A tabu search heuristic for the Equitable Coloring Problem

The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several applications. Due to the hardness of the problem, current exact algorithms can not solve large-sized instances. Such instances must be addressed only via heuristic methods. In this paper we present a tabu search heuristic for the Equitable Coloring Problem. This algorithm is an adaptation of the dynamic TabuCol version of Galinier and Hao. In order to satisfy equity constraints, new local search criteria are given. Computational experiments are carried out in order to find the best combination of parameters involved in the dynamic tenure of the heuristic. Finally, we show the good performance of our heuristic over known benchmark instances

Assessing relative spending needs of devolved government: the case of healthcare spending in the UK

The system used to allocate resources to the UK's devolved territories, known as the Barnett formula, takes no account of the relative expenditure needs of the territories. In this paper we investigate the prospects of developing a needs based model for allocating healthcare resources to Scotland, Wales and Northern Ireland. We compare the method used by the National Health Service in England to allocate resources geographically within England with the method used by the NHS in Scotland to allocate resources to territorial Health Boards. By applying both approaches to the UK's devolved territories, we are able to examine similarities and differences in the two methods, and explore implications for an assessment of the relative healthcare expenditure need of each territory. The implications for the way in which revenue is distributed to Wales, Scotland and Northern Ireland are discussed

Parameter tuning patterns for random graph coloring with quantum annealing.

Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and/or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades