TY - GEN

T1 - Constrained routing between non-visible vertices

AU - Bose, Prosenjit

AU - Korman, Matias

AU - van Renssen, André

AU - Verdonschot, Sander

N1 - Funding Information:
P. Bose is supported in part by NSERC. M. Korman was partially supported by MEXT KAKENHI Nos. 12H00855, 15H02665, and 17K12635. A. van Renssen was supported by JST ERATO Grant Number JPMJER1305, Japan. S. Verdonschot is supported in part by NSERC, the Ontario Ministry of Research and Innovation, and the Carleton-Fields Postdoctoral Award.

PY - 2017

Y1 - 2017

N2 - Routing is an important problem in networks. We look at routing in the presence of line segment constraints (i.e., obstacles that our edges are not allowed to cross). Let P be a set of n vertices in the plane and let S be a set of line segments between the vertices in P, with no two line segments intersecting properly. We present the first 1-local O(1)-memory routing algorithm on the visibility graph of P with respect to a set of constraints S (i.e., it never looks beyond the direct neighbours of the current location and does not need to store more than O(1)-information to reach the target). We also show that when routing on any triangulation T of P such that S\subseteq T, no o(n)-competitive routing algorithm exists when only considering the triangles intersected by the line segment from the source to the target (a technique commonly used in the unconstrained setting). Finally, we provide an O(n)-competitive 1-local O(1)-memory routing algorithm on any such T, which is optimal in the worst case, given the lower bound.

AB - Routing is an important problem in networks. We look at routing in the presence of line segment constraints (i.e., obstacles that our edges are not allowed to cross). Let P be a set of n vertices in the plane and let S be a set of line segments between the vertices in P, with no two line segments intersecting properly. We present the first 1-local O(1)-memory routing algorithm on the visibility graph of P with respect to a set of constraints S (i.e., it never looks beyond the direct neighbours of the current location and does not need to store more than O(1)-information to reach the target). We also show that when routing on any triangulation T of P such that S\subseteq T, no o(n)-competitive routing algorithm exists when only considering the triangles intersected by the line segment from the source to the target (a technique commonly used in the unconstrained setting). Finally, we provide an O(n)-competitive 1-local O(1)-memory routing algorithm on any such T, which is optimal in the worst case, given the lower bound.

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U2 - 10.1007/978-3-319-62389-4_6

DO - 10.1007/978-3-319-62389-4_6

M3 - Conference contribution

AN - SCOPUS:85028471100

SN - 9783319623887

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 62

EP - 74

BT - Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings

A2 - Cao, Yixin

A2 - Chen, Jianer

PB - Springer Verlag

T2 - 23rd International Conference on Computing and Combinatorics, COCOON 2017

Y2 - 3 August 2017 through 5 August 2017

ER -