they will be deployed. We use this characterization result to identify the optimal uniform protocol in several scenarios: for example, the Shapley protocol is optimal in directed graphs, while the optimal protocol in undirected graphs, a simple priority scheme, has exponentially smaller worstcase price of anarchy than the Shapley protocol. We also provide several matching upper and lower bounds on the bestpossible performance of nonuniform costsharing protocols.