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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 138 (25 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
ConstantTime Distributed Dominating Set Approximation*
"... ABSTRACT 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 \Delta, our algorithm computes a d ..."
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ABSTRACT 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 \Delta, our algorithm computes a
Digital Object Identifier (DOI) 10.1007/s0044600401125 Constanttime distributed dominating set approximation ⋆
"... Abstract. Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree ∆, our algo ..."
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Abstract. Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree ∆, our
ConstantTime Approximation . . .
"... We present a technique for transforming classical approximation algorithms into constanttime algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based o ..."
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We present a technique for transforming classical approximation algorithms into constanttime algorithms that approximate the size of the optimal solution. Our technique is applicable to a certain subclass of algorithms that compute a solution in a constant number of phases. The technique is based
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
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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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
Results 1  10
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