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.
Publisher Copyright:
© 2017, Springer International Publishing AG.
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 -