## Optimal Sports League Realignment

We consider approaches for optimally organizing competitive sports leagues in light of competitive and logistical considerations. A common objective is to assign teams to divisions so that intradivisional travel is minimized. We present a bilinear programming formulation based on k-way equipartitioning, and show how this formulation can be extended to account for additional constraints and … Read more

## An efficient semidefinite programming relaxation for the graph partition problem

We derive a new semidefinite programming relaxation for the general graph partition problem (GPP). Our relaxation is based on matrix lifting with matrix variable having order equal to the number of vertices of the graph. We show that this relaxation is equivalent to the Frieze-Jerrum relaxation [A. Frieze and M. Jerrum. Improved approximation algorithms for … Read more

## Finding optimal realignments in sports leagues using a branch-and-cut-and-price approach

The sports team realignment problem can be modelled as \$k\$-way equipartition: given a complete graph \$K_{n}=(V,E)\$, with edge weight \$c_{e}\$ on each edge, partition the vertices \$V\$ into \$k\$ divisions that have exactly \$S\$ vertices, so as to minimize the total weight of the edges that have both endpoints in the same division. In this … Read more

## Branch-and-cut for the k-way equipartition problem

We investigate the polyhedral structure of a formulation of the k-way equipartition problem and a branch-and-cut algorithm for the problem. The k-way equipartition problem requires dividing the vertices of a weighted graph into k equally sized sets, so as to minimize the total weight of edges that have both endpoints in the same set. Applications … Read more

## Realignment in the NFL

The National Football League (NFL) in the United States will expand to 32 teams in 2002 with the addition of a team in Houston. At that point, the league will be realigned into eight divisions, each containing four teams. We describe a branch-and-cut algorithm for minimizing the sum of intradivisional travel distances. We consider first … Read more