Abstract
Given a set \(\mathcal P\) of h pairwise disjoint convex polygonal obstacles in the plane, defined with n vertices, we preprocess \(\mathcal P\) and compute one routing table at each vertex in a subset of vertices of \(\mathcal P\). For routing a packet from any vertex \(s \in \mathcal P\) to any vertex \(t \in \mathcal P\), our scheme computes a routing path with a multiplicative stretch \(1+\epsilon \) and an additive stretch \(2 k \ell \), by consulting routing tables at only a subset of vertices along that path. Here, k is the number of obstacles of \(\mathcal P\) the routing path intersects, and \(\ell \) depends on the geometry of obstacles in \(\mathcal P\). During the preprocessing phase, we construct routing tables of size \(O(n + \frac{h^3}{\epsilon ^2} \mathrm {polylog}{(\frac{h}{\epsilon })})\) in \(O(n+\frac{h^3}{\epsilon ^2}\mathrm {polylog}{(\frac{h}{\epsilon })})\) time, where \(\epsilon < 1\) is an input parameter.
R. Inkulu—This research is supported in part by SERB MATRICS grant MTR/2017/000474.
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Inkulu, R., Kumar, P. (2021). Routing Among Convex Polygonal Obstacles in the Plane. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_1
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