Realignment in the National Football League: Did they do it right?

Mitchell, John E.

doi:10.1002/nav.10084

Cited by 31 publications

(29 citation statements)

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“…The minimum k-partition problem (MkP) is a well-known optimization problem encountered in various applications such as network planning (Eisenblätter 2002), VLSI layout design (Barahona et al 1988), micro-aggregation of statistical data (Domingo-Ferrer and Mateo-Sanz 2002), sports team scheduling (Mitchell 2003;Elf et al 2003), and statistical physics (Liers et al 2004). It is known to be N P-hard in general and difficult to solve in practice.…”

Section: Introductionmentioning

confidence: 99%

A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem

2008

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The minimum k-partition (MkP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite programming (SBC) for the MkP problem. The two key ingredients for this algorithm are: the combination of semidefinite programming with polyhedral results; and a novel iterative clustering heuristic (ICH) that finds feasible solutions for the MkP problem. We compare ICH to the hyperplane rounding techniques of Goemans and Williamson and of Frieze and Jerrum, and the computational results support the conclusion that ICH consistently provides better feasible solutions for the MkP problem. ICH is used in our SBC algorithm to provide feasible solutions at each node of the branch-and-bound tree. The SBC algorithm computes globally optimal solutions for dense graphs with up to 60 vertices, for grid graphs with up to 100 vertices, and for different values of k, providing a fast exact approach for k ≥ 3.Keywords Minimum k-partition · Semidefinite programming · Branch-and-cut · Polyhedral cuts Dedicated to the memory of Peter L. Hammer and in celebration of his outstanding contribution to the field of operations research.

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Section: Introductionmentioning

confidence: 99%

A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem

2008

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“…In American Football, the National Football League was reorganised in 2002 into eight divisions of four teams, with the declared objective of minimising travel. Mitchell (2003) treated this as a classical optimisation problem, which he solved using branch-and-cut methods. The conclusion was that the reorganisation was very close to optimal, under reasonable assumptions about constraints concerning the importance of traditional rivals being in the same division as one another.…”

Section: Organisation Of Teams Into Divisions/groupsmentioning

confidence: 99%

OR analysis of sporting rules – A survey

Wright

2014

European Journal of Operational Research

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This paper surveys the academic OR/analytics literature describing research into the laws and rules of sports and sporting competitions. The literature is divided into post hoc analyses and proposals for future changes, and is also divided into laws/rules of sports themselves and rules/organisation of tournaments or competitions.The survey outlines a large number of studies covering 21 sports in many parts of the world. The analytical approaches most commonly used are found to be various forms of regression analysis and simulation. Issues highlighted by this survey include the different views of what constitutes fairness and the frequency with which changes produce unintended consequences.

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“…19 Good algorithms for the k-way equipartition problem when sample sizes are small can be found in Ji and Mitchell (2005) and (≈ 100) Mitchell (2003). This restriction makes these algorithms impractical for our purposes.…”

Section: The Minimum-partitioning Problemmentioning

confidence: 99%

Measuring the Compactness of Political Districting Plans

Fryer

Holden

2007

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. AbstractWe 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 identically to our index. We then calculate the relative proximity index for the 106th Congress, which requires us to solve for each state's maximal compactness-a problem that is nondeterministic polynomial-time hard (NP hard). The correlations between our index and the commonly used measures of dispersion and perimeter are Ϫ.37 and Ϫ.29, respectively. We conclude by estimating seatvote curves under maximally compact districts for several large states. The fraction of additional seats a party obtains when its average vote increases is significantly greater under maximally compact districting plans relative to the existing plans.

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Realignment in the National Football League: Did they do it right?

Cited by 31 publications

References 31 publications

A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem

A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem

OR analysis of sporting rules – A survey

Measuring the Compactness of Political Districting Plans

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