Results 1  10
of
403,536
LogP: Towards a Realistic Model of Parallel Computation
, 1993
"... A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding developme ..."
Abstract

Cited by 562 (15 self)
 Add to MetaCart
development of techniques that yield performance across a range of current and future parallel machines. This paper offers a new parallel machine model, called LogP, that reflects the critical technology trends underlying parallel computers. It is intended to serve as a basis for developing fast, portable
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
Abstract

Cited by 534 (48 self)
 Add to MetaCart
increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
Abstract

Cited by 2837 (11 self)
 Add to MetaCart
simple notion of monotone reducibility and exhibit complete problems. This provides a framework for stating existing results and asking new questions. We show that mNL (monotone nondeterministic logspace) is not closed under complementation, in contrast to Immerman's and Szelepcs &apos
Critical Power for Asymptotic Connectivity in Wireless Networks
, 1998
"... : In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' pack ..."
Abstract

Cited by 548 (19 self)
 Add to MetaCart
as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ! 2 and each node transmits at a power level so as to cover an area of ßr 2 = (log n + c(n))=n, then the resulting network is asymptotically connected with probability one if and only
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 ..."
Abstract

Cited by 778 (5 self)
 Add to MetaCart
o(1)) ln n), and previous results of Lund and Yannakakis, that showed hardness of approximation within a ratio of (log 2 n)=2 ' 0:72 lnn. For max kcover we show an approximation threshold of (1 \Gamma 1=e) (up to low order terms), under the assumption that P != NP .
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract

Cited by 543 (11 self)
 Add to MetaCart
are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract

Cited by 557 (12 self)
 Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique and maximum stable set problems in perfect graphs, the maximum k partite subgraph problem in graphs, and va...
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
Abstract

Cited by 1231 (13 self)
 Add to MetaCart
We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Transductive Inference for Text Classification using Support Vector Machines
, 1999
"... This paper introduces Transductive Support Vector Machines (TSVMs) for text classification. While regular Support Vector Machines (SVMs) try to induce a general decision function for a learning task, Transductive Support Vector Machines take into account a particular test set and try to minimiz ..."
Abstract

Cited by 887 (4 self)
 Add to MetaCart
This paper introduces Transductive Support Vector Machines (TSVMs) for text classification. While regular Support Vector Machines (SVMs) try to induce a general decision function for a learning task, Transductive Support Vector Machines take into account a particular test set and try to minimize misclassifications of just those particular examples. The paper presents an analysis of why TSVMs are well suited for text classification. These theoretical findings are supported by experiments on three test collections. The experiments show substantial improvements over inductive methods, especially for small training sets, cutting the number of labeled training examples down to a twentieth on some tasks. This work also proposes an algorithm for training TSVMs efficiently, handling 10,000 examples and more.
Results 1  10
of
403,536