Local Routing in Sparse and Lightweight Geometric Graphs

Ashvinkumar, VikrantUniv Sydney, Sydney, NSW, Australia.,University of Sydney (författare)

Online routing in a planar embedded graph is central to a number of fields and has been studied extensively in the literature. For most planar graphs no O (1)-competitive online routing algorithm exists. A notable exception is the Delaunay triangulation for which Bose and Morin (SIAM J Comput 33(4):937-951, 2004) showed that there exists an online routing algorithm that is O(1)-competitive. However, a Delaunay triangulation can have Omega (n) vertex degree and a total weight that is a linear factor greater than the weight of a minimum spanning tree. We show a simple construction, given a set V of n points in the Euclidean plane, of a planar geometric graph on V that has small weight (within a constant factor of the weight of a minimum spanning tree on V), constant degree, and that admits a local routing strategy that is O (1)-competitive. Moreover, the technique used to bound the weight works generally for any planar geometric graph whilst preserving the admission of an O (1)-competitive routing strategy.

Gudmundsson, JoachimUniv Sydney, Sydney, NSW, Australia.,University of Sydney(Swepub:lu)csz-jmg (författare)
Levcopoulos, ChristosLund University,Lunds universitet,Institutionen för datavetenskap,Institutioner vid LTH,Lunds Tekniska Högskola,Naturvetenskapliga fakulteten,Department of Computer Science,Departments at LTH,Faculty of Engineering, LTH,Faculty of Science(Swepub:lu)cs-cle (författare)
Nilsson, Bengt J.Malmö University,Malmö universitet,Institutionen för datavetenskap och medieteknik (DVMT)(Swepub:mau)tsbeni (författare)
van Renssen, AndreUniv Sydney, Sydney, NSW, Australia.,University of Sydney (författare)
Univ Sydney, Sydney, NSW, Australia.University of Sydney (creator_code:org_t)

Av författaren/redakt...: Ashvinkumar, Vik ...; Gudmundsson, Joa ...; Levcopoulos, Chr ...; Nilsson, Bengt J ...; van Renssen, And ...

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