• Publications
  • Influence
Path coupling: A technique for proving rapid mixing in Markov chains
  • Russ Bubley, M. Dyer
  • Mathematics, Computer Science
  • Proceedings 38th Annual Symposium on Foundations…
  • 19 October 1997
TLDR
A new approach to the coupling technique, which is called path coupling, for bounding mixing rates, is illustrated, which may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method. Expand
Formulating the single machine sequencing problem with release dates as a mixed integer program
  • M. Dyer, L. Wolsey
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 1 February 1990
TLDR
A hierarchy of relaxations obtained by combining enumeration of initial sequences with Smith's rule can be formulated as a linear programming problem in an enlarged space of variables and new valid inequalities for the problem are obtained. Expand
The complexity of counting graph homomorphisms
TLDR
The theorems provide the first proof of #P-completeness of the partition function of certain models from statistical physics, such as the Widom–Rowlinson model, even in graphs of maximum degree 3. Expand
Locating the Phase Transition in Binary Constraint Satisfaction Problems
TLDR
It is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction. Expand
Linear Time Algorithms for Two- and Three-Variable Linear Programs
  • M. Dyer
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1 February 1984
TLDR
Algorithms for linear programming problems with two or three variables and n constraints are described, improving the previously known best bounds of $O(n\log n)$ time. Expand
A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies
We present a randomised polynomial time algorithm for approximating the volume of a convex body K in n -dimensional Euclidean space. The proof of correctness of the algorithm relies on recent theoryExpand
The Stable Marriage Problem: Structure and Algorithms
  • M. Dyer
  • Computer Science
  • 1 March 1991
On Counting Independent Sets in Sparse Graphs
TLDR
Two results are proved concerning approximate counting of independent sets in graphs with constant maximum degree $\Delta$ that imply that the Markov chain Monte Carlo technique is likely to fail and that no fully polynomial randomized approximation scheme can exist for $\Delta \geq 25$ unless $\mathrm{RP}=\mathrm(NP)$. Expand
A more rapidly mixing Markov chain for graph colorings
TLDR
A new Markov chain is defined on k-colourings of graphs, and its convergence properties are related to the maximum degree ∆ of the graph, and it is shown to have bounds on convergence time appreciably better than those for the wellknown Jerrum/Salas–Sokal chain in most circumstances. Expand
On the Complexity of Computing the Volume of a Polyhedron
We show that computing the volume of a polyhedron given either as a list of facets or as a list of vertices is as hard as computing the permanent of a matrix.
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