Approximating the minimum quadratic assignment problems

Approximating the Maximum Quadratic Assignment Problem1

Solving Quadratic Assignment Problems

We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual infor...

Approximating Minimum Linear Ordering Problems

This paper addresses the Minimum Linear Ordering Problem (MLOP): Given a nonnegative set function f on a finite set V , find a linear ordering on V such that the sum of the function values for all the suffixes is minimized. This problem generalizes well-known problems such as the Minimum Linear Arrangement, Min Sum Set Cover, Minimum Latency Set Cover, and Multiple Intents Ranking. Extending a ...

Approximating minimum cost connectivity problems

We survey approximation algorithms and hardness results for versions of the Generalized Steiner Network (GSN) problem in which we seek to find a low cost subgraph (where the cost of a subgraph is the sum of the costs of its edges) that satisfies prescribed connectivity requirements. These problems include the following well known problems: min-cost k-flow, min-cost spanning tree, traveling sale...

Solving Large Quadratic Assignment Problems

Quadratic Assignment problems are in practice among the most diicult to solve in the class of NP-complete problems. The only successful approach hitherto has been Branch-and-Bound-based algorithms, but such algorithms are crucially dependent on good bound functions to limit the size of the space searched. Much work has been done to identify such functions for the QAP, but with limited success. ...