This article illustrates how the relationship between political geography and the electoral bias of a districting plan, as measured by the efficiency gap, can be analyzed in a statistically rigorous manner using computer simulations of the legislative redistricting process. By generating a large number of different districting plans designed to optimize on traditional redistricting criteria, th...

Regular security controls on a day by day basis are an essential and important mechanism to prevent theft and vandalism in business buildings. Typically, security workers patrol through a set of objects where each object requires a particular number of visits on all or some days within a given planning horizon, and each of these visits has to be performed in a specific time window. An important...

The aim of districting problems is to get an optimized partition of a territory into smaller units, called districts or zones, subject to some side constraints such as balance, contiguity, and compactness. Logistics districting problems usuually involve additional optimization criteria and constraints. Districting problems are called continuous when the underlying space, both for facility sites...

The City of Philadelphia recently redesigned districts for its council members based upon the 2010 census. The districting process evinced considerable public interest and engagement because council districts from the prior census had significant shortcomings. During the 2010 redistricting process, several public interest groups came together to organize a districting contest. The organizers ho...

Political Districting Problem is one of the critical issues in political elections, it can be expressed as: how to partition a state into reasonable districts for parliament election and presidential election. In this paper, the political districting problem for parliament election is modelled as a doubly weighted graph partition problem and it is formulated into quadratic programming model. Us...

We develop a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable, which we coin the relative proximity index. Any compactness measure that satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identi...

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis the problem without constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies sharp contrast between proportionality competitiveness how might be overcome a properly formulated objective function. It...