Jerrum, Mark
Overview
Works:  49 works in 135 publications in 1 language and 561 library holdings 

Roles:  Author 
Classifications:  QA164.8, 511.62 
Publication Timeline
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Most widely held works by
Mark Jerrum
Counting, sampling and integrating : algorithms and complexity by
Mark Jerrum(
Book
)
11 editions published in 2003 in English and Undetermined and held by 200 WorldCat member libraries worldwide
11 editions published in 2003 in English and Undetermined and held by 200 WorldCat member libraries worldwide
A polynomial algorithm for deciding bisimilarity of normed contextfree processes by
Y Hirshfeld(
Book
)
5 editions published in 1994 in English and held by 16 WorldCat member libraries worldwide
5 editions published in 1994 in English and held by 16 WorldCat member libraries worldwide
Design and analysis of randomized and approximation algorithms 05201 abstracts collection ; Dagstuhl seminar(
)
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 16 WorldCat member libraries worldwide
Uniform sampling modulo a group of symmetries using Markov chain simulation by
Mark Jerrum(
Book
)
4 editions published in 1993 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 14 WorldCat member libraries worldwide
A polynomialtime algorithm for deciding bisimulation equivalence of normed basic parallel processes by
Yoram Hirshfeld(
Book
)
4 editions published in 1994 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1994 in English and held by 14 WorldCat member libraries worldwide
A sublogarithmic communication algorithm for the completely connected optical communication parallel computer by
Leslie Ann Goldberg(
Book
)
3 editions published in 1992 in English and held by 13 WorldCat member libraries worldwide
GerébGraus and Tsantilas have asked whether there is a faster algorithm for h = o(log p), in particular, whether a 2relation can be realized in o(log p) expected time on a pprocessor OCPC. In this paper we show that a 2relation can indeed be realized in sublogarithmic time. More generally, we give an algorithm that realizes an arbitrary hrelation on a pprocessor OCPC. We show that if h = O(log[superscript 1/2]p) then the expected running time of the algorithm is [theta](h log[superscript 1/2]p) and the probability that it takes more than [theta](h log[superscript 1/2]p) steps can be made as small as p[superscript alpha] for any positive constant [alpha]. Our algorithm is pure in the sense of Geréb Graus and Tsantilas."
3 editions published in 1992 in English and held by 13 WorldCat member libraries worldwide
GerébGraus and Tsantilas have asked whether there is a faster algorithm for h = o(log p), in particular, whether a 2relation can be realized in o(log p) expected time on a pprocessor OCPC. In this paper we show that a 2relation can indeed be realized in sublogarithmic time. More generally, we give an algorithm that realizes an arbitrary hrelation on a pprocessor OCPC. We show that if h = O(log[superscript 1/2]p) then the expected running time of the algorithm is [theta](h log[superscript 1/2]p) and the probability that it takes more than [theta](h log[superscript 1/2]p) steps can be made as small as p[superscript alpha] for any positive constant [alpha]. Our algorithm is pure in the sense of Geréb Graus and Tsantilas."
Computational Pólya theory by
Mark Jerrum(
Book
)
4 editions published in 1995 in English and held by 13 WorldCat member libraries worldwide
Abstract: "A permutation group G of degree n has a natural induced action on words of length n over a finite alphabet [sigma], in which the image x[superscript g] of x under permutation g [element of] G is obtained by permuting the positions of symbols in x according to g. The key result in 'Pólya theory' is that the number of orbits of this action is given by an evaluation of the cycleindex polynomial P[subscript G](z₁, ..., z[subscript n]) of G at the point z₁ = ... = z[subscript n] = [absolute value of sigma]. In many cases it is possible to count the number of essentially distinct instances of a combinatorial structure of a given size by evaluating the cycleindex polynomial of an appropriate symmetry group G. We address the question 'to what extent can Pólya theory be mechanised?' There are compelling complexitytheoretic reasons for believing that there is no efficient, uniform procedure for computing the cycleindex exactly, but less is known about approximate evaluation, say to within a specified relative error. The known results  positive and negative  will be surveyed."
4 editions published in 1995 in English and held by 13 WorldCat member libraries worldwide
Abstract: "A permutation group G of degree n has a natural induced action on words of length n over a finite alphabet [sigma], in which the image x[superscript g] of x under permutation g [element of] G is obtained by permuting the positions of symbols in x according to g. The key result in 'Pólya theory' is that the number of orbits of this action is given by an evaluation of the cycleindex polynomial P[subscript G](z₁, ..., z[subscript n]) of G at the point z₁ = ... = z[subscript n] = [absolute value of sigma]. In many cases it is possible to count the number of essentially distinct instances of a combinatorial structure of a given size by evaluating the cycleindex polynomial of an appropriate symmetry group G. We address the question 'to what extent can Pólya theory be mechanised?' There are compelling complexitytheoretic reasons for believing that there is no efficient, uniform procedure for computing the cycleindex exactly, but less is known about approximate evaluation, say to within a specified relative error. The known results  positive and negative  will be surveyed."
A mildly exponential approximation algorithm for the permanent by
Mark Jerrum(
Book
)
6 editions published in 1991 in English and held by 13 WorldCat member libraries worldwide
Abstract: "A new approximation algorithm for the permanent of an n x n 0,1matrix is presented. The algorithm is shown to have worstcase time complexity exp(O(n[superscript 1/2] log²n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worstcase time complexity of the form e[superscipt theta(n)]."
6 editions published in 1991 in English and held by 13 WorldCat member libraries worldwide
Abstract: "A new approximation algorithm for the permanent of an n x n 0,1matrix is presented. The algorithm is shown to have worstcase time complexity exp(O(n[superscript 1/2] log²n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worstcase time complexity of the form e[superscipt theta(n)]."
A very simple algorithm for estimating the number of kcolourings of a lowdegree graph by
Mark Jerrum(
Book
)
4 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
4 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
Approximately counting Hamilton cycles in dense graphs by
Martyn Dyer(
Book
)
4 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
Abstract: "We describe a fully polynomial randomized approximation scheme for the problem of determining the number of Hamiltonian cycles in an nvertex graph with minimum degree (1/2 + [epsilon])n, for any fixed [epsilon]> 0. We also show that the exact counting problem is #Pcomplete."
4 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
Abstract: "We describe a fully polynomial randomized approximation scheme for the problem of determining the number of Hamiltonian cycles in an nvertex graph with minimum degree (1/2 + [epsilon])n, for any fixed [epsilon]> 0. We also show that the exact counting problem is #Pcomplete."
Improved approximation algorithms for MAX kCUT and MAX BISECTION by
Alan Frieze(
Book
)
4 editions published in 1994 in English and held by 12 WorldCat member libraries worldwide
Abstract: "Polynomialtime approximation algorithms with nontrivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximise the weight of crossing edges, and (b) partitioning the vertices of a weighted graph into two blocks of equal cardinality, again so as to maximise the weight of crossing edges. The approach, pioneered by Goemans and Williamson, is via a semidefinite relaxation."
4 editions published in 1994 in English and held by 12 WorldCat member libraries worldwide
Abstract: "Polynomialtime approximation algorithms with nontrivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximise the weight of crossing edges, and (b) partitioning the vertices of a weighted graph into two blocks of equal cardinality, again so as to maximise the weight of crossing edges. The approach, pioneered by Goemans and Williamson, is via a semidefinite relaxation."
An analysis of a Monte Carlo algorithm for estimating the permanent by
Mark Jerrum(
Book
)
4 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
The conjecture is shown to be true; indeed for almost every 0,1 matrix, O(n[omega](n)[epsilon][superscript 2]) trials suffice to obtain a reliable approximation that is within a factor (1 + [epsilon]) of the correct value. Here [omega](n) is any function tending to infinity as n [approaches] [infinity]."
4 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
The conjecture is shown to be true; indeed for almost every 0,1 matrix, O(n[omega](n)[epsilon][superscript 2]) trials suffice to obtain a reliable approximation that is within a factor (1 + [epsilon]) of the correct value. Here [omega](n) is any function tending to infinity as n [approaches] [infinity]."
