# DIMACS Princeton Theory Seminar

## Title:

Nearly Linear Time Approximation Schemes for Euclidean TSP and Other Geometric Problems

## Speaker:

- Sanjeev Arora
- Princeton University

## Place:

- Room 402, Computer Science Building
- 35 Olden Street
- Princeton University.

## Time:

- 12:05 PM (Lunch will be served at 11:45 AM)
- Thursday, April 10, 1997

## Contact:

- Sanjeev Arora (arora@cs.princeton.edu)

## Abstract:

The Euclidean Traveling Salesman Problem is NP-hard. In 1976,
Christofides discovered a polynomial-time approximation algorithm that
finds a salesman tour of cost at most 1.5 times the optimal.
Last year we presented a new algorithm that is an approximation
scheme: for any fixed c>0, it computes a tour of cost at most
1+c times the optimal. The scheme's running time was n^{O(1/c)}.

This talk will describe an approximation scheme that is simpler and
much more efficient. For any fixed c>0, it finds a (1+c)-approximate
tour in n*polylog(n) time, which is nearly linear in n. The scheme
also works in nearly linear time on instances in d dimensions (for
fixed d).

Our algorithm generalizes to many other geometric problems,
including the famous Minimum Steiner Tree problem, and the Euclidean
Matching problem.

Document last modified on March 28, 1997