Algorithms for hub label optimization

We consider the problem of approximating optimal hub labelings in the context of labeling algorithms for the shortest path problem. A previous result was a O(logn) approximating for minimizing the total label size. We give an O(logn)-approximation algorithm for the maximum label size. We also give O(logn)-approximation algorithms for natural generalizations of the problem: Minimizing an ℓp norm of the labeling and simultaneously minimizing ℓp and ℓq norms.