Routing in unit disk graphs

Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Let S C R2 be a set of n sites. The unit disk graph UD(S) on S has vertex set S and an edge between two distinct sites s,t Î S if and only if s and t have Euclidean distance |st| ≤ 1. A routing scheme R for UD(S) assigns to each site s Î S a label l(s) and a routing table ρ(s). For any two sites s,t ÎS, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label l(t), the scheme R may consult the current routing table ρ(r) to compute a new site r’ and a new header h’, where r’ is a neighbor of r. The packet is then routed to r’, and the process is repeated until the packet reaches t. The resulting sequence of sites is called the routing path. The stretch of R is the maximum ratio of the (Euclidean) length of the routing path of R and the shortest path in UD(S), over all pairs of sites in S. For any given ε > 0, we show how to construct a routing scheme for UD(S) with stretch 1 + ε using labels of O(log n) bits and routing tables of O(ε-5 log2 n log2 D) bits, where D is the (Euclidean) diameter of UD(S). The header size is O(log n log D) bits.

Original languageEnglish
Title of host publicationLATIN 2016
Subtitle of host publicationTheoretical Informatics - 12th Latin American Symposium, Proceedings
EditorsGonzalo Navarro, Evangelos Kranakis, Edgar Chávez
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783662495285
StatePublished - 2016
Event12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico
Duration: 11 Apr 201615 Apr 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th Latin American Symposium on Theoretical Informatics, LATIN 2016


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