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
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
Fundamentals of Partial Rejection SamplingJerrum M
Probability Surveys,
Institute of Mathematical Statistics 03-09-20242023
A simple polynomial-time approximation algorithm for the total variation distance between two product distributionsJerrum M Guo H Wang J
Theoretics,
Episciences 15-06-20232022
Counting vertices of integral polytopes defined by facetsGuo H
Discrete and Computational Geometry,
Springer 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 graphsJerrum M Dyer M Heinrich M
Combinatorics, Probability and Computing,
Cambridge University Press (Cup) 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 ModelJerrum M
Acm Transactions on Computation Theory,
Association For Computing Machinery vol. 11 (4)
01-07-2019
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.
09-05-20192018
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 JERRUM MR
Annals of Applied Probability,
Institute of Mathematical Statistics 11-04-20182017
The parameterised complexity of counting even and odd induced subgraphsJerrum M
Combinatorica vol. 37 (5), 965-990.
01-10-2017
Uniform sampling through the Lovász Local LemmaGuo H Jerrum M
STOC’17, Montreal, Canada. vol. Part F128415, 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
Functional clones and expressibility of partition functionsBulatov A Goldberg LA Jerrum M
Theoretical Computer Science 11-05-2017
A complexity trichotomy for approximately counting list H-colouringsJERRUM MR Galanis A Goldberg LA
Acm Transactions on Computation Theory,
Association For Computing Maachinery vol. 9 (2)
01-05-2017
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
A complexity trichotomy for approximately counting list H-colouringsGalanis A Jerrum M
Leibniz International Proceedings in Informatics Lipics. vol. 55
01-08-2016
APPROXIMATELY COUNTING H-COLORINGS IS #BIS-HARDGalanis A Goldberg LA
Siam Journal on Computing vol. 45 (3), 680-711.
19-05-20162015
#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 Vigoda E
Journal of Computer and System Sciences vol. 82 (5), 690-711.
02-12-2015
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 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
The parameterised complexity of counting connected subgraphs and graph motifsJerrum M Meeks K
Journal of Computer and System Sciences vol. 81 (4), 702-716.
24-11-2014
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
Glauber dynamics for the hard-core model on bounded-degree H-free graphsJerrum M
Combinatorics, Probability and Computing,
Cambridge University Press
The complexity of counting locally maximal satisfying assignments of Boolean CSPsJERRUM MR
Theoretical Computer Science,
Elsevier
Uniform Sampling through the Lovász Local LemmaJERRUM MR GUO H LIU J
Journal of The Association For Computing Machinery (Acm),
Association For Computing Machinery
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)
Perfect Sampling in Infinite Spin Systems via Strong Spatial MixingAnand K Jerrum M
Siam Journal on Computing,
Society For Industrial and Applied Mathematics
Perfect Sampling of q-Spin Systems on Z^2 via Weak Spatial MixingJerrum M Anand K
Annales De L’Institut Henri Poincaré D,
Ems Press