The Boyd Conjecture

A proof of the Boyd-Carr conjecture

Determining the precise integrality gap for the subtour LP relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years in the general case of symmetric costs that obey triangle inequality. Boyd and Carr [3] observe that we do not even know the worst-case upper bound on the ratio of the optimal 2-matching to the subtour LP; they conjectu...

2-Matchings, the Traveling Salesman Problem, and the Subtour LP: A Proof of the Boyd-Carr Conjecture

In this paper,we study the integrality gap of the subtour LP relaxation for thetraveling salesman problem in the special case when all edge costs are either 1 or 2. Forthe general case of symmetric costs that obey triangle inequality, a famous conjectureis that the integrality gap is 4/3. Little progress towards resolving this conjecturehas been made in 30years. We conjecture th...

Jesse Boyd Abstract MS

Elizabeth Boyd

Modified Boyd amputation.

Amputation is one of the oldest procedures in surgery; this is shown on the wall of the Temple of Rameses III near Luxor. In the foot, amputation between the tarsometatarsal level and the level of the Syme procedure results in an equinus deformity due to imbalance between tendons acting at the ankle. Syme’s amputation is simple and produces a stump with end-bearing properties and good proprioce...