Research
Applied probability, Combinatorics, Theoretical computer science
Interests
I am interested combinatorics, computational complexity and stochastic processes. All of these ingredients come together in the study of randomised algorithms: computational procedures that exploit the surprising power of making random choices. A strong theme in this work is the analysis of the mixing time of combinatorially or geometrically defined Markov chains. More generally, I work on the computational complexity of counting problems, including weighted counted problems as exemplified by partition functions and generating functions. Statistical physics, Constraint Satisfaction Problems and graph polynomials provide a rich source of motivating examples.
Publications

Publications of specific relevance to the Centre for Combinatorics, Algebra and Number Theory
2026
Zero‐free regions for the independence polynomial on restricted graph classesJerrum M Patel V
Journal of The London Mathematical Society,
Wiley vol. 113 (2)
01-02-20262025
Glauber dynamics for the hard-core model on bounded-degree $H$ -free graphsJerrum M
Combinatorics Probability Computing,
Cambridge University Press (Cup) vol. 34 (6), 803-814.
19-09-2025
Rapid Mixing of the Flip Chain over Non-Crossing Spanning TreesAnand K Feng W Freifeld G Guo H Jerrum M Wang J
Leibniz International Proceedings in Informatics Lipics. vol. 332
20-06-20252024
Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$ via weak spatial mixingAnand K Jerrum M
Annales De L’Institut Henri Poincaré D Combinatorics Physics and Their Interactions,
European Mathematical Society - Ems - Publishing House vol. 13 (1), 165-189.
02-08-2024
Fundamentals of partial rejection samplingJerrum M
Probability Surveys,
Institute of Mathematical Statistics vol. 21 (none)
01-01-20242023
A simple polynomial-time approximation algorithm for the total variation distance between two product distributionsFeng W Guo H Jerrum M
Theoretics,
Centre Pour La Communication Scientifique Directe (Ccsd) vol. Volume 2
15-06-20232022
Perfect Sampling in Infinite Spin Systems Via Strong Spatial MixingAnand K Jerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 51 (4), 1280-1295.
26-07-2022
Counting Vertices of Integral Polytopes Defined by FacetsGuo H Jerrum M
Discrete & Computational Geometry,
Springer Nature vol. 70 (3), 975-990.
05-07-20222021
Counting weighted independent sets beyond the permanentJerrum M Dyer M Müller H
Siam Journal on Discrete Mathematics,
Society For Industrial and Applied Mathematics vol. 35 (2), 1503-1524.
24-06-2021
Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphsDyer M Heinrich M Jerrum M
Combinatorics Probability Computing,
Cambridge University Press (Cup) vol. 30 (6), 905-921.
12-04-2021
The Size of the Giant Joint Component in a Binomial Random Double GraphJerrum M
The Electronic Journal of Combinatorics vol. 28 (1)
12-02-2021
Sharp thresholds of graph properties, and the k-sat problemJerrum MR
Bulletin of The American Mathematical Society vol. 58 (2), 267-268.
01-01-20212020
Random Walks on Small World NetworksJerrum M Galanis A Vigoda E Dyer M
Acm Transactions on Algorithms,
Association For Computing Machinery vol. 16 (3)
01-06-20202019
Approximating Pairwise Correlations in the Ising ModelGoldberg LA Jerrum M
Acm Transactions on Computation Theory,
Association For Computing Machinery (Acm) vol. 11 (4), 1-20.
23-07-2019
Uniform Sampling Through the Lovász Local LemmaGuo H Jerrum M
Journal of The Acm,
Association For Computing Machinery (Acm) vol. 66 (3), 1-31.
12-04-2019
A Polynomial-Time Approximation Algorithm for All-Terminal Network ReliabilityGuo H
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 48 (3), 964-978.
01-01-20192018
Perfect simulation of the hard disks model by partial rejection samplingGuo H Jerrum M
Leibniz International Proceedings in Informatics Lipics. vol. 107
01-07-2018
A polynomial-time approximation algorithm for all-terminal network reliabilityGuo H Jerrum M
Leibniz International Proceedings in Informatics Lipics. vol. 107
01-07-2018
Random cluster dynamics for the Ising model is rapidly mixingGuo H
The Annals of Applied Probability,
Institute of Mathematical Statistics vol. 28 (2), 1292-1313.
01-04-20182017
Functional clones and expressibility of partition functionsBulatov A Goldberg LA Richerby D
Theoretical Computer Science,
Elsevier vol. 687, 11-39.
01-07-2017
Uniform sampling through the Lovasz local lemmaGuo H Jerrum M
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing., 342-355.
19-06-2017
On the switch Markov chain for perfect matchingsDyer M JERRUM MR
Journal of The Association For Computing Machinery (Acm),
Association For Computing Machinery vol. 64 (2)
12-05-2017
A Complexity Trichotomy for Approximately Counting List H-ColoringsGalanis A Goldberg LA Jerrum M
Acm Transactions on Computation Theory,
Association For Computing Machinery (Acm) vol. 9 (2), 1-22.
27-04-2017
Counting Constraint Satisfaction Problems.Jerrum M Krokhin AA Zivný S
In
The Constraint Satisfaction Problem,
Schloss Dagstuhl - Leibniz-Zentrum FüR Informatik 205-231.
01-01-20172016
The parameterised complexity of counting even and odd induced subgraphsJerrum M
Combinatorica,
Springer Nature vol. 37 (5), 965-990.
24-10-2016
#BIS-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness regionCai J-Y Galanis A Goldberg LA Guo H Jerrum M
Journal of Computer and System Sciences,
Elsevier vol. 82 (5), 690-711.
01-08-2016
A complexity trichotomy for approximately counting list H-colouringsGalanis A Jerrum M
Leibniz International Proceedings in Informatics Lipics. vol. 55
01-08-2016
The complexity of counting locally maximal satisfying assignments of Boolean CSPsGoldberg LA Jerrum M
Theoretical Computer Science,
Elsevier vol. 634, 35-46.
01-06-2016
Approximately Counting $H$-Colorings is $\#\mathrm{BIS}$-HardGalanis A Goldberg LA
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 45 (3), 680-711.
01-01-20162015
A complexity classification of spin systems with an external field.Goldberg LA
Proceedings of The National Academy of Sciences of The United States of America vol. 112 (43), 13161-13166.
01-10-2015
Some Hard Families of Parameterized Counting ProblemsJerrum M Meeks K
Acm Transactions on Computation Theory,
Association For Computing Machinery (Acm) vol. 7 (3), 1-18.
09-07-2015
The parameterised complexity of counting connected subgraphs and graph motifsJerrum M Meeks K
Journal of Computer and System Sciences,
Elsevier vol. 81 (4), 702-716.
01-06-2015
The complexity of parity graph homomorphism: An initial investigationFaben J Jerrum M
Theory of Computing vol. 11, 35-57.
14-03-2015
The complexity of approximating conservative counting CSPsChen X Goldberg LA Jerrum M Lu P McQuillan C
Journal of Computer and System Sciences vol. 81 (1), 311-329.
01-02-2015
Approximately Counting H-Colourings is #BIS-HardGalanis A Goldberg LA Jerrum M
Lecture Notes in Computer Science. vol. 9134, 529-541.
01-01-2015
Approximately Counting H-Colourings is #\mathrm BIS # BIS -Hard.Galanis A Goldberg LA Halldórsson MM Iwama K Kobayashi N Speckmann B
ICALP (1). vol. 9134, 529-541.
01-01-2015
Approximating the partition function of planar two-state spin systems.Goldberg LA Jerrum M McQuillan C
J. Comput. Syst. Sci. vol. 81, 330-358.
01-01-20152014
BIS-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness regionCai JY Galanis A Goldberg LA Guo H Jerrum M
Leibniz International Proceedings in Informatics Lipics. vol. 28, 582-595.
01-09-2014
The Complexity of Approximately Counting Tree HomomorphismsGoldberg LA Jerrum M
Acm Transactions on Computation Theory,
Association For Computing Machinery (Acm) vol. 6 (2), 1-31.
01-05-2014
The Complexity of Computing the Sign of the Tutte PolynomialGoldberg LA Jerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 43 (6), 1921-1952.
01-01-20142013
The expressibility of functions on the Boolean domain, with applications to Counting CSPsBulatov A Dyer M Goldberg LA Jerrum M
J. Assoc. Comput. Mach.,
Acm Digital Library vol. 60 (5)
01-10-2013
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomialsGoldberg LA
Journal of Computer and System Sciences vol. 79 (1), 68-78.
01-01-2013
A Polynomial-Time Algorithm for Estimating the Partition Function of the Ferromagnetic Ising Model on a Regular Matroid.Goldberg LA Jerrum M
Siam J. Comput. vol. 42, 1132-1157.
01-01-2013
The complexity of approximating conservative counting CSPs.Chen X Dyer ME Goldberg LA Jerrum M Lu P Richerby D Portier N Wilke T
STACS. vol. 20, 148-159.
