An exact algorithm for the minimum dilation triangulation problem

Sattar Sattari () and Mohammad Izadi ()
Additional contact information
Sattar Sattari: Sharif University of Technology
Mohammad Izadi: Sharif University of Technology

Journal of Global Optimization, 2017, vol. 69, issue 2, No 3, 343-367

Abstract: Abstract Given a triangulation of a point set on the plane, dilation of any pair of the points is the ratio of their shortest path length to their Euclidean distance. The maximum dilation over all pairs of points is called the dilation of this triangulation. Minimum dilation triangulation problem seeks a triangulation with the least possible dilation of an input point set. For this problem no polynomial time algorithm is known. We present an exact algorithm based on a branch and bound method for finding minimum dilation triangulations. This deterministic algorithm after generating an initial solution, iteratively computes a lower bound for the answer and then applies a branch and bound method to find a better solution. It also uses a local search method to improve the initial solution and the obtained solution of the branch and bound method. We implemented our algorithm and conducted computational experiments on some benchmark instances. The efficacy of the approach is demonstrated by comparing its results with two other published methods.

Keywords: Triangulation; Dilation; Branch and bound (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-017-0517-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0517-x

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-017-0517-x

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().