Spanners, Weak Spanners, and Power Spanners for Wireless Networks

For c ∈ R, a c-spanner is a subgraph of a complete Euclidean graph satisfying that between any two vertices there exists a path of weighted length at most c times their geometric distance. Based on this property to approximate a complete weighted graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks. In a weak c-spanner, this path may be arbitrary long but must remain within a disk of radius c-times the Euclidean distance between the vertices. Finally in a c-power spanner, the total energy consumed on such a path, where the energy is given by the sum of the squares of the edge lengths on this path, must be at most c-times the square of the geometric distance of the direct link. While it is known that any c-spanner is also both a weak C1-spanner and a C2-power spanner (for appropriate C1, C2 depending only on c but not on the graph under consideration), we show that the converse fails: There exists a family of c1-power spanners th...

• Type: Conference
• Year: 2004
• Where: ISAAC
• Authors: Christian Schindelhauer, Klaus Volbert, Martin Ziegler
• Keywords: ISAAC 2004, Sparse Spanners, Weak C-spanners, δ)-power Spanner