Results 1  10
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58
Modeling sensor networks
, 2008
"... In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challe ..."
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Cited by 28 (5 self)
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In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challenging task. On the one hand, a
Leveraging Linial’s Locality Limit
"... www.dcg.ethz.ch Abstract. In this paper we extend the lower bound technique by Linial for local coloring and maximal independent sets. We show that constant approximations to maximum independent sets on a ring require at least logstar time. More generally, the product of approximation quality and r ..."
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Cited by 17 (8 self)
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www.dcg.ethz.ch Abstract. In this paper we extend the lower bound technique by Linial for local coloring and maximal independent sets. We show that constant approximations to maximum independent sets on a ring require at least logstar time. More generally, the product of approximation quality and running time cannot be less than logstar. Using a generalized ring topology, we gain identical lower bounds for approximations to minimum dominating sets. Since our generalized ring topology is contained in a number of geometric graphs such as the unit disk graph, our bounds directly apply as lower bounds for quite a few algorithmic problems in wireless networking. Having in mind these and other results about local approximations of maximum independent sets and minimum dominating sets, one might think that the former are always at least as difficult to obtain as the latter. Conversely, we show that graphs exist, where a maximum independent set can be determined without any communication, while finding even an approximation to a minimum dominating set is as hard as in general graphs. 1
Distributed approximate matching
, 2007
"... We consider distributed algorithms for approximate maximum matching on general graphs. Our main result is a randomized (4 + ɛ)approximation distributed algorithm for weighted maximum matching, whose running time is O(log n) for any constant ɛ> 0, where n is the number of nodes in the graph. In a ..."
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Cited by 15 (2 self)
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We consider distributed algorithms for approximate maximum matching on general graphs. Our main result is a randomized (4 + ɛ)approximation distributed algorithm for weighted maximum matching, whose running time is O(log n) for any constant ɛ> 0, where n is the number of nodes in the graph. In addition, we consider the dynamic case, where nodes are inserted and deleted one at a time. For unweighted dynamic graphs, we give an algorithm that maintains a (1 + ɛ)approximation in O(1/ɛ) time for each node insertion or deletion. For weighted dynamic graphs we give a constantfactor approximation algorithm that runs in constant time for each insertion or deletion.
FaultTolerant Clustering in Ad Hoc and Sensor Networks
 In 26th International Conference on Distributed Computing Systems (ICDCS
, 2006
"... In this paper, we study distributed approximation algorithms for faulttolerant clustering in wireless ad hoc and sensor networks. A kfold dominating set of a graph G =(V,E) is a subset S of V such that every node v ∈ V \ S has at least k neighbors in S. We study the problem in two network models. ..."
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Cited by 13 (1 self)
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In this paper, we study distributed approximation algorithms for faulttolerant clustering in wireless ad hoc and sensor networks. A kfold dominating set of a graph G =(V,E) is a subset S of V such that every node v ∈ V \ S has at least k neighbors in S. We study the problem in two network models. In general graphs, for arbitrary parameter t, we propose a distributed algorithm that runs in time O(t 2) and achieves an approximation ratio of O(t ∆ 2/t log ∆), wheren and ∆ denote the number of nodes in the network and the maximal degree, respectively. When the network is modeled as a unit disk graph, we give a probabilistic algorithm that runs in time O(log log n) and achieves an O(1) approximation in expectation. Both algorithms require only small messages of size O(log n) bits. 1
Distance approximation in boundeddegree and general sparse graphs
 In Proceedings of the Tenth International Workshop on Randomization and Computation (RANDOM
, 2006
"... We address the problem of approximating the distance of bounded degree and general sparse graphs from having some predetermined graph property P. Namely, we are interested in sublinear algorithms for estimating the fraction of edges that should be added to / removed from a graph so that it obtains P ..."
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Cited by 12 (4 self)
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We address the problem of approximating the distance of bounded degree and general sparse graphs from having some predetermined graph property P. Namely, we are interested in sublinear algorithms for estimating the fraction of edges that should be added to / removed from a graph so that it obtains P. This fraction is taken with respect to a given upper bound m on the number of edges. In particular, for graphs with degree bound d over n vertices, m = dn. To perform such an approximation the algorithm may ask for the degree of any vertex of its choice, and may ask for the neighbors of any vertex. The problem of estimating the distance to having a property was first explicitly addressed by Parnas et. al. (ECCC 2004). In the context of graphs this problem was studied by Fischer and Newman (FOCS 2005) in the densegraphs model. In this model the fraction of edge modifications is taken with respect to n 2, and the algorithm may ask for the existence of an edge between any pair of vertices of its choice. Fischer and Newman showed that every graph property that has a testing algorithm in this model with query complexity that is independent of the size of the graph, also has a distanceapproximation algorithm with query complexity that is independent of the size of the graph. In this work we focus on boundeddegree and general sparse graphs, and give algorithms for all properties that were shown to have efficient testing algorithms by Goldreich and Ron (Algorithmica, 2002). Specifically, these properties are kedge connectivity, subgraphfreeness (for constant size subgraphs), being a Eulerian graph, and cyclefreeness. A variant of our subgraphfreeness algorithm approximates the size of a minimum vertex cover of a graph in sublinear time. This approximation improves on a recent result of Parnas and Ron (ECCC 2005).
T.: Distributed approximation of capacitated dominating sets
 In: Proc. 19th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2007
"... We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardin ..."
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Cited by 11 (1 self)
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We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently nonlocal, i.e., every distributed algorithm achieving a nontrivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter ɛ> 0, capacities can be violated by a factor of 1 + ɛ, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bicriteria algorithm that achieves an O(log ∆)approximation in time O(log 3 n + log(n)/ɛ), where n and ∆ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the nonuniform problem remains entirely nonlocal.
Improved Distributed Approximate Matching
"... We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1 − ɛ)approximation in O(log n) time for any constant ɛ> 0. This result improves on the classical 1approximation due 2 to Isr ..."
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Cited by 10 (2 self)
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We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1 − ɛ)approximation in O(log n) time for any constant ɛ> 0. This result improves on the classical 1approximation due 2 to Israeli and Itai. As a byproduct, we also provide an improved algorithm for unweighted matchings in bipartite graphs. In the context of weighted graphs, we give another algorithm which provides ( 1 − ɛ) approximation in general 2 graphs in O(log n) time. The latter result improves on the − ɛ)approximation in O(log n) time. known ( 1 4
Networks Cannot Compute Their Diameter in Sublinear Time preliminary version please check for updates
, 2011
"... We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but short) message to each of its neighbors. We provide an ˜ Ω(n) lower bound for the number of commun ..."
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Cited by 10 (2 self)
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We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but short) message to each of its neighbors. We provide an ˜ Ω(n) lower bound for the number of communication rounds needed, where n denotes the number of nodes in the network. This lower bound is valid even if the diameter of the network is a small constant. We also show that a (3/2 − ε)approximation of the diameter requires ˜ Ω ( √ n) rounds. Furthermore we use our new technique to prove an ˜ Ω ( √ n) lower bound on approximating the girth of a graph by a factor 2 − ε. Contact author:
Efficient distributed approximation algorithms via probabilistic tree embeddings
 IN: PROC. OF THE 27TH SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 2008
"... We present a uniform approach to design efficient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar [10] (FRT embedding). We show how to efficiently compute an ..."
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Cited by 9 (2 self)
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We present a uniform approach to design efficient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar [10] (FRT embedding). We show how to efficiently compute an (implicit) FRT embedding in a decentralized manner and how to use the embedding to obtain expected O(log n)approximate distributed algorithms for the generalized Steiner forest problem, the minimum routing cost spanning tree problem, and the ksource shortest paths problem in arbitrary networks. The time complexities of our algorithms are within a polylogarithmic factor of the optimum. The distributed construction of the FRT embedding is based on the computation of least elements (LE) lists, a distributed data structure that might be of independent interest. Assuming a global order on the nodes of a network, the LE list of a node stores the smallest node (w.r.t. the given order) within every distance d (cf. Cohen [3], Cohen and Kaplan [4]). Assuming a random order on the nodes, we give an almostoptimal distributed algorithm for computing LE lists on weighted graphs. For unweighted graphs, our LE lists computation has asymptotically optimal time complexity O(D), where D is the diameter of the network. As a byproduct, we get an improved synchronous leader election algorithm for general networks.
Distributed and Parallel Algorithms for Weighted Vertex Cover . . .
, 2009
"... The paper presents distributed and parallel δapproximation algorithms for covering problems, where δ is the maximum number of variables on which any constraint depends (for example, δ = 2 for vertex cover). Specific results include the following. • For weighted vertex cover, the first distributed 2 ..."
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Cited by 9 (3 self)
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The paper presents distributed and parallel δapproximation algorithms for covering problems, where δ is the maximum number of variables on which any constraint depends (for example, δ = 2 for vertex cover). Specific results include the following. • For weighted vertex cover, the first distributed 2approximation algorithm taking O(log n) rounds and the first parallel 2approximation algorithm in RNC. The algorithms generalize to covering mixed integer linear programs (CMIP) with two variables per constraint (δ = 2). • For any covering problem with monotone constraints and submodular cost, a distributed δapproximation algorithm taking O(log² C) rounds, where C is the number of constraints. (Special cases include CMIP, facility location, and probabilistic (twostage) variants of these problems.)