Sökning: onr:"swepub:oai:DiVA.org:liu-132697"
> (2016) >
Computing Nonsimple...
Computing Nonsimple Polygons of Minimum Perimeter
-
- Fekete, Sandor P. (författare)
- TU Braunschweig, Germany
-
- Haas, Andreas (författare)
- TU Braunschweig, Germany
-
- Hemmer, Michael (författare)
- TU Braunschweig, Germany
-
visa fler...
-
- Hoffmann, Michael (författare)
- Swiss Federal Institute Technology, Switzerland
-
- Kostitsyna, Irina (författare)
- TU Eindhoven, Netherlands
-
- Krupke, Dominik (författare)
- TU Braunschweig, Germany
-
- Maurer, Florian (författare)
- TU Braunschweig, Germany
-
- Mitchell, Joseph S. B. (författare)
- SUNY Stony Brook, NY 11794 USA
-
- Schmidt, Arne (författare)
- TU Braunschweig, Germany
-
- Schmidt, Christiane (författare)
- Linköpings universitet,Kommunikations- och transportsystem,Tekniska fakulteten
-
- Troegel, Julian (författare)
- TU Braunschweig, Germany
-
visa färre...
-
(creator_code:org_t)
- 2016-06-01
- 2016
- Engelska.
-
Ingår i: EXPERIMENTAL ALGORITHMS, SEA 2016. - Cham : SPRINGER INT PUBLISHING AG. - 9783319388502 - 9783319388519 ; , s. 134-149
- Relaterad länk:
-
https://www.research...
-
visa fler...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
visa färre...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- Traveling Salesman Problem (TSP); Minimum Perimeter Polygon (MPP); Curve reconstruction; NP-hardness; Exact optimization; Integer programming; Computational geometry meets combinatorial optimization
Publikations- och innehållstyp
- ref (ämneskategori)
- kon (ämneskategori)
Hitta via bibliotek
Till lärosätets databas
- Av författaren/redakt...
-
Fekete, Sandor P ...
-
Haas, Andreas
-
Hemmer, Michael
-
Hoffmann, Michae ...
-
Kostitsyna, Irin ...
-
Krupke, Dominik
-
visa fler...
-
Maurer, Florian
-
Mitchell, Joseph ...
-
Schmidt, Arne
-
Schmidt, Christi ...
-
Troegel, Julian
-
visa färre...
- Om ämnet
-
- NATURVETENSKAP
-
NATURVETENSKAP
-
och Matematik
-
och Diskret matemati ...
- Artiklar i publikationen
-
EXPERIMENTAL ALG ...
- Av lärosätet
-
Linköpings universitet