2013/02/13 by Joseph S. B. Mitchell, Mitchell, Joseph S. B., Valentin Polishchuk +3 · 2 citations
Computer Science · #68W01 #Computational Geometry (cs.CG) #F.2.2 #FOS: Computer and information sciences #I.3.5 #acm:68W01 #cs.CG #msc:68W01
paper · pdf · doi:10.48550/arxiv.1302.3091
29 pages, 22 figures
arxiv created 2013/02/13 · arxiv updated 2013/02/14
A path or a polygonal domain is C-oriented if the orientations of its edges belong to a set of C given orientations; this is a generalization of the notable rectilinear case (C = 2). We study exact and approximation algorithms for minimum-link C-oriented paths and paths with unrestricted orientations, both in C-oriented and in general domains. Our two main algorithms are as follows: A subquadratic-time algorithm with a non-trivial approximation guarantee for general (unrestricted-orientation) minimum-link paths in general domains. An algorithm to find a minimum-link C-oriented path in a C-oriented domain. Our algorithm is simpler and more time-space efficient than the prior algorithm. We also obtain several related results: - 3SUM-hardness of determining the link distance with unrestricted orientations (even in a rectilinear domain). - An optimal algorithm for finding a minimum-link rectilinear path in a rectilinear domain. The algorithm and its analysis are simpler than the existing ones. - An extension of our methods to find a C-oriented minimum-link path in a general (not necessarily C-oriented) domain. - A more efficient algorithm to compute a 2-approximate C-oriented minimum-link path. - A notion of "robust" paths. We show how minimum-link C-oriented paths approximate the robust paths with unrestricted orientations to within an additive error of 1.