liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Computing Nonsimple Polygons of Minimum Perimeter
TU Braunschweig, Germany.
TU Braunschweig, Germany.
TU Braunschweig, Germany.
Swiss Federal Institute Technology, Switzerland.
Show others and affiliations
2016 (English)In: EXPERIMENTAL ALGORITHMS, SEA 2016, SPRINGER INT PUBLISHING AG , 2016, Vol. 9685, p. 134-149Conference paper, Published paper (Refereed)
Abstract [en]

We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP) asks for a (not necessarily simply connected) polygon with shortest possible boundary length. Even though the closely related problem of finding a minimum cycle cover is polynomially solvable by matching techniques, we prove how the topological structure of a polygon leads to NP-hardness of the MPP. On the positive side, we show how to achieve a constant-factor approximation. When trying to solve MPP instances to provable optimality by means of integer programming, an additional difficulty compared to the TSP is the fact that only a subset of subtour constraints is valid, depending not on combinatorics, but on geometry. We overcome this difficulty by establishing and exploiting additional geometric properties. This allows us to reliably solve a wide range of benchmark instances with up to 600 vertices within reasonable time on a standard machine. We also show that using a natural geometry-based sparsification yields results that are on average within 0.5% of the optimum.

Place, publisher, year, edition, pages
SPRINGER INT PUBLISHING AG , 2016. Vol. 9685, p. 134-149
Series
Lecture Notes in Computer Science, ISSN 0302-9743
Keywords [en]
Traveling Salesman Problem (TSP); Minimum Perimeter Polygon (MPP); Curve reconstruction; NP-hardness; Exact optimization; Integer programming; Computational geometry meets combinatorial optimization
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-132697DOI: 10.1007/978-3-319-38851-9_10ISI: 000386324300010ISBN: 978-3-319-38850-2; 978-3-319-38851-9 (print)OAI: oai:DiVA.org:liu-132697DiVA, id: diva2:1048099
Conference
15th International Symposium on Experimental Algorithms (SEA)
Available from: 2016-11-20 Created: 2016-11-18 Last updated: 2016-11-20

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Schmidt, Christiane
By organisation
Communications and Transport SystemsFaculty of Science & Engineering
Discrete Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 48 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf