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37
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 161 (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 133 (22 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.
An Efficient Distributed Algorithm for Constructing Small Dominating Sets
, 2001
"... The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node ..."
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Cited by 95 (1 self)
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The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NPcomplete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the wellknown logarithmic approximation result for the closely related set cover problem.
On LinearTime Deterministic Algorithms for Optimization Problems in Fixed Dimension
, 1992
"... We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a lineartime deterministic one. The constant of proportionality is d O(d) , which is better than for previously known such algorithms. ..."
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Cited by 92 (10 self)
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We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a lineartime deterministic one. The constant of proportionality is d O(d) , which is better than for previously known such algorithms. We show that the algorithm works in a fairly general abstract setting, which allows us to solve various other problems (such as finding the maximum volume ellipsoid inscribed into the intersection of n halfspaces) in linear time.
Splitters and nearoptimal derandomization
"... We present a fairly general method for finding deterministic constructions obeying what we call krestrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)universal sets (a collection of binary vectors of lengt ..."
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Cited by 60 (1 self)
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We present a fairly general method for finding deterministic constructions obeying what we call krestrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2k configurations appear) and families of perfect hash functions. The nearoptimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixedsubgraph finding algorithms, and of near optimal threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a localcoloring protocol, and for exhaustive testing of circuits.
The probabilistic method yields deterministic parallel algorithms
 J. Comput. Syst. Sci
, 1994
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Polynomialtime Learning of Elementary Formal Systems
 Theoretical Computer Science
, 2000
"... An elementary formal system (EFS) is a logic program con sisting of definite clauses whose arguments have patterns instead of firstorder terms. We investigate EFSs for polynomialtime PAClearnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pat ..."
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Cited by 38 (8 self)
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An elementary formal system (EFS) is a logic program con sisting of definite clauses whose arguments have patterns instead of firstorder terms. We investigate EFSs for polynomialtime PAClearnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pattern in the head. With this new notion, we show that HEFS(ra, k, t, r) is polynomialtime learnable, which is the class of languages definable by EFSs consisting of at most ra hereditary definite clauses with predicate symbols of arity at most r, where k and t bound the number of variable occurrences in the head and the number of atoms in the body, respectively. The class defined by all finite unions of EFSs in HEFS(ra, k, t, r) is also polynomialtime learnable. We also show an interesting series of NClearnable classes of EFSs. As hardness results, the class of regular pattern languages is shown not polynomialtime learnable unless RP=NP. Furthermore, the related problem of deciding whether there is a common subsequence which is consistent with given positive and negative examples is shown NPcomplete.
Primaldual rnc approximation algorithms for (multi)set (multi)cover and covering integer programs
 SIAM J. on Computing
, 1993
"... Abstract. We build on the classical greedy sequential set cover algorithm, in the spirit of the primaldual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of indep ..."
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Cited by 22 (0 self)
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Abstract. We build on the classical greedy sequential set cover algorithm, in the spirit of the primaldual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of independent interest. Fast parallel approximation algorithms were known before for set cover, though not for the generalizations considered in this paper.
A PrimalDual Parallel Approximation Technique Applied to Weighted Set and Vertex Cover
, 1994
"... We give an efficient deterministic parallel approximation algorithm for the minimumweight vertex ..."
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Cited by 20 (2 self)
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We give an efficient deterministic parallel approximation algorithm for the minimumweight vertex
Fast greedy algorithms in mapreduce and streaming
 In SPAA
, 2013
"... Greedy algorithms are practitioners ’ best friends—they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advant ..."
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Cited by 20 (1 self)
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Greedy algorithms are practitioners ’ best friends—they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power. Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. We then show how to use this primitive to adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to psystem constraints. Our method yields efficient algorithms that run in a logarithmic number of rounds, while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint, and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or psystem constraints. Finally, we empirically validate our algorithms, and show that they achieve the same quality of the solution as standard greedy algorithms but run in a substantially fewer number of rounds. Categories and Subject Descriptors