Quadratic Assignment on Different Data Models

  • Soledad Villar | New York University

Quadratic assignment is a very general problem in theoretical computer science. It includes graph matching, the traveling salesman problem, and the Gromov-Hausdorff distance between finite metric spaces as particular cases. Quadratic assignment is in general NP-hard and even hard to approximate, but in fact, the problem can be tractable for a large subset of instances. In this talk, we present different algorithmic approaches that lead to meaningful results for different data models. A semidefinite relaxation provides a pseudometric that can be computed in polynomial-time and has similar topological properties to the GH distance. A projected power iteration algorithm succeeds at aligning noisy networks. And a graph neural network can actually learn an algorithm to solve network alignment and the traveling salesman problem from solved problem instances.

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