01-01-20132012
A counterexample to rapid mixing of the Ge-Stefankovic processGoldberg LA Jerrum M
Electronic Communications in Probability vol. 17, 1-6.
01-01-2012
The complexity of weighted and unweighted #CSPBulatov A Dyer M Goldberg LA Jalsenius M
Journal of Computer and System Sciences vol. 78 (2), 681-688.
01-01-2012
Inapproximability of the Tutte polynomial of a planar graphGoldberg LA
Computational Complexity vol. 21 (4), 605-642.
01-01-2012
Approximating the Partition Function of the Ferromagnetic Potts ModelGoldberg LA
Journal of The Acm vol. 59 (5)
01-01-2012
Approximating the partition function of planar two-state spin systemsGoldberg LA Jerrum M
Corr vol. abs/1208.4987
01-01-2012
Log-supermodular functions, functional clones and counting CSPs.Bulatov AA Dyer ME Jerrum M Dürr C Wilke T
STACS. vol. 14, 302-313.
01-01-2012
The complexity of approximating conservative counting CSPsChen X Dyer ME Goldberg LA Jerrum M Lu P Richerby D
Corr vol. abs/1208.1783
01-01-2012
The Complexity of Computing the Sign of the Tutte Polynomial (and Consequent #P-hardness of Approximation).Goldberg LA Czumaj A Mehlhorn K Pitts AM Wattenhofer R
ICALP (1). vol. 7391, 399-410.
01-01-20122011
A Polynomial-Time Algorithm for Estimating the Partition Function of the Ferromagnetic Ising Model on a Regular Matroid.Goldberg LA Aceto L Henzinger M Sgall J
ICALP (1). vol. 6755, 521-532.
01-01-20112010
A Complexity Dichotomy For Hypergraph Partition FunctionsDyer M Goldberg LA Jerrum M
Comput Complex vol. 19 (4), 605-633.
01-12-2010
Technical Perspective Constraint Satisfaction Problems and Computational ComplexityJerrum M
Commun Acm vol. 53 (9), 98-98.
01-09-2010
The Mixing Time of Glauber Dynamics for Coloring Regular TreesGoldberg LA Jerrum M
Random Struct Algor vol. 36 (4), 464-476.
01-07-2010
An approximation trichotomy for Boolean #CSPDyer M Goldberg LA Jerrum M
J Comput Syst Sci vol. 76 (3-4), 267-277.
01-05-2010
Approximating the Partition Function of the Ferromagnetic Potts ModelGoldberg LA Jerrum M Abramsky S Gavoille C Kirchner C MeyerAufDerHeide F Spirakis PG
AUTOMATA, LANGUAGES AND PROGRAMMING, PT I. vol. 6198, 396-407.
01-01-2010
Approximating the Partition Function of the Ferromagnetic Potts Model.Goldberg LA Abramsky S Gavoille C Kirchner C Heide FMAD Spirakis PG
ICALP (1). vol. 6198, 396-407.
01-01-2010
A COMPLEXITY DICHOTOMY FOR PARTITION FUNCTIONS WITH MIXED SIGNSGoldberg LA Grohe M
Siam J Comput vol. 39 (7), 3336-3402.
01-01-20102009
MATRIX NORMS AND RAPID MIXING FOR SPIN SYSTEMSDyer M Jerrum M
Ann Appl Probab vol. 19 (1), 71-107.
01-02-2009
A Complexity Dichotomy for Partition Functions with Mixed Signs.Goldberg LA Grohe M Jerrum M Albers S Marion J-Y
STACS. vol. 3, 493-504.
01-01-20092008
Dobrushin Conditions and Systematic ScanDyer M Goldberg LA Jerrum M
Comb Probab Comput vol. 17 (6), 761-779.
01-11-2008
Inapproximability of the Tutte polynomialGoldberg LA Jerrum M
Inform Comput vol. 206 (7), 908-929.
01-07-2008
THE COMPLEXITY OF WEIGHTED BOOLEAN #CSPDyer M Goldberg LA
Siam J Comput vol. 38 (5), 1970-1986.
01-01-20082007
Inapproximability of the Tutte polynomial.Goldberg LA Johnson DS Feige U
STOC., 459-468.
01-01-2007
Inapproximability of the Tutte PolynomialGoldberg LA
STOC 07: PROCEEDINGS OF THE 39TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING., 459-468.
01-01-2007
The complexity of ferromagnetic ising with local fieldsGoldberg LA Jerrum M
Comb Probab Comput vol. 16 (1), 43-61.
