Karp, Richard M. 1935Overview
Publication Timeline
Most widely held works about
Richard M Karp
Most widely held works by
Richard M Karp
Complexity of computation
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Book
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10 editions published in 1974 in English and Undetermined and held by 372 WorldCat member libraries worldwide
NPcomplete problems
by Richard M Karp
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Visual
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1 edition published in 1993 in English and held by 76 WorldCat member libraries worldwide Defines NPcomplete problems. A combinatorial search problem involves searching through a finite, but very large, set of possible patterns or arrangements for one that satisfies a stated set of constraints
Complexity and real computation
by Lenore Blum
(
Book
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3 editions published between 1997 and 1998 in English and held by 60 WorldCat member libraries worldwide The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NPcompleteness theorems of CookKarp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing
A survey of parallel algorithms for sharedmemory machines
by Richard M Karp
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Book
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5 editions published in 1988 in English and Undetermined and held by 11 WorldCat member libraries worldwide Section 3 studies the relationships among several variants of the PRAM model which differ in their implementation of concurrent reading and/or concurrent writing, presents lower bounds on the time to solve certain elementary problems on various kinds of P RAMs, and compares the PRAM with other models such as boundedfanin and unboundedfanin circuits, alternating Turing machines and vector machines. Section 3 also introduces NC, a hierarchy of problems solvable by deterministic algorithms that operate in polylog time using a polynomial bounded number of processors
The differencing method of set partitioning
by Narendra Karmarkar
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Book
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2 editions published in 1982 in English and held by 8 WorldCat member libraries worldwide
The complexity of parallel search
by Richard M Karp
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Book
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3 editions published in 1986 in English and held by 8 WorldCat member libraries worldwide
When is the assignment bound tight for the asymmetric traveling salesman problem?
by Alan Frieze
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Book
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6 editions published in 1992 in English and German and held by 8 WorldCat member libraries worldwide Abstract: "We consider the probabilistic relationship between the value of a random asymmetric traveling salesman problem ATSP(M) and the value of its assignment relaxation AP(M). We assume here that the costs are given by an n X n matrix M whose entries are independently and identically distributed. We focus on the relationship between Pr(ATSP(M) = AP(M)) and the probability p[subscript n] that any particular entry is zero. If np[subscript n] > [infinity] with n then we prove that ATSP(M) = AP(M) with probability 1o(1). This is shown to be best possible in the sense that if np(n) > c, c> 0 and constant, then Pr(ATSP(M) = AP(M)) <1  [phi](c) for some positive function [phi]. Finally, if np[subscript n] > 0 then Pr(ATSP(M) = AP(M)) > 0
On linear characterization of combinatorial optimization problems
by Richard M Karp
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Book
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1 edition published in 1980 in English and held by 7 WorldCat member libraries worldwide
A new MonteCarlo method for estimating the failure probability of an ncomponent system
by Richard M Karp
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Book
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2 editions published in 1983 in English and held by 7 WorldCat member libraries worldwide A new formula for the probability of a union of events is used to express the failure probability fo an ncomponent system. A very simple MonteCarlo algorithm based on the new probability formula is presented. The input to the algorithm gives the failure probabilities of the n components of the system and a list of the failure sets of the system. The output is an unbiased estimator of the failure probability of the system. We show that the average value of the estimator over many runs of the algorthm tends to converge quickly to the failure Probability of the system. The overall time to estimate the failure probability with high accuracy compares very favorably with the execution times of other methods used for solving this problem
Constructing a perfect matching is in random NC
by Richard M Karp
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Book
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3 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide This document shows that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomialbounded number of processors. It is also shown that several related problems lie in Random NC. These include: Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; Constructing a maximumcardinality matching; Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; and Constructing a maximum st flow in a directed graph whose edge weights are given in unary. Additional keywords: rank functions. (Author)
Deferred data structuring
by Richard M Karp
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Book
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2 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide We consider the problem of answering a series of on line queries on a static data set. The conventional approach to such problems involves a preprocessing phase which constructs a data structure with good search behavior. The data structure representing the data set then remains fixed throughout the processing of the queries. Our approach involves dynamic or query driven structuring of the data set; our algorithm processes the data set only when doing so is required for answering a query. A data structure constructed progressively in this fashion is called a deferred data structure
Probabilistic analysis of combinatorial algorithms : an annotated bibliography
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Book
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4 editions published between 1984 and 1985 in English and held by 5 WorldCat member libraries worldwide
Probabilistic analysis of network flow algorithms
by Richard M Karp
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Book
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2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
Efficient PRAM simulation on a distributed memory machine
by Richard M Karp
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Book
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3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide The best previous simulations use a simpler scheme based on hashing and have much larger delay: [theta](log(n)/loglog(n)) for the simulation of an n processor PRAM on an n processor DMM, and [theta](log(n)) in the case where the simulation is timeprocessor optimal."
A linear algorithm for testing equivalence of finite automata
by John E Hopcroft
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Book
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3 editions published in 1971 in English and held by 3 WorldCat member libraries worldwide An algorithm is given for determining if two finite automata with start states are equivalent. The asymptotic running time of the algorithm is bounded by a constant times the product of the number of states of the larger automation with the size of the input alphabet. (Author)
The transitive closure of a random digraph
by Richard M Karp
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Book
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1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
Average case analysis of a heuristic for the assignment problem
by Richard M Karp
(
Book
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2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
A patching algorithm for the nonsymmetric travelingsalesman problem
by Richard M Karp
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Book
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1 edition published in 1978 in English and held by 2 WorldCat member libraries worldwide
LOGOS : a hierarchical Bayesian Markovian motif model capturing local sitedependencies and global motif distributions
by Eric P Xing
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Book
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1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
Probabilistic recurrence relations
by Richard M Karp
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Book
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1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide Abstract: "This paper is concerned with recurrence relations that arise frequently in the analysis of divideandconquer algorithms. In order to solve a problem instance of size x, such an algorithm invests an amount of work a(x) to break the problem into subproblems of sizes h₁(x), h₂(x) ..., h[subscript k](x) and then proceeds to solve the subproblems. Our particular interest is in the case where the sizes h[subscript i](x) are random variables; this may occur either because of randomization within the algorithm or because the instances to be solved are assumed to be drawn from a probability distribution. When the h[subscript i] are random variables the running time of the algorithm on instances of size x is also a random variable T(x) more
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Associated Subjects
Algorithms Assignment problems (Programming) Canada College teachers Combinatorial optimization Computational complexity Computer algorithms Computer science Computer scientists ComputersReliability Data structures (Computer science) Difference sets Directed graphs Electrical engineers Graph theoryData processing Information theory Linear programming Logic, Symbolic and mathematical Matching theoryData processing Mathematical optimization Mathematicians Mathematics Multiprocessors NPcomplete problems Parallel processing (Electronic computers) Parallel programming (Computer science) Partitions (Mathematics) Realtime data processing Scientists Search theory Sequential machine theory Set theory Traveling salesman problem United States

Alternative Names
Karp, R., 1935
Karp, R. M., 1935
Karp, Richard, 1935
Karp, Richard M.
Karp, Richard Manning, 1935
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