A mini–max spanning forest approach to the political districting problem

Abstract

We formulate the problem of political districting as a mini–max spanning forest problem, and present some local search-based heuristics to solve the problem approximately. Through numerical experiments, we evaluate the performance of the developed algorithms. We also give a case study of a prefecture in Japan for the election of the Lower House Members of the National Diet. We observe that ‘hyperopic’ algorithm usually gives satisfactory solutions, with the resulting districts all connected and usually balanced in size.

Keywords:

• political districting
• heuristic algorithm
• spanning forest
• mini–max optimisation