# Professor Colin McDiarmid

### Professor of Combinatorics

Fellow of **Corpus Christi College**

+44 (0)1865 272872 (Direct)

+44 (0)1865 276700 (College) cmcd at stats.ox.ac.uk

**Research interests**

Discrete mathematics, random structures, algorithms and complexity, combinatorial optimisation, mathematics of operational research.

**Selected publications:**1. 'Random channel assignment problems' - In one model for random radio channel assignment, points corresponding to transmitters are thrown down at random in the plane, and we are to assign a radio channel to each point so that neighbouring points get different channels (to avoid interference).

'

**Random channel assignment in the plane**',

*Rando*

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*Structure*s

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*Algorithm*s 22 (2003) 187 – 212.

In the second model, each pair of transmitters u and v are given minimum distance 0,1 or 2 at random, and we are assign channels 1, 2, 3, .. so that the channels assigned to u and v must differ by at least the specified minimum distance (again, to avoid interference). '

**On the span of random channel assignment problem**',

*Combinatorica*, 27 (2007) 183-203.

2.** ** *Load balancing* - A simple but powerful method for minimising the maximum load of a processor involves picking two processor queues at random and joining the shorter.

'**On the power of two choices': balls and bins in continuous time**, *Annal**s* *of* *Applie**d* *Probabilit*y 15 (2005) 1733-1764. (Joint with Malwina Luczak.)

'**On the maximum queue length in the supermarket model**, *Annal**s* *of* *Probabilit**y* 34 (2006) 493-527. (Joint with Malwina Luczak.)

3. *Random planar graphs* - There has been a huge and successful endeavour investigating random graphs where edges appear independently, but what if , say, we wish to find typical properties of planar graphs after 'Random planar graphs'?

'Random planar graphs', *J*. *Combinatoria**l* *Theor*y B 93 (2005) 187-206. (Joint with Angelika Steger and Dominic Welsh.)

'**Random graphs on surfaces'****,** J*. Combinatorial Theory* B, 98 (2008) 778-797.

**Random graphs from a minor-closed class,** *Combinatorics, Probability and Computing,* 19 (2010) 87-98

**List of** **publications**** (recent and some not so recent) **

**Biographical**I have been based in Oxford as a Fellow of Corpus Christi College since 1989 (having previously been a Fellow of Wolfson College), closely associated with both the Mathematical Institute and the Department of Statistics. I was Head of Department from 2005 to 2009.

**CV**

Research group **Oxford Combinatorics**

**Teaching :**