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
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Strong orientations of planar graphs with bounded stretch factor
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
The capacity of wireless networks
IEEE Transactions on Information Theory
Guaranteed performance heuristics for the bottleneck travelling salesman problem
Operations Research Letters
| Hi-index | 0.04 |
We study the problem of orienting a subset of edges of a given plane graph such that the resulting sub-digraph is strongly connected and spans all vertices of the graph. We are interested in orientations with minimum number of arcs which at the same time produce a digraph with smallest possible 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 2-edge connected plane graph and let @F(G) be the degree of the largest face in G. Our constructions are based on a face coloring of G, say with @l colors. The first construction gives a strongly connected orientation with at most (2-4@l-6@l(@l-1))|E| arcs and the stretch factor at most @F(G)-1. The second construction gives a strongly connected orientation with |E| arcs and the stretch factor at most (@F(G)-1)^@?^@l^+^1^2^@?. The third construction can be applied to plane graphs which are 3-edge connected. It uses a particular 6-face coloring and for any integer k=1 it produces a strongly connected orientation with at most (1-k10(k+1))|E| arcs and the stretch factor at most @F^2(G)(@F(G)-1)^2^k^+^4. Since the stretch factor solely depends only on @F(G), @l, and k, if these three parameters are bounded, our constructions result in orientations with bounded stretch factor.