Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
On Even Triangulations of 2-Connected Embedded Graphs
SIAM Journal on Computing
Communication in wireless networks with directional antennas
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Sensor network connectivity with multiple directional antennae of a given angular sum
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
Graph Orientations with Set Connectivity Requirements
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Local 7-coloring for planar subgraphs of unit disk graphs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
The capacity of wireless networks
IEEE Transactions on Information Theory
Strongly connected orientations of plane graphs
Discrete Applied Mathematics
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We study the problem of orienting some edges of given planar graph such that the resulting subdigraph is strongly connected and spans all vertices of the graph. We are interested in orientations with minimum number of arcs and such that they produce a digraph with bounded stretch factor. Such orientations have applications into the problem of establishing strongly connected sensor network when sensors are equipped with directional antennae. We present three constructions for such orientations. Let G=(V, E) be a connected planar graph without cut edges and let Φ(G) be the degree of largest face in G. Our constructions are based on a face coloring, say with λ colors. First construction gives a strong orientation with at most $\left( 2 - \frac{4 \lambda - 6}{\lambda (\lambda - 1)} \right) |E|$ arcs and stretch factor at most Φ(G)−1. The second construction gives a strong orientation with at most |E| arcs and stretch factor at most $(\Phi (G) - 1)^{\lceil \frac{\lambda + 1}{2} \rceil}$. The third construction can be applied to planar graphs which are 3-edge connected. It uses a particular 6-face coloring and for any integer k≥1 produces a strong orientation with at most $\left(1 - \frac{k}{10 (k + 1)}\right) |E|$ arcs and stretch factor at most Φ2 (G) (Φ(G)−1)2 k+4. These are worst-case upper bounds. In fact the stretch factors depend on the faces being traversed by a path.