Greedy and Local Search Heuristics to Build Area-Optimal Polygons

Abstract

In this article, we present our heuristic solutions to the problems of finding the maximum and minimum area polygons with a given set of vertices. Our solutions are based mostly on two simple algorithmic paradigms: greedy and local search. The greedy heuristic starts with a simple polygon and adds vertices one by one, according to a weight function. A crucial ingredient to obtain good solutions is the choice of an appropriate weight function that avoids long edges, since long edges impede the insertion of too many different edges later on. The local search part consists of moving consecutive vertices to another location in the polygonal chain. We also discuss the different implementation techniques that are necessary to reduce the running time.

Area-Optimal Simple Polygonalizations: The CG Challenge 2019

“…• Julien Lepagnot, Laurent Moalic, Dominique Schmitt: Optimal area polygonization by triangulation and raytracing [19] • Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard: Greedy and Local Search Solutions to the Minimum and Maximum Are [7] • Nir Goren, Efi Fogel, Dan Halperin: Area-optimal polygonization using simulated annealing [18] • Günther Eder, Martin Held, Steinpor Jasonarson, Philipp Mayer, Peter Palfrader: 2-Opt moves and flips for area-optimal polygonizations [9] • Natanael Ramos, Rai Caetan de Jesus, Pedro de Rezende, Cid de Souza, Fabio Luiz Usberti: Heuristics for area optimal polygonizations [29] In addition, there is one paper focusing on exact methods for computing provably optimal solutions.…”

“…2 0 1 9 -0 3 -0 1 2 0 1 9 -0 3 -1 5 2 0 1 9 -0 4 -0 1 2 0 1 9 -0 4 -1 5 2 0 1 9 -0 5 -0 1 2 0 1 9 -0 5 -1 5 2 0 1 9 -0 6 -0 1 (1) Team OMEGA/Mulhouse (France): Julien Lepagnot, Laurent Moalic, Dominique Schmitt [19] (2) Team lcrombez/Clermont Auvergne(France): Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard [7] (3) Team cgl@tau/Tel Aviv (Israel): Nir Goren, Efi Fogel, Dan Halperin [18] (4) Team CGA/Salzburg (France): Günther Eder, Martin Held, Steinthor Jasonarson, Philipp Mayer, Peter Palfrader [9].…”

Area-Optimal Simple Polygonalizations: The CG Challenge 2019

“…(Here shown for b (P) = 11 and i (P) = 6. )-Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard: Greedy and local search solutions to the minimum and maximum area[7]. -Nir Goren, Efi Fogel, Dan Halperin: Area-optimal polygonization using simulated annealing[18].…”