 
Summary: University of Washington Math 523A Lecture 7
Lecturer: Eyal Lubetzky
Monday, April 20, 2009
1 Another application of HoeffdingAzuma
Here we discuss an application of the HoeffdingAzuma inequality in which it's important to
use nonuniform bounds on the increments (as opposed to our previous applications, which
used a uniform bound). We will apply HoeffdingAzuma to a random version of the Traveling
Salesman Problem.
1.1 Problem description
We first describe the deterministic version of TSP:
Traveling Salesman Problem (TSP): Find an optimal circuit traversing n points p1, . . . , pn
in the unit square. More explicitly,
· Input: p1, . . . , pn [0, 1]2
· Goal: Find a permutation Sn which minimizes the sum
n
i=1
p(i+1)  p(i) ,
where we identify pn+1 with p1, and · denotes the Euclidean norm.
Unlike our previous applications (e.g. finding the chromatic number of a graph), TSP
has a good polynomialtime approximation scheme. However, it is NPhard to nail down the