Simulated annealing for graph bisection by
Mark Jerrum(
Book
)
4 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
Abstract: "We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in G[subscript npr] when p  r = [theta](n[superscript delta  2]) for [delta] [<or =] 2. (The random graph model G[subscript npr] specifies a 'planted' bisection of density r, separating two n/2vertex subsets of slightly higher density p.) We show that simulated 'annealing' at an appropriate fixed temperature (i.e., the Metropolis algorithm) finds the unique smallest bisection in O(n[superscript 2 + [epsilon]] steps with very high probability, provided [delta]> 11/6
4 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
Abstract: "We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in G[subscript npr] when p  r = [theta](n[superscript delta  2]) for [delta] [<or =] 2. (The random graph model G[subscript npr] specifies a 'planted' bisection of density r, separating two n/2vertex subsets of slightly higher density p.) We show that simulated 'annealing' at an appropriate fixed temperature (i.e., the Metropolis algorithm) finds the unique smallest bisection in O(n[superscript 2 + [epsilon]] steps with very high probability, provided [delta]> 11/6
The computational complexity of counting by
Mark Jerrum(
Book
)
3 editions published in 1994 in English and held by 11 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 11 WorldCat member libraries worldwide
A quasipolynomialtime algorithm for sampling words from a contextfree language by Vivek Gore(
Book
)
3 editions published in 1995 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 10 WorldCat member libraries worldwide
The elusiveness of large cliques in a random graph by
Mark Jerrum(
Book
)
3 editions published in 1990 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 9 WorldCat member libraries worldwide
Simple translationinvariant concepts are hard to learn by
Mark Jerrum(
Book
)
3 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
Despite their obvious simplicity, TCM concepts are apparently difficult to learn. Indeed: (i) the concept class TCM is not polynomially learnable unless RP=NP; (ii) TCM is polynomially predictable if the only if the concept class of DNF formulas is polynomially predictable; (iii) TCM is not polynomially predictable from positive examples alone. The second of these results relates the computational complexity of predicting TCM concepts to a well known open problem in computational learning theory."
3 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
Despite their obvious simplicity, TCM concepts are apparently difficult to learn. Indeed: (i) the concept class TCM is not polynomially learnable unless RP=NP; (ii) TCM is polynomially predictable if the only if the concept class of DNF formulas is polynomially predictable; (iii) TCM is not polynomially predictable from positive examples alone. The second of these results relates the computational complexity of predicting TCM concepts to a well known open problem in computational learning theory."
Polynomialtime approximation algorithms for the Ising model by
Mark Jerrum(
Book
)
3 editions published in 1990 in English and held by 8 WorldCat member libraries worldwide
Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation algorithms are presented for the mean energy and the mean magnetic moment of ferromagnetic Ising systems. The algorithms are based on Monte Carlo simulation of a suitably defined ergodic Markov chain. The states of the chain are not, as is customary, Ising spin configurations, but spanning subgraphs of the interaction graph of the system. It is shown that the expectations of simple operators on these configurations give numerical information about the partition function and related quantities
3 editions published in 1990 in English and held by 8 WorldCat member libraries worldwide
Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation algorithms are presented for the mean energy and the mean magnetic moment of ferromagnetic Ising systems. The algorithms are based on Monte Carlo simulation of a suitably defined ergodic Markov chain. The states of the chain are not, as is customary, Ising spin configurations, but spanning subgraphs of the interaction graph of the system. It is shown that the expectations of simple operators on these configurations give numerical information about the partition function and related quantities
The SwendsenWang process does not always mix rapidly by Vivek K Gore(
Book
)
3 editions published in 1996 in English and held by 8 WorldCat member libraries worldwide
Abstract: "The SwendsenWang process provides one possible dynamics for the Qstate Potts model in statistical physics. Computer simulations of this process are widely used to estimate the expectations of various observables (random variables) of a Potts system in the equilibrium (or Gibbs) distribution. The legitimacy of such simulations depends on the rate of convergence of the process to equilibrium, often known as the mixing rate. Empirical observations suggest that the SwendsenWang process mixes rapidly in many instances of practical interest. In spite of this, we show that there are occasions on which the SwendsenWang process requires exponential time (in the size of the system) to approach equilibrium."
3 editions published in 1996 in English and held by 8 WorldCat member libraries worldwide
Abstract: "The SwendsenWang process provides one possible dynamics for the Qstate Potts model in statistical physics. Computer simulations of this process are widely used to estimate the expectations of various observables (random variables) of a Potts system in the equilibrium (or Gibbs) distribution. The legitimacy of such simulations depends on the rate of convergence of the process to equilibrium, often known as the mixing rate. Empirical observations suggest that the SwendsenWang process mixes rapidly in many instances of practical interest. In spite of this, we show that there are occasions on which the SwendsenWang process requires exponential time (in the size of the system) to approach equilibrium."
Counting, Sampling and Integrating: Algorithm and Complexity by
Mark Jerrum(
)
2 editions published in 2003 in English and held by 0 WorldCat member libraries worldwide
The subject of these notes is counting (of combinatorial structures) and related topics, viewed from a computational perspective. "Related topics" include sampling combinatorial structures (being computationally equivalent to approximate counting via efficient reductions), evaluating partition functions (being weighted counting), and calculating the volume of bodies (being counting in the limit). A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk (i.e., simulating a Markov chain) on those structures. (This is for the discrete setting; one can also learn about a geometric body by performing a walk within it.) The running time of such an algorithm depends on the rate of convergence to equilibrium of this Markov chain, as formalised in the notion of "mixing time" of the Markov chain. A significant proportion of the volume is given over to an investigation of techniques for bounding the mixing time in cases of computational interest. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers in the field of computational complexity who wish to become acquainted with recent work on nonasymptotic analysis of Markov chains, and their counterparts in stochastic processes who wish to discover how their subject sits within a computational context. For the first time this body of knowledge has been brought together in a single volume
2 editions published in 2003 in English and held by 0 WorldCat member libraries worldwide
The subject of these notes is counting (of combinatorial structures) and related topics, viewed from a computational perspective. "Related topics" include sampling combinatorial structures (being computationally equivalent to approximate counting via efficient reductions), evaluating partition functions (being weighted counting), and calculating the volume of bodies (being counting in the limit). A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk (i.e., simulating a Markov chain) on those structures. (This is for the discrete setting; one can also learn about a geometric body by performing a walk within it.) The running time of such an algorithm depends on the rate of convergence to equilibrium of this Markov chain, as formalised in the notion of "mixing time" of the Markov chain. A significant proportion of the volume is given over to an investigation of techniques for bounding the mixing time in cases of computational interest. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers in the field of computational complexity who wish to become acquainted with recent work on nonasymptotic analysis of Markov chains, and their counterparts in stochastic processes who wish to discover how their subject sits within a computational context. For the first time this body of knowledge has been brought together in a single volume
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Related Identities
 University of Edinburgh Laboratory for Foundations of Computer Science
 University of Edinburgh Department of Computer Science
 Dyer, Martin Author
 Hirshfeld, Y. (Yoram) Author
 Moller, Faron
 Frieze, Alan 1945 Author
 University of Edinburgh Laboratory for Foundation of Computer Science
 Sinclair, Alistair Author
 Goldberg, Leslie Ann Author
 Karpinski, Marek
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Associated Subjects
Algebra Algorithms Approximation theory Combinatorial analysis Combinatorial enumeration problems Computational complexity Computers Computers, Optical Computer science Computer software Distribution (Probability theory) Ferromagnetism Graph theory Hamiltonian systems Ising model Machine theory Markov processes Mathematical statistics Mathematics Monte Carlo method Operations research Parallel computers Polynomials Simulated annealing (Mathematics) Statistical physics
Alternative Names
Jerrum, Mark
Mark Jerrum britischer Informatiker
Mark Jerrum Brits informaticus
Mark Jerrum informático teórico del Reino Unido
Mark Jerrum Theoretical computer scientist
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