Surveys in Combinatorics, 1989: On the method of bounded differences
- C. McDiarmid
- Mathematics
- 1 August 1989
Concentration
- C. McDiarmid
- Mathematics, Computer ScienceThe Dental register
- 1 June 1862
This paper introduces and surveys two approaches for bounding probabilities of large deviations for sums of bounded independent random variables, and some of their applications.
Colouring random graphs
- C. McDiarmid
- Mathematics, Computer ScienceMathematical Proceedings of the Cambridge…
- 1 March 1975
This work discusses some results concerned with the behaviour of colouring algorithms on large random graphs and investigates the role of noise in the choice of colours.
SIMULATED ANNEALING AND BOLTZMANN MACHINES A Stochastic Approach to Combinatorial Optimization and Neural Computing
- C. McDiarmid
- Computer Science
- 1 November 1991
Channel assignment and weighted coloring
- C. McDiarmid, B. Reed
- MathematicsNetworks
- 1 September 2000
A hardness result and an efficient algorithm yielding an approximate solution to the corresponding weighted coloring problem of assigning sets of colors to vertices of the triangular lattice so that the sets of Colors assigned to adjacent vertices are disjoint.
Acyclic Coloring of Graphs
- N. Alon, C. McDiarmid, B. Reed
- MathematicsRandom Struct. Algorithms
- 1 September 1991
It is shown that if G has maximum degree d, then A(G) = 0(d4/3) as d → ∞, which settles a problem of Erdos who conjectured, in 1976, that A( G) = o(d2) as d →∞.
Concentration for Independent Permutations
- C. McDiarmid
- MathematicsCombinatorics, probability & computing
- 1 March 2002
We give a concentration inequality involving a family of independent random permutations, which is useful for analysing certain randomized methods for graph colouring.
Small transversals in hypergraphs
- V. Chvátal, C. McDiarmid
- MathematicsComb.
- 1 March 1992
It is shown that eachAk withk≥2 has infinitely many extreme points and conjecture that, for every positive ε, it has only finitely manyextreme points [a, b] witha≥ε.
On integer points in polyhedra
- W. Cook, M. Hartmann, R. Kannan, C. McDiarmid
- MathematicsComb.
- 1 March 1992
An algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1+ε in time polynomial inm, ϕ and 1/ε when the dimensionn is fixed is described.
Volumes Spanned by Random Points in the Hypercube
- M. Dyer, Z. Füredi, C. McDiarmid
- MathematicsRandom Struct. Algorithms
- 1992
It is shown that, as n→∞, Vn→0 if N(n)⩽(k−ϵ)n →1 if N (n) ⩾ (k + ϵ) n, and that the same result holds for sampling uniformly from within the hypercube.
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