Featured Research

from universities, journals, and other organizations

A Travelling Salesman Problem special case: 30-year-old problem solved

Date:
September 13, 2012
Source:
University of Warwick
Summary:
The science of computational complexity aims to solve the TSP -- the Travelling Salesman Problem -- when the time required to find an optimal solution is vital for practical solutions to modern-day problems such as air traffic control and delivery of fresh food. Researchers have now solved a 30-year-old TSP special case problem.

The science of computational complexity aims to solve the TSP -- the Travelling Salesman Problem -- when the time required to find an optimal solution is vital for practical solutions to modern-day problems such as air traffic control and delivery of fresh food. Warwick Business School's Dr Vladimir Deineko and colleagues have now solved a 30-year-old TSP special case problem.

The Travelling Salesman Problem, or TSP, was first defined around 150 years ago. The problem then was to find the shortest possible route for salesmen to visit each of their customers once and finish back where they started. In the 21st century, this same problem now applies to a multitude of activities -- delivering fresh stock to supermarkets, supplying manufacturing lines, air traffic control, and even DNA sequencing. Complex and sophisticated computer programmes using optimisation -- where algorithms produce the best possible result from multiple choices -- now form the basis of solutions to these modern-day problems. The time required to find an optimal solution is vital for practical application of the TSP. How long can lorry drivers wait for their route to be finalised when the salads they hope to deliver will only be fresh for another 24 hours? How long can air traffic control keep an airliner flying in circles around Heathrow Airport?

The theoretical background behind these types of questions is studied in the theory of computational complexity. The TSP is of paramount significance for this branch of knowledge. Even a small incremental step in understanding the nature of this problem is of interest and benefit to the scientific community.

Associate Professor Dr Vladimir Deineko of Warwick Business School, together with Eranda Cela (University of Technology Graz, Austria) and Gerhard Woeginger (Eindhoven University, the Netherlands) have addressed a special case of the TSP, or open problem as it is termed, first identified 30 years ago. Dr Deineko's and his colleagues' work gives a solution of theoretical significance for computer science and operational research.

Dr Deineko comments, "The TSP has served as a benchmark problem for all new and significant approaches developed in optimisation. It belongs to the set of so called NP-hard problems. There are obviously some special cases when the TSP can be solved efficiently. The simplest possible case is when the cities are the points on a straight line and the distances are as-the-crow-flies-distances. One can easily get the shortest route for visiting all the points in this case. Probably the next simplest case would be the case when the cities are the points on two perpendicular lines and the distances are again as-the-crow-flies-distances (so-called X-and-Y-axes TSP).

"Despite its apparent simplicity, this special case problem has been circulating in the scientific community for around 30 years. Until our work, it was not known whether an algorithm existed which would guarantee finding an optimal solution to any instance of these problems within a reasonable amount of time. We have now proved that the X-and-Y axes TSP can be easily solved in a number of steps proportional to the square of the number of cities."

Dean of WBS, Professor Mark Taylor, comments, "I congratulate Dr Deineko and his colleagues in advancing our knowledge of this enormously complex subject. They have produced cutting-edge research which is not only of great importance to the scientific community, but ultimately also of great relevance to all of us who depend on modern technology as we go about our daily lives."


Story Source:

The above story is based on materials provided by University of Warwick. Note: Materials may be edited for content and length.


Journal Reference:

  1. Eranda Ηela, Vladimir Deineko, Gerhard J. Woeginger. The x-and-y-axes travelling salesman problem. European Journal of Operational Research, 2012; 223 (2): 333 DOI: 10.1016/j.ejor.2012.06.036

Cite This Page:

University of Warwick. "A Travelling Salesman Problem special case: 30-year-old problem solved." ScienceDaily. ScienceDaily, 13 September 2012. <www.sciencedaily.com/releases/2012/09/120913091939.htm>.
University of Warwick. (2012, September 13). A Travelling Salesman Problem special case: 30-year-old problem solved. ScienceDaily. Retrieved April 23, 2014 from www.sciencedaily.com/releases/2012/09/120913091939.htm
University of Warwick. "A Travelling Salesman Problem special case: 30-year-old problem solved." ScienceDaily. www.sciencedaily.com/releases/2012/09/120913091939.htm (accessed April 23, 2014).

Share This



More Computers & Math News

Wednesday, April 23, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

High Court to Hear Dispute of TV Over Internet

High Court to Hear Dispute of TV Over Internet

AP (Apr. 22, 2014) — The future of Aereo, an online service that provides over-the-air TV channels, hinges on a battle with broadcasters that goes before the U.S. Supreme Court on Tuesday. (April 22) Video provided by AP
Powered by NewsLook.com
Aereo Takes on Broadcast TV Titans in Supreme Court Today

Aereo Takes on Broadcast TV Titans in Supreme Court Today

TheStreet (Apr. 22, 2014) — Aereo heads to the Supreme Court today to fight for its right to stream broadcast TV over the Internet -- against broadcasters who say the start-up infringes upon copyright law. TheStreet Deputy Managing Editor Leon Lazaroff explains the importance of the case in the TV industry and details what the outcome of it could mean for broadcasters and for cloud storage services -- as Aereo allows its subscribers to not just watch live TV shows but also store content to a DVR in the cloud. Video provided by TheStreet
Powered by NewsLook.com
Lytro Introduces 'Illum,' A Professional Light-Field Camera

Lytro Introduces 'Illum,' A Professional Light-Field Camera

Newsy (Apr. 22, 2014) — The light-field photography engineers at Lytro unveiled their next innovation: a professional DSLR-like camera called "Illum." Video provided by Newsy
Powered by NewsLook.com
Netflix To Raise Prices For New Subscribers

Netflix To Raise Prices For New Subscribers

Newsy (Apr. 21, 2014) — Netflix executives say they don't think a $1 or $2 price hike will hurt the service, and they have their sites set on overtaking HBO. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins