Results 1  10
of
674
SelfTesting/Correcting with Applications to Numerical Problems
, 1990
"... Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute ..."
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Cited by 340 (26 self)
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Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute f(x) correctly as long as P is not too faulty on average. Furthermore, both (1) and (2) take time only slightly more than Computer Science Division, U.C. Berkeley, Berkeley, California 94720, Supported by NSF Grant No. CCR 8813632. y International Computer Science Institute, Berkeley, California 94704 z Computer Science Division, U.C. Berkeley, Berkeley, California 94720, Supported by an IBM Graduate Fellowship and NSF Grant No. CCR 8813632. the original running time of P . We present general techniques for constructing simple to program selftesting /correcting pairs for a variety of numerical problems, including integer multiplication, modular multiplication, matrix multiplicatio...
ROCK: A Robust Clustering Algorithm for Categorical Attributes
 In Proc.ofthe15thInt.Conf.onDataEngineering
, 2000
"... Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than point ..."
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Cited by 337 (2 self)
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Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than points in different partitions. In this paper, we study clustering algorithms for data with boolean and categorical attributes. We show that traditional clustering algorithms that use distances between points for clustering are not appropriate for boolean and categorical attributes. Instead, we propose a novel concept of links to measure the similarity/proximity between a pair of data points. We develop a robust hierarchical clustering algorithm ROCK that employs links and not distances when merging clusters.
Polynomial time algorithms for multicast network code construction
 IEEE Trans. on Info. Thy
"... Abstract—The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the int ..."
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Cited by 183 (15 self)
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Abstract—The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures. Index Terms—Communication networks, efficient algorithms, linear coding, multicasting rate maximization. I.
Algorithms for Sequential Decision Making
, 1996
"... Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one ..."
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Cited by 175 (8 self)
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Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one of a finite set of actions, "should" is maximize a longrun measure of reward, and "I" is an automated planning or learning system (agent). In particular,
On the complexity of solving Markov decision problems
 IN PROC. OF THE ELEVENTH INTERNATIONAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 1995
"... Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving MDPs and the running time of MDP solution algorithms. We argu ..."
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Cited by 131 (10 self)
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Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving MDPs and the running time of MDP solution algorithms. We argue that, although MDPs can be solved efficiently in theory, more study is needed to reveal practical algorithms for solving large problems quickly. To encourage future research, we sketch some alternative methods of analysis that rely on the structure of MDPs.
Generating Random Spanning Trees More Quickly than the Cover Time
 PROCEEDINGS OF THE TWENTYEIGHTH ANNUAL ACM SYMPOSIUM ON THE THEORY OF COMPUTING
, 1996
"... ..."
Polynomial Time Algorithms for Network Information Flow
 in 15th ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that t ..."
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Cited by 96 (1 self)
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The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. In contrast, we present graphs where without coding the rate must be a factor jV j) smaller. However, so far no fast algorithms for constructing appropriate coding schemes were known. Our main result are polynomial time algorithms for constructing coding schemes for multicasting at the maximal data rate.
The algorithmic aspects of the Regularity Lemma
 J. Algorithms
, 1994
"... The Regularity Lemma of Szemerédi is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. Here we first demonstrate the computational difficulty of finding a regular partition; we show that ..."
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Cited by 94 (31 self)
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The Regularity Lemma of Szemerédi is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. Here we first demonstrate the computational difficulty of finding a regular partition; we show that deciding if a given partition of an input graph satisfies the properties guaranteed by the lemma is coNPcomplete. However, we also prove that despite this difficulty the lemma can be made constructive; we show how to obtain, for any input graph, a partition with the properties guaranteed by the lemma, efficiently. The desired partition, for an nvertex graph, can be found in time O(M(n)), where M(n) = O(n 2.376) is the time needed to multiply two n by n matrices with 0, 1entries over the integers. The algorithm can be parallelized and implemented in NC 1. Besides the curious phenomenon of exhibiting a natural problem in which the search for a solution is easy whereas the decision if a given instance is a solution is difficult (if P and NP differ), our constructive version of the Regularity Lemma supplies efficient sequential and parallel algorithms for many problems, some of which are naturally motivated by the study of various graph embedding and graph coloring problems.
Improved approximation algorithms for large matrices via random projections
 in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
"... Recently several results appeared that show significant reduction in time for matrix multiplication, singular value decomposition as well as linear (ℓ2) regression, all based on data dependent random sampling. Our key idea is that low dimensional embeddings can be used to eliminate data dependence a ..."
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Cited by 93 (3 self)
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Recently several results appeared that show significant reduction in time for matrix multiplication, singular value decomposition as well as linear (ℓ2) regression, all based on data dependent random sampling. Our key idea is that low dimensional embeddings can be used to eliminate data dependence and provide more versatile, linear time pass efficient matrix computation. Our main contribution is summarized as follows. • Independent of the recent results of HarPeled and of Deshpande and Vempala, one of the first – and to the best of our knowledge the most efficient – relativeerror (1 + ɛ) ‖A − Ak‖F approximation algorithms for the singular value decomposition of an m × n matrix A with M nonzero entries that requires 2 passes over the data and runs in time O M k + (n + m)k2 ɛ ɛ2) log 1 δ • The first o(nd 2) time (1+ɛ) relativeerror approximation algorithm for n×d linear (ℓ2) regression. • A matrix multiplication algorithm that easily applies to implicitly given matrices. 1
All Pairs Almost Shortest Paths
 SIAM Journal on Computing
, 1996
"... Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time ..."
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Cited by 83 (8 self)
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Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time algorithm APASP 2 for computing all distances in G with an additive onesided error of at most 2. The algorithm APASP 2 is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm. Furthermore, for every even k ? 2, we describe an g) time algorithm APASP k for computing all distances in G with an additive onesided error of at most k.