Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

University of Washington Math 523A Lecture 7 Lecturer: Eyal Lubetzky

Summary: University of Washington Math 523A Lecture 7
Lecturer: Eyal Lubetzky
Monday, April 20, 2009
1 Another application of Hoeffding-Azuma
Here we discuss an application of the Hoeffding-Azuma 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 Hoeffding-Azuma 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
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 polynomial-time approximation scheme. However, it is NP-hard to nail down the


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle


Collections: Computer Technologies and Information Sciences