Karp, Richard M. 1935
Overview
Works:  72 works in 138 publications in 3 languages and 690 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Author of introduction 
Classifications:  QA76, 511.3 
Publication Timeline
.
Most widely held works about
Richard M Karp
Most widely held works by
Richard M Karp
Complexity of computation by
American Mathematical Society(
Book
)
15 editions published in 1974 in English and Undetermined and held by 373 WorldCat member libraries worldwide
15 editions published in 1974 in English and Undetermined and held by 373 WorldCat member libraries worldwide
Complexity and real computation by
Lenore Blum(
Book
)
3 editions published between 1997 and 1998 in English and held by 72 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
3 editions published between 1997 and 1998 in English and held by 72 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
NPcomplete problems by
Richard M Karp(
Visual
)
2 editions published in 1993 in English and held by 60 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
2 editions published in 1993 in English and held by 60 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
A survey of parallel algorithms for sharedmemory machines by
Richard M Karp(
Book
)
5 editions published in 1988 in English and Undetermined and held by 11 WorldCat member libraries worldwide
This paper is a survey of the growing body of theory concerned with parallel algorithms and the complexity of parallel computation. The principal computation that we consider is the parallel random access machine (PRAM), in which it is assumed that each processor has random access in unit time to any cell of a global memory. This model permits the logical structure of parallel computation to be studied in a context divorced from issues of interprocessor communication
5 editions published in 1988 in English and Undetermined and held by 11 WorldCat member libraries worldwide
This paper is a survey of the growing body of theory concerned with parallel algorithms and the complexity of parallel computation. The principal computation that we consider is the parallel random access machine (PRAM), in which it is assumed that each processor has random access in unit time to any cell of a global memory. This model permits the logical structure of parallel computation to be studied in a context divorced from issues of interprocessor communication
Constructing a perfect matching is in random NC by
Richard M Karp(
Book
)
4 editions published in 1985 in English and held by 8 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)
4 editions published in 1985 in English and held by 8 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)
The differencing method of set partitioning by Narendra Karmarkar(
Book
)
2 editions published in 1982 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1982 in English and held by 8 WorldCat member libraries worldwide
The complexity of parallel search by
Richard M Karp(
Book
)
4 editions published in 1986 in English and held by 8 WorldCat member libraries worldwide
4 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(
Book
)
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
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
Some applications of logical syntax to digital computer programming : a thesis by
Richard M Karp(
Book
)
4 editions published in 1959 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1959 in English and held by 7 WorldCat member libraries worldwide
On linear characterization of combinatorial optimization problems by
Richard M Karp(
Book
)
2 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
Probabilistic analysis of combinatorial algorithms : an annotated bibliography by
Richard M Karp(
Book
)
7 editions published between 1984 and 1985 in English and Dutch and held by 6 WorldCat member libraries worldwide
7 editions published between 1984 and 1985 in English and Dutch and held by 6 WorldCat member libraries worldwide
Deferred data structuring by
Richard M Karp(
Book
)
2 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
We develop the notion of deferred data structures by solving the problem of answering membership queries on an ordered set. We obtain a randomized algorithm which achieves asymptotically optimal performance with high probability. We then present optimal deferred data structures for the following problems in the plane: testing convex hull membership, halfplane intersection queries and fixed constraint multiobjective linear programming. We also apply the deferred data structuring technique to multidimensional dominance query problems
2 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
We develop the notion of deferred data structures by solving the problem of answering membership queries on an ordered set. We obtain a randomized algorithm which achieves asymptotically optimal performance with high probability. We then present optimal deferred data structures for the following problems in the plane: testing convex hull membership, halfplane intersection queries and fixed constraint multiobjective linear programming. We also apply the deferred data structuring technique to multidimensional dominance query problems
A new MonteCarlo method for estimating the failure probability of an ncomponent system by
Richard M Karp(
Book
)
2 editions published in 1983 in English and held by 6 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
2 editions published in 1983 in English and held by 6 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
Probabilistic analysis of network flow algorithms by
Richard M Karp(
Book
)
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 5 WorldCat member libraries worldwide
Probabilistic recurrence relations by
Richard M Karp(
Book
)
3 editions published in 1991 in English and held by 4 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)
3 editions published in 1991 in English and held by 4 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)
Efficient PRAM simulation on a distributed memory machine by
Richard M Karp(
Book
)
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."
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."
Parallel combinatorial computing by
Richard M Karp(
Book
)
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this article we suggest that the application of highly parallel computers to applications with a combinatorial or logical flavor will grow in importance. We briefly survey the work of theoretical computer scientists on the construction of efficient parallel algorithms for basic combinatorial problems. We then discuss a twostage algorithm design methodology, in which an algorithm is first designed to run on a PRAM and then implemented for a distributedmemory machine. Finally, we propose the class of node expansion algorithms as fruitful domain for the application of highly parallel computers."
3 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this article we suggest that the application of highly parallel computers to applications with a combinatorial or logical flavor will grow in importance. We briefly survey the work of theoretical computer scientists on the construction of efficient parallel algorithms for basic combinatorial problems. We then discuss a twostage algorithm design methodology, in which an algorithm is first designed to run on a PRAM and then implemented for a distributedmemory machine. Finally, we propose the class of node expansion algorithms as fruitful domain for the application of highly parallel computers."
The transitive closure of a random digraph by
Richard M Karp(
Book
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
A Linear Algorithm for Testing Equivalence of Finite Automata by
John E Hopcroft(
Book
)
5 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)
5 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)
Average case analysis of a heuristic for the assignment problem by
Richard M Karp(
Book
)
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
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Algorithms Assignment problems (Programming) Canada College teachers Combinatorial optimization CommunicationNetwork analysis Computational complexity Computer algorithms Computer networks Computer programming Computer science Computer scienceMathematics Computer scientists ComputersReliability Data structures (Computer science) Difference sets Directed graphs Electrical engineers Electronic data processing Graph theoryData processing Information theory Linear programming Logic Logic, Symbolic and mathematical Machine theory Matching theoryData processing Mathematical optimization Mathematicians Mathematics Multiprocessors NPcomplete problems Parallel computers Parallel processing (Electronic computers) Parallel programming (Computer science) Partitions (Mathematics) Programming languages (Electronic computers)Syntax 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
Ričard Karp
Richard Karp Amerikaans wiskundige
Richard Karp informaticien américain
Richard Karp informatico statunitense
Richard M. Karp amerikanischer Informatiker
Richard M. Karp amerikansk datavetare och matematiker
Richard M. Karp amerikansk informatikar og matematikar
Richard M. Karp amerikansk informatiker og matematiker
Карп, Ричард Мэннинг
Ричард Карп
Річард Карп
ריצ'רד קארפ
ريتشارد كارب
ریچارد کارپ ریاضیدان و دانشمند علوم کامپیوتر آمریکایی
রিচার্ড কার্প
ริชาร์ด คาร์ป
リチャード・カープ
理察·卡普
理查德·卡普
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