Computing an $$L_1$$L1 shortest path among splinegonal obstacles in the plane

Tameem Choudhury () and R. Inkulu ()
Additional contact information
Tameem Choudhury: IIT Guwahati
R. Inkulu: IIT Guwahati

Journal of Combinatorial Optimization, No 0, 21 pages

Abstract: Abstract We reduce the problem of computing an $$L_1$$L1 shortest path between two given points s and t in the given splinegonal domain $$\mathcal {S}$$S to the problem of computing an $$L_1$$L1 shortest path between two points in the polygonal domain. Our reduction algorithm defines a polygonal domain $$\mathcal {P}$$P from $$\mathcal {S}$$S by identifying a coreset of points on the boundaries of splinegons in $$\mathcal {S}$$S. Further, it transforms a shortest path between s and t among polygonal obstacles in $$\mathcal {P}$$P to a shortest path between s and t among splinegonal obstacles in $$\mathcal {S}$$S. When $$\mathcal {S}$$S is comprised of h pairwise disjoint simple splinegons defined with a total of n vertices, excluding the time to compute an $$L_1$$L1 shortest path among simple polygonal obstacles in $$\mathcal {P}$$P, our reduction algorithm takes $$O(n + h \lg {n} + (\lg {h})^{1+\epsilon })$$O(n+hlgn+(lgh)1+ϵ) time. Here, $$\epsilon $$ϵ is a small positive constant [resulting from the triangulation of the free space using Bar-Yehuda and Chazelle (Int J Comput Geom Appl 4(4):475–481, 1994)]. For the special case of $$\mathcal {S}$$S comprising of concave-out splinegons, we have devised another reduction algorithm. This algorithm does not rely on the structures used in the algorithm (Inkulu and Kapoor in Comput Geom 42(9):873–884, 2009) to compute an $$L_1$$L1 shortest path in the polygonal domain. Further, we have characterized few of the properties of $$L_1$$L1 shortest paths among splinegons which could be of independent interest.

Keywords: Computational geometry; Shortest paths; Splinegon obstacles (search for similar items in EconPapers)
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-020-00524-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00524-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-020-00524-0

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().