scholarly journals Local Construction and Coloring of Spanners of Location Aware Unit Disk Graphs

2008 ◽  
pp. 372-383 ◽  
Author(s):  
Andreas Wiese ◽  
Evangelos Kranakis
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs ◽  
Location Aware ◽  
Local Construction

scholarly journals Impact of Locality on Location Aware Unit Disk Graphs

Algorithms ◽  
2008 ◽  
Vol 1 (1) ◽  
pp. 2-29 ◽  
Author(s):  
Andreas Wiese ◽  
Evangelos Kranakis
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs ◽  
Location Aware

Local Construction of Planar Spanners in Unit Disk Graphs with Irregular Transmission Ranges

2006 ◽  
pp. 286-297 ◽  
Author(s):  
Edgar Chávez ◽  
Stefan Dobrev ◽  
Evangelos Kranakis ◽  
Jaroslav Opatrny ◽  
Ladislav Stacho ◽  
...  
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs ◽  
Local Construction

scholarly journals LOCAL CONSTRUCTION AND COLORING OF SPANNERS OF LOCATION AWARE UNIT DISK GRAPHS

2009 ◽  
Vol 01 (04) ◽  
pp. 555-588 ◽  
Author(s):  
ANDREAS WIESE ◽  
EVANGELOS KRANAKIS
Keyword(s):  
Unit Disk ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Local Approximation ◽  
Vertex Coloring ◽  
Local Algorithm ◽  
Unit Disk Graph ◽  
Unit Disk Graphs ◽  
Vertex Coloring Problem ◽  
Local Construction

We look at the problem of coloring locally specially constructed spanners of unit disk graphs. First we present a local approximation algorithm for the vertex coloring problem in Unit Disk Graphs (UDGs) which uses at most four times as many colors as an optimal solution requires. Next we look at the colorability of spanners of UDGs. In particular we present a local algorithm for constructing a 4-colorable spanner of a unit disk graph. The output consists of the spanner and the 4-coloring. The computed spanner also has the properties that it is planar, the degree of a vertex in the spanner is at most 5 and the angles between two edges are at least π/3. By enlarging the locality distance (i.e. the size of the neighborhood which a vertex has to explore in order to compute its color) we can ensure the total weight of the spanner to be arbitrarily close to the weight of a minimum spanning tree. We prove that a local algorithm cannot compute a bipartite spanner of a unit disk graph and therefore our algorithm needs at most one color more than any local algorithm for the task requires. Moreover, we prove that there is no local algorithm for 3-coloring UDGs or spanners of UDGs, even if the 3-colorability of the graph (or the spanner respectively) is guaranteed in advance.

scholarly journals Analysing local algorithms in location-aware quasi-unit-disk graphs

2011 ◽  
Vol 159 (15) ◽  
pp. 1566-1580 ◽  
Author(s):  
Marja Hassinen ◽  
Joel Kaasinen ◽  
Evangelos Kranakis ◽  
Valentin Polishchuk ◽  
Jukka Suomela ◽  
...  
Keyword(s):  
Unit Disk ◽  
Local Algorithms ◽  
Unit Disk Graphs ◽  
Location Aware

scholarly journals Sparse hop spanners for unit disk graphs

2021 ◽  
pp. 101808
Author(s):  
Adrian Dumitrescu ◽  
Anirban Ghosh ◽  
Csaba D. Tóth
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs

scholarly journals Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs

2021 ◽  
Author(s):  
A. Karim Abu-Affash ◽  
Paz Carmi ◽  
Anil Maheshwari ◽  
Pat Morin ◽  
Michiel Smid ◽  
...  
Keyword(s):  
Unit Disk ◽  
Maximum Diameter ◽  
Unit Disk Graphs
Sign in / Sign up

Export Citation Format

Share Document