TY - GEN

T1 - New results on stabbing segments with a polygon

AU - Díaz-Báñez, José Miguel

AU - Korman, Matias

AU - Pérez-Lantero, Pablo

AU - Pilz, Alexander

AU - Seara, Carlos

AU - Silveira, Rodrigo I.

PY - 2013

Y1 - 2013

N2 - We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.

AB - We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.

UR - http://www.scopus.com/inward/record.url?scp=84883326318&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883326318&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-38233-8_13

DO - 10.1007/978-3-642-38233-8_13

M3 - Conference contribution

AN - SCOPUS:84883326318

SN - 9783642382321

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 157

BT - Algorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings

T2 - 8th International Conference on Algorithms and Complexity, CIAC 2013

Y2 - 22 May 2013 through 24 May 2013

ER -