TY - GEN

T1 - Routing in unit disk graphs

AU - Kaplan, Haim

AU - Mulzer, Wolfgang

AU - Roditty, Liam

AU - Seiferth, Paul

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84961755011&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-49529-2_40

DO - 10.1007/978-3-662-49529-2_40

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AN - SCOPUS:84961755011

SN - 9783662495285

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

SP - 536

EP - 548

BT - LATIN 2016

A2 - Navarro, Gonzalo

A2 - Kranakis, Evangelos

A2 - Chávez, Edgar

PB - Springer Verlag

T2 - 12th Latin American Symposium on Theoretical Informatics, LATIN 2016

Y2 - 11 April 2016 through 15 April 2016

ER -