Geometric spanners: Recent results and open directions

The last few years have witnessed a substantial amount of work on geometric spanners due to their important applications in network communications, and in particular, in wireless communications. The topic of geometric spanners is very rich spanning several areas of computer science, including computational geometry, graph theory, and distributed computing. In the current paper, we report on some of the recent progress made on geometric spanners. We also list important questions about geometric spanners that are currently open.