01-01-20072006
Families of Fixed Degree Graphs for Processor InterconnectionJerrum MR
IEEE Transactions on Computers,
Institute of Electrical and Electronics Engineers (IEEE) vol. C-33 (2), 190-194.
21-08-2006
On the approximation of one Markov chain by anotherJerrum M
Probab Theory Rel vol. 135 (1), 1-14.
01-05-2006
Systematic scan for sampling coloringsDyer M Goldberg LA
Ann Appl Probab vol. 16 (1), 185-230.
01-02-2006
Dobrushin Conditions and Systematic Scan.Dyer ME Goldberg LA Díaz J Jansen K Rolim JDP Zwick U
APPROX-RANDOM. vol. 4110, 327-338.
01-01-2006
Dobrushin conditions and systematic scanDyer M Goldberg LA Draz J Jansen K Rolim JDP Zwick U
APPROXIMATION, RANDOMIZATION AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES. vol. 4110, 327-338.
01-01-2006
Rapidly mixing Markov chains for sampling contingency tables with a constant number of rowsCryan M Dyer M Goldberg LA Jerrum M
Siam J Comput vol. 36 (1), 247-278.
01-01-2006
Two remarks concerning balanced matroidsJerrum M
Combinatorica vol. 26 (6), 733-742.
01-01-2006
Markov chain comparisonJERRUM MR Martin R Dyer M Goldberg LA
Probability Surveys vol. 3, 89-111.
01-01-20062004
Elementary bounds on Poincare and log-Sobolev constants for decomposable Markov chainsJerrum M Tetali P Vigoda E
Ann Appl Probab vol. 14 (4), 1741-1765.
01-11-2004
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entriesJerrum M Sinclair A
J Acm vol. 51 (4), 671-697.
01-07-2004
Special issue on Isaac Newton Institute Programme - Computation, combinatorics and probability: Part I - PrefaceDyer M Jerrum M
Random Struct Algor vol. 24 (3), 233-233.
01-05-2004
The relative complexity of approximate counting problemsDyer M Goldberg LA Greenhill C
Algorithmica vol. 38 (3), 471-500.
01-03-2004
Counting and sampling H-colouringsDyer M Goldberg LA
Inform Comput vol. 189 (1), 1-16.
25-02-2004
A bound on the capacity of backoff and acknowledgment-based protocolsGoldberg LA Jerrum M Kannan S
Siam J Comput vol. 33 (2), 313-331.
01-01-20042003
The computational complexity of two-state spin systemsGoldberg LA Jerrum M
Random Struct Algor vol. 23 (2), 133-154.
01-09-2003
Counting, Sampling and Integrating: Algorithm and ComplexityJerrum M
01-01-20032002
On counting independent sets in sparse graphsDyer M Frieze A
SIAM JOURNAL ON COMPUTING. vol. 31 (5), 1527-1541.
15-08-2002
Convergence of the iterated prisoner's dilemma gameDyer M Goldberg LA Greenhill C
Comb Probab Comput vol. 11 (2), 135-147.
01-03-2002
The 'Burnside process' converges slowlyGoldberg LA
Comb Probab Comput vol. 11 (1), 21-34.
01-01-2002
Rapidly mixing Markov chains for sampling contingency tables with a constant number of rowsCryan M Dyer M Jerrum M
FOCS 2002: 43RD ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS., 711-720.
01-01-2002
Counting and Sampling H-Colourings.Dyer ME Goldberg LA Rolim JDP Vadhan SP
RANDOM. vol. 2483, 51-67.
01-01-2002
Rapidly Mixing Markov Chains for Dismantleable Constraint Graphs.Dyer ME Jerrum M Rolim JDP Vadhan SP
RANDOM. vol. 2483, 68-77.
01-01-2002
Spectral gap and log-Sobolev constant for balanced matroidsJerrum M
FOCS 2002: 43RD ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS., 721-729.
01-01-20022001
An extension of path coupling and its application to the Glauber dynamics for graph coloringsDyer M Goldberg LA Jerrum M Mitzenmacher M
Siam J Comput vol. 30 (6), 1962-1975.
01-01-2001
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries.Jerrum M Sinclair A Vitter JS Spirakis PG Yannakakis M
STOC., 712-721.
01-01-2001
Rapidly Mixing Markov Chains for Dismantleable Constraint Graphs.Dyer ME Vigoda E Nesetril J Winkler P
Graphs, Morphisms and Statistical Physics. vol. 63, 87-95.
01-01-20012000
Randomly Sampling MoleculesGoldberg LA
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 29 (3), 834-853.
