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1,656
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3393 (12 self)
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performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the distances between
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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tiply connected networks: When loops are present, the network is no longer singly connected and local propaga tion schemes will invariably run into trouble . We believe there are general undiscovered theorems about the performance of belief propagation on loopy DAGs. These theo rems, which may have
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 386 (15 self)
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that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision
An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Cl ..."
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Cited by 360 (0 self)
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constructed using the GomoryHu algorithm. However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm
The generalized distributive law
 Information Theory, IEEE Transactions on
"... Abstract—In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence ..."
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Cited by 359 (2 self)
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algorithm, and the turbo decoding algorithm. Although this algorithm is guaranteed to give exact answers only in certain cases (the “junction tree ” condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting
Guarantee
"... In this paper, we study the problem of scheduling task sets with (m,k) constraints. Our scheduling approach, similar to some previous work, is to partition the jobs of each task into two sets: mandatory or optional. Mandatory jobs are scheduled according to their fixedpriorities while optional jobs ..."
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jobs are assigned to the lowest priority. We show that finding the optimal partition as well as determining the schedulability of the resultant task set are both NPhard problems. A new technique, based on the General Chinese Remainder Theorem, is proposed to quantify the interference among the tasks
ORDERINGS FOR TERMREWRITING SYSTEMS
, 1982
"... Methods of proving that a termrewriting system terminates are presented. They are based on the intuitive notion of 'simplification orderings'. orderings in which any term that is syntactically simpler than another is smaller than the other. M a consequence of Kruskal's Tree Theorem ..."
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Cited by 294 (24 self)
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Theorem, any nonterminating system must be selfembedding in the sense that it allows for the derivation of some term from a simpler one; thus termination is guaranteed jf every rule in the system as a reduction in some simplification ordering. Most 01 the orderings that have been used for proving
APPROXIMATION ALGORITHMS FOR SCHEDULING UNRELATED PARALLEL MACHINES
, 1990
"... We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomi ..."
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Cited by 265 (7 self)
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polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer
Results 1  10
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1,656