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  • 1.
    Mitchell, Joseph S. B.
    et al.
    Stony Brook University, USA.
    Polishchuk, Valentin
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. University of Helsinki, Finland.
    Sysikaski, Mikko
    University of Helsinki, Finland .
    Minimum-link paths revisited2014In: Computational geometry, ISSN 0925-7721, E-ISSN 1879-081X, Vol. 47, no 6, p. 651-667Article in journal (Refereed)
    Abstract [en]

    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.

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