01-01-2000
Counting Unlabelled Subtrees of a Tree is #P-completeGoldberg LA Jerrum M
Lms Journal of Computation and Mathematics,
Wiley vol. 3, 117-124.
01-01-20001999
The Swendsen–Wang Process Does Not Always Mix RapidlyGore VK
Journal of Statistical Physics,
Springer Nature vol. 97 (1-2), 67-86.
01-10-1999
On Approximately Counting Colorings of Small Degree GraphsBubley R Greenhill C
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 29 (2), 387-400.
01-01-19991998
Approximately Counting Hamilton Paths and Cycles in Dense GraphsDyer M Frieze A Jerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 27 (5), 1262-1272.
01-10-1998
An $\Omega(\sqrt{\,\log\log n}\,)$ Lower Bound for Routing in Optical NetworksGoldberg LA Jerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 27 (4), 1083-1098.
01-08-1998
An elementary analysis of a procedure for sampling points in a convex bodyBubley R Jerrum M
Random Structures and Algorithms,
Wiley vol. 12 (3), 213-235.
01-05-1998
The Metropolis algorithm for graph bisectionJerrum M Sorkin GB
Discrete Applied Mathematics,
Elsevier vol. 82 (1-3), 155-175.
01-03-19981997
Doubly Logarithmic Communication Algorithms for Optical-Communication Parallel ComputersGoldberg LA Jerrum M Leighton T
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 26 (4), 1100-1119.
01-08-1997
Improved approximation algorithms for MAXk-CUT and MAX BISECTIONFrieze A Jerrum M
Algorithmica,
Springer Nature vol. 18 (1), 67-81.
01-05-19971995
A very simple algorithm for estimating the number of k‐colorings of a low‐degree graphJerrum M
Random Structures and Algorithms,
Wiley vol. 7 (2), 157-165.
01-09-19951994
Simple Translation-Invariant Concepts Are Hard to LearnJerrum M
Information and Computation,
Elsevier vol. 113 (2), 300-311.
01-09-1994
Counting trees in a graph is #P-completeJerrum M
Information Processing Letters,
Elsevier vol. 51 (3), 111-116.
01-08-1994
Three-dimensional Statistical Data Security ProblemsIrving RW
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 23 (1), 170-184.
01-02-19941993
Polynomial-Time Approximation Algorithms for the Ising ModelJerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 22 (5), 1087-1116.
01-10-19931992
Large Cliques Elude the Metropolis ProcessJerrum M
Random Structures and Algorithms,
Wiley vol. 3 (4), 347-359.
01-01-19921990
Fast uniform generation of regular graphsJerrum M Sinclair A
Theoretical Computer Science,
Elsevier vol. 73 (1), 91-100.
01-06-1990
Two-dimensional monomer-dimer systems are computationally intractableJerrum M
Journal of Statistical Physics,
Springer Nature vol. 59 (3-4), 1087-1088.
01-05-19901989
Approximating the PermanentJerrum M
Siam Journal on Computing,
Society For Industrial & Applied Mathematics (Siam) vol. 18 (6), 1149-1178.
01-12-1989
Approximate counting, uniform generation and rapidly mixing Markov chainsSinclair A Jerrum M
Information and Computation,
Elsevier vol. 82 (1), 93-133.
01-07-19891987
Two-dimensional monomer-dimer systems are computationally intractableJerrum M
Journal of Statistical Physics,
Springer Nature vol. 48 (1-2), 121-134.
01-07-19871986
A compact representation for permutation groupsJerrum M
Journal of Algorithms,
Elsevier vol. 7 (1), 60-78.
01-03-1986
Random generation of combinatorial structures from a uniform distributionJerrum MR Valiant LG
Theoretical Computer Science,
Elsevier vol. 43, 169-188.
01-01-19861985
The complexity of finding minimum-length generator sequencesJerrum MR
Theoretical Computer Science,
Elsevier vol. 36, 265-289.
01-01-19851982
Some Exact Complexity Results for Straight-Line Computations over SemiringsJerrum M Snir M
Journal of The Acm,
Association For Computing Machinery (Acm) vol. 29 (3), 874-897.
01-07-1982
Perfect Simulation of the Hard Disks Model by Partial Rejection SamplingJerrum M Guo H
Annales De L’Institut Henri Poincaré D (Aihpd),
European Mathematical Society (Ems)
Approximately counting bases of bicircular matroidsJerrum M Guo H
Combinatorics, Probability and Computing,
Cambridge University Press (Cup)