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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 15 (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
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
Human domination of Earth’s ecosystems
 Science
, 1997
"... Human alteration of Earth is substantial and growing. Between onethird and onehalf interact with the atmosphere, with aquatic of the land surface has been transformed by human action; the carbon dioxide con systems, and with surrounding land. Morecentration in the atmosphere has increased by near ..."
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Cited by 551 (6 self)
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Human alteration of Earth is substantial and growing. Between onethird and onehalf interact with the atmosphere, with aquatic of the land surface has been transformed by human action; the carbon dioxide con systems, and with surrounding land. Morecentration in the atmosphere has increased by nearly 30 percent since the beginning of over, land trallsformation interacts strongly the Industrial Revolution; more atmospheric nitrogen is fixed by humanity than by all with most other components of global ennatural terrestrial sources combined; more than half of all accessible surface fresh water rironmental change. is put to use by humanity; and about onequarter of the bird species on Earth have been The measurement of land transformadriven to extinction. By these and other standards, it is clear that we live on a human tion on a global scale is challenging; changdominated planet. es can be measured more or less straightforwardly at a eiven site, but it is difficult to aggregate these changes regionally and globallv. In contrast to analvses of human alA11 organisms modify their environment, reasonably well quantified; all are ongoing, teraiion of the global carbon cycle, we and humans are no exceotion. As the hu These relativelv welldocumented changes cannot install instruments on a tro~ical man population has and the power of in turn entrail; further alterations to;he mountain to collect evidence of land tianstechnology has expanded, the scope and f~~nctioning of the Earth system, most no formation. Remote sensing is a most useful
Approximating discrete probability distributions with dependence trees
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1968
"... A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n variables ..."
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Cited by 874 (0 self)
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A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
Determining the Number of Factors in Approximate Factor Models
, 2000
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
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Cited by 538 (29 self)
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In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors can be consistently estimated using the criterion. The theory is developed under the framework of large crosssections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criterion yields almost precise estimates of the number of factors for configurations of the panel data encountered in practice. The idea that variations in a large number of economic variables can be modelled bya small number of reference variables is appealing and is used in manyeconomic analysis. In the finance literature, the arbitrage pricing theory(APT) of Ross (1976) assumes that a small number of factors can be used to explain a large number of asset returns.
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query
Results 1  10
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2,862,238