ISAAC 2015: Algorithms and Computation pp 23-34

# Competitive Local Routing with Constraints

• Prosenjit Bose
• Rolf Fagerberg
• André van Renssen
• Sander Verdonschot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)

## Abstract

Let P be a set of n vertices in the plane and S a set of non-crossing line segments between vertices in P, called constraints. Two vertices are visible if the straight line segment connecting them does not properly intersect any constraints. The constrained $$\theta _m$$-graph is constructed by partitioning the plane around each vertex into m disjoint cones with aperture $$\theta = 2\uppi /m$$, and adding an edge to the ‘closest’ visible vertex in each cone. We consider how to route on the constrained $$\theta _6$$-graph. We first show that no deterministic 1-local routing algorithm is $$o(\sqrt{n})$$-competitive on all pairs of vertices of the constrained $$\theta _6$$-graph. After that, we show how to route between any two visible vertices using only 1-local information, while guaranteeing that the returned path has length at most 2 times the Euclidean distance between the source and destination. To the best of our knowledge, this is the first local routing algorithm in the constrained setting with guarantees on the path length.

## Keywords

Short Path Line Segment Positive Cone Straight Line Segment Short Path Length
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Prosenjit Bose
• 1
• Rolf Fagerberg
• 2
• André van Renssen
• 3
• 4
• Sander Verdonschot
• 1
1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
3. 3.National Institute of Informatics (NII)TokyoJapan
4. 4.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan