The Traveling Salesman Problem for random points in the unit square: An experimental and statistical study – University of Copenhagen

The Traveling Salesman Problem for random points in the unit square: An experimental and statistical study

EADS Talk by David S. Johnson from Columbia University

Abstract

TSP instances generated by placing cities uniformly at random within the unit square provide reasonable surrogates for the instances arising in many real-world TSP applications.  They are also an interesting object of study on their own. The optimal tour length is known to grow as c\sqrt{n} for some constant c, but the exact value of c and the details of the convergence rate have not been determined. In this talk I report on an ongoing study of this and related questions with David Applegate and Bill Cook, based on experiments with millions of instances using the Concorde software package. Interesting statistical questions arise.

David S. Johnson

David S. Johnson

In 2010 the ACM Special Interest Group on Algorithms and Computation Theory presented its 2010 Knuth Prize to David S. Johnson of AT&T Labs for his contributions to theoretical and experimental analysis of algorithms. Johnson’s innovations helped lay the foundation for algorithms used to address optimization problems, which involve the process of finding the best solution from all feasible solutions. In addition, Johnson made many contributions to the early development of NP-completeness theory, which helps identify those problems that are hard to solve efficiently.

Johnson’s research in approximation techniques to solve computational problems set up the basic theoretical framework and approach for searching for an “almost” optimal solution. His work over the years has addressed the approximation of many problems including bin packing, which is an NP-hard problem that applies to filling up containers, loading trucks with weight capacity, and creating file backup in removable media. It also addresses TSP (the Traveling Salesman Problem), which can be useful in planning, logistics, and the manufacture of microchips, as well as DNA sequencing.

In addition to his theoretical analysis, Johnson has authored a set of highly influential papers on the experimental analysis of approximation algorithms. This research established equally rigorous standards for experimental algorithms, which focus on implementations as the standard of value and provide the key to the transfer of research results from paper to production code.

Johnson is an acknowledged expert on NP-completeness, a reference to the hardest search problems. His 1979 book, Computers and Intractability: A Guide to the Theory of NP-Completeness, which he coauthored with Michael Garey, remains the standard reference on the topic. Johnson has also written continuously on NP-completeness in his columns for the Journal of Algorithms and ACM Transactions on Algorithms.

An active leader in the theoretical computer science community, Johnson founded the ACM-SIAM (Society for Industrial and Applied Mathematics) Symposium on Discrete Algorithms (SODA) and the ongoing series of DIMACS (Center for Discrete Mathematics and Theoretical Computer Science) Implementation Challenges. He served on the ACM Council as Member-at-Large from 1996-2004, and chaired ACM SIGACT from 1987-1991. He was editor of the Journal of the Association for Computing Machinery (JACM) from 1983-1987, and ACM Transactions on Mathematical Software (TOMS) from 1991-2006. He has also served as associate editor of ACM Transactions on Algorithms (TALG) since its founding in 2004. (ACM)