Jerrum, Mark
Overview
Works:  46 works in 124 publications in 1 language and 523 library holdings 

Roles:  Author 
Classifications:  QA164.8, 511.62 
Publication Timeline
.
Most widely held works by
Mark Jerrum
Counting, sampling and integrating : algorithms and complexity by
Mark Jerrum(
Book
)
13 editions published in 2003 in English and Undetermined and held by 199 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
13 editions published in 2003 in English and Undetermined and held by 199 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
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
A polynomial algorithm for deciding bisimilarity of normed contextfree processes by
University of Edinburgh(
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
A very simple algorithm for estimating the number of kcolourings of a lowdegree graph by
Mark Jerrum(
Book
)
5 editions published in 1994 in English and held by 14 WorldCat member libraries worldwide
5 editions published in 1994 in English and held by 14 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
Abstract: "In this paper we consider the problem of interprocessor communication on a Completely Connected Optical Communication Parallel Computer (OCPC). The particular problem we study is that of realizing an hrelation. In this problem, each processor has at most h messages to send and at most h messages to receive. It is clear that any 1relation can be realized in one step on an OCPC. However, the best known pprocessor OCPC algorithm for realizing an arbitrary hrelation for h> 1 runs in [theta](h+log p) expected time. (This algorithm is due to Valiant and is based on earlier work of Anderson and Miller.)
3 editions published in 1992 in English and held by 13 WorldCat member libraries worldwide
Abstract: "In this paper we consider the problem of interprocessor communication on a Completely Connected Optical Communication Parallel Computer (OCPC). The particular problem we study is that of realizing an hrelation. In this problem, each processor has at most h messages to send and at most h messages to receive. It is clear that any 1relation can be realized in one step on an OCPC. However, the best known pprocessor OCPC algorithm for realizing an arbitrary hrelation for h> 1 runs in [theta](h+log p) expected time. (This algorithm is due to Valiant and is based on earlier work of Anderson and Miller.)
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)]."
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."
Approximately counting Hamilton cycles in dense graphs by
Martyn Dyer(
Book
)
5 editions published in 1993 in English and held by 13 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."
5 editions published in 1993 in English and held by 13 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."
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
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]."
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."
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 V 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
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
The performance guarantees for the algorithms are rigorously derived, and rest on the fact that the Markov chain in question is rapidly mixing, i.e., converges to its equilibrium distribution in a polynomial number of steps. This is apparently the first time that rapid mixing has been demonstrated at all temperatures for a Markov chain related to the Ising problem."
3 editions published in 1990 in English and held by 8 WorldCat member libraries worldwide
The performance guarantees for the algorithms are rigorously derived, and rest on the fact that the Markov chain in question is rapidly mixing, i.e., converges to its equilibrium distribution in a polynomial number of steps. This is apparently the first time that rapid mixing has been demonstrated at all temperatures for a Markov chain related to the Ising problem."
When is a graphical sequence stable? by
Mark Jerrum(
Book
)
2 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
Abstract: "The function which maps each graphical sequence d to the number of graphs with degree sequence d is considered, with particular attention being directed at the stability of the function under small perturbations in d. In some parts of its domain this function varies smoothly, and in other parts erratically. The boundary between these two behaviors is here sharply characterised in terms of the minimum, maximum, and average of the components of d. The result clarifies the range of applicability of some efficient randomised algorithms which sample and count degreeconstrained graphs. Furthermore, the result appears to set theoretical limits on the range of validity of asymtotic formulas for the number of graphs with given degree sequence."
2 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
Abstract: "The function which maps each graphical sequence d to the number of graphs with degree sequence d is considered, with particular attention being directed at the stability of the function under small perturbations in d. In some parts of its domain this function varies smoothly, and in other parts erratically. The boundary between these two behaviors is here sharply characterised in terms of the minimum, maximum, and average of the components of d. The result clarifies the range of applicability of some efficient randomised algorithms which sample and count degreeconstrained graphs. Furthermore, the result appears to set theoretical limits on the range of validity of asymtotic formulas for the number of graphs with given degree sequence."
Complementary partial orders and rectangle packing by
Mark Jerrum(
Book
)
2 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
Approximate counting, uniform generation and rapidly mixing Markov chains by
Alison Sinclair(
Book
)
2 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 6 WorldCat member libraries worldwide
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Related Identities
 University of Edinburgh Laboratory for Foundations of Computer Science
 University of Edinburgh Department of Computer Science
 Frieze, Alan 1945 Author
 Moller, Faron
 Dyer, Martin Author
 University of Edinburgh Laboratory for Foundation of Computer Science
 Goldberg, Leslie Ann Author
 Sinclair, Alistair Author
 Karpinski, Marek
 Hirshfeld, Y. (Yoram) Author
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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) Ergodic theory Ferromagnetism Fiber optics Graph theory Graph theoryData processing Hamiltonian graph theory Hamiltonian systems Ising model Machine theory Mappings (Mathematics) Markov processes Mathematical statistics Mathematics Monte Carlo method Operations research Parallel computers Partially ordered sets Paths and cycles (Graph theory) Polynomials Simulated annealing (Mathematics)
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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