A divide-and-conquer based preprocessing for routing in a simple polygon

Siddharth Gaur () and R. Inkulu ()
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Siddharth Gaur: Indian Institute of Technology Guwahati
R. Inkulu: Indian Institute of Technology Guwahati

Journal of Combinatorial Optimization, 2025, vol. 50, issue 2, No 6, 18 pages

Abstract: Abstract Given a simple polygon P defined with n vertices in the plane, we preprocess P and compute routing tables at every vertex of P. In the routing phase, a packet originating at any source vertex of P is routed to its destination vertex belonging to P. At every vertex v of P along the routing path, until the packet reaches its destination, the next hop is determined using the routing tables at v and the additional information (including the packet’s destination vertex label) in the packet. We show our routing scheme constructs routing tables in $$O\big (n \big (1+\frac{1}{\epsilon }\big ) \big (\lg {n}\big )^3\big )$$ time and the routing tables at all the vertices of P together use $$O\big (n+\frac{n}{\epsilon }\big (\lg {n}\big )^3\big )$$ space. The multiplicative stretch factor of the routing path computed by our algorithm is upper bounded by $$(2+\epsilon )\lg {n}$$ . Here, $$\epsilon > 0$$ is an input parameter.

Keywords: Computational geometry; Geometric shortest paths; Geometric routing; Approximation algorithms (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01345-9

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