2012/11/07 by Díaz-Báñez, José Miguel, Korman, Matias, Pérez-Lantero, Pablo +3
#Computational Complexity (cs.CC) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1211.1490
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.