Publications Details
Towards a 4/3 approximation for the asymmetric traveling salesman problem
A long-standing conjecture in combinatorial optimization says that the integrality gap of the famous Held-Karp relaxation of the symmetric TSP is precisely 4/3. In this paper, we show that a slight strengthening of this conjecture implies a tight 4/3 integrality gap for a linear programming relaxation of the asymmetric TSP. This is surprising since no constant-factor approximation is known for the latter problem. Our main tools are a new characterization of the integrality gap for linear objective functions over polyhedra, and the isolation of `hard-to-round' solutions of the relaxations.