Invited Speakers

Dr Ruth Hoffmann, University of St Andrews

Composable Constraint Models for Permutation Patterns and their enumeration

Permutation pattern research started off as investigating which sequences of numbers can be sorted by using a stack. This has now extended into many fields such as using permutations which contain or avoid certain types of patterns when investigating for example Mahonian statistics. Constraint programming is a way of solving combinatorial problems by taking variables, the values they can take and constraints which involve the variables. It then searches for one (all, or the optimal) solution (variable, value assignments) which does not violate the constraints. We will explore different permutation patterns, properties and statistics. While giving you the many definitions we will see how each translates into a constraint model. Having these many models means that we can now easily mix and match them into useful tools to help solve or help investigate permutation problems computationally.

Prof Steve Linton, University of St Andrews

Title and abstract to appear

Prof David Manlove, University of Glasgow

Models and Algorithms for the Kidney Exchange Problem

A patient who requires a kidney transplant, and who has a willing but incompatible donor, may be able to ‘swap’ his or her donor with that of another patient, who is in a similar situation, in a cyclic fashion. Altruistic donors can also trigger “chains” of transplants involving multiple recipients together with their willing but incompatible donors. Kidney exchange programmes (KEPs) organise the systemic detection of optimal sets of cycles and chains based on their pools of donors and recipients. There are many examples of KEPs around the world, including the UK Living Kidney Sharing Scheme (UKLKSS). In this talk I will describe integer programming models and algorithms that can be used to solve the underlying optimisation problem involved in a KEP. This includes the algorithms developed at Glasgow that have been used by NHS Blood and Transplant for the UKLKSS since 2008.

Prof Faron Moller, Swansea University

Title and abstract to appear

Dr Syed Waqar Nabi, University of Glasgow

Title and abstract to appear