Local Construction of Bounded-Degree Network Topologies Using Only Incidence Information

We consider ad-hoc networks consisting of n wireless nodes that are located on R. Any two given nodes are called neighbors if they are located within a certain distance from one another. A given node can be directly connected to any one of its neighbors and picks its connections according to a unique topology control algorithm that is available at every node. Given that each node knows only the indices of its oneand two-hop neighbors, we identify an algorithm that preserves connectivity and can operate without the need of any synchronization among nodes. Moreover, the algorithm results