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29
Topology Control and Routing in Ad hoc Networks: A Survey
 SIGACT News
, 2002
"... this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. T ..."
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Cited by 115 (0 self)
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this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author
ConstantTime Distributed Dominating Set Approximation
 In Proc. of the 22 nd ACM Symposium on the Principles of Distributed Computing (PODC
, 2003
"... Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set ..."
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Cited by 111 (24 self)
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Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set of expected size O k# log #DSOPT rounds where each node has to send O k messages of size O(log #). This is the first algorithm which achieves a nontrivial approximation ratio in a constant number of rounds.
Greedy Facility Location Algorithms analyzed using Dual Fitting with FactorRevealing LP
 Journal of the ACM
, 2001
"... We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying c ..."
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Cited by 100 (13 self)
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We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.
The price of being nearsighted
 In SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality o ..."
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Cited by 59 (13 self)
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Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/kapproximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its kneighborhood. 1
On the RedBlue Set Cover Problem
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... Given a finite set of "red" elements R, a finite set of "blue" elements B and a family S ` 2 R[B , the redblue set cover problem is to find a subfamily C ` S which covers all blue elements, but which covers the minimum possible number of red elements. We note that RedBlue Set Cover is closely r ..."
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Cited by 34 (0 self)
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Given a finite set of "red" elements R, a finite set of "blue" elements B and a family S ` 2 R[B , the redblue set cover problem is to find a subfamily C ` S which covers all blue elements, but which covers the minimum possible number of red elements. We note that RedBlue Set Cover is closely related to several combinatorial optimization problems studied earlier. These include the group Steiner problem, directed Steiner problem, minimum label path, minimum monotone satisfying assignment and symmetric label cover. From the equivalence of RedBlue Set Cover and MMSA3 it follows that, unless P=NP, even the restriction of RedBlue Set Cover where every set contains only one blue and two red elements cannot be approximated to within O(2 log 1\Gammaffi n ) , where ffi = 1= log log c n, for any constant c ! 1=2 (where n = S). We give integer programming formulations of the problem and use them to obtain a 2 p n approximation algorithm for the restricted case of RedBlue Set Cove...
Robust submodular observation selection
, 2008
"... In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations wh ..."
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Cited by 30 (3 self)
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In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective functions. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for cases where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We show how our algorithm can be extended to handle complex cost functions (incorporating nonunit observation cost or communication and path costs). We also show how the algorithm can be used to nearoptimally trade off expectedcase (e.g., the Mean Square Prediction Error in Gaussian Process regression) and worstcase (e.g., maximum predictive variance) performance. We show that many important machine learning problems fit our robust submodular observation selection formalism, and provide extensive empirical evaluation on several realworld problems. For Gaussian Process regression, our algorithm compares favorably with stateoftheart heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDPbased algorithms.
Facility location: distributed approximation
 In Proceedings of the twentyfourth annual ACM symposium on Principles of distributed computing
, 2005
"... In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves ..."
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Cited by 27 (1 self)
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In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a tradeoff between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves an O ( √ k(mρ) 1/ √ k log (m + n)) approximation in O(k) communication rounds where message size is bounded to O(log n) bits. The number of facilities and clients are m and n, respectively, and ρ is a coefficient that depends on the cost values of the instance. Our technique is based on a distributed primaldual approach for approximating a linear program, that does not form a covering or packing program.
Algorithmic Derandomization via Complexity Theory
 In Proceedings of the 34th annual ACM Symposium on Theory of Computing (STOC
, 2002
"... We point out how the methods of Nisan [Nis90, Nis92], originally developed for derandomizing spacebounded computations, may be applied to obtain polynomialtime and NC derandomizations of several probabilistic algorithms. Our list includes the randomized rounding steps of linear and semidefinit ..."
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Cited by 25 (1 self)
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We point out how the methods of Nisan [Nis90, Nis92], originally developed for derandomizing spacebounded computations, may be applied to obtain polynomialtime and NC derandomizations of several probabilistic algorithms. Our list includes the randomized rounding steps of linear and semidefinite programming relaxations of optimization problems, parallel derandomization of discrepancytype problems, and the JohnsonLindenstrauss lemma, to name a few.
On the approximability of Dodgson and Young elections
, 2008
"... The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorith ..."
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Cited by 24 (11 self)
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The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LPbased randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(log m) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in N P have quasipolynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that
Constrained relay node placement in wireless sensor networks to meet connectivity and survivability requirements
 in Proc. IEEE INFOCOM
"... Abstract—One approach to prolong the lifetime of a wireless sensor network (WSN) is to deploy some relay nodes to communicate with the sensor nodes, other relay nodes, and the base stations. The relay node placement problem for wireless sensor networks is concerned with placing a minimum number of r ..."
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Cited by 21 (1 self)
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Abstract—One approach to prolong the lifetime of a wireless sensor network (WSN) is to deploy some relay nodes to communicate with the sensor nodes, other relay nodes, and the base stations. The relay node placement problem for wireless sensor networks is concerned with placing a minimum number of relay nodes into a wireless sensor network to meet certain connectivity or survivability requirements. Previous studies have concentrated on the unconstrained version of the problem in the sense that relay nodes can be placed anywhere. In practice, there may be some physical constraints on the placement of relay nodes. To address this issue, we study constrained versions of the relay node placement problem, where relay nodes can only be placed at a set of candidate locations. In the connected relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with a base station through a bidirectional path. In the survivable relay node placement problem, we want to place a minimum number of relay nodes to ensure that each sensor node is connected with two base stations (or the only base station in case there is only one base station) through two nodedisjoint bidirectional paths. For each of the two problems, we discuss its computational complexity and present a framework of polynomial time (1)approximation algorithms with small approximation ratios. Extensive numerical results show that our approximation algorithms can produce solutions very close to optimal solutions. Index Terms—Approximation algorithms, connectivity and survivability, relay node placement, wireless sensor networks (WSNs). I.