WorldCat Identities

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
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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 non-asymptotic 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

A polynomial algorithm for deciding bisimilarity of normed context-free processes by University of Edinburgh( Book )

5 editions published in 1994 in English and held by 16 WorldCat member libraries worldwide

A very simple algorithm for estimating the number of k-colourings of a low-degree graph by Mark Jerrum( Book )

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

A polynomial-time 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

A sub-logarithmic 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 h-relation. In this problem, each processor has at most h messages to send and at most h messages to receive. It is clear that any 1-relation can be realized in one step on an OCPC. However, the best known p-processor OCPC algorithm for realizing an arbitrary h-relation 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 0,1-matrix is presented. The algorithm is shown to have worst-case time complexity exp(O(n[superscript 1/2] log²n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worst-case 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 cycle-index 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 cycle-index polynomial of an appropriate symmetry group G. We address the question 'to what extent can Pólya theory be mechanised?' There are compelling complexity-theoretic reasons for believing that there is no efficient, uniform procedure for computing the cycle-index 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 n-vertex graph with minimum degree (1/2 + [epsilon])n, for any fixed [epsilon]> 0. We also show that the exact counting problem is #P-complete."
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/2-vertex 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]."
Improved approximation algorithms for MAX k-CUT and MAX BISECTION by Alan Frieze( Book )

4 editions published in 1994 in English and held by 12 WorldCat member libraries worldwide

Abstract: "Polynomial-time approximation algorithms with non-trivial 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

A quasi-polynomial-time algorithm for sampling words from a context-free language by V Gore( Book )

3 editions published in 1995 in English and held by 10 WorldCat member libraries worldwide

Simple translation-invariant 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."
Polynomial-time 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."
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 degree-constrained 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

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

 
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Counting, sampling and integrating : algorithms and complexity
Alternative Names
Jerrum, Mark

Mark Jerrum britischer Informatiker

Mark Jerrum Brits informaticus

Mark Jerrum informático teórico del Reino Unido

Mark Jerrum Theoretical computer scientist

Languages
English (79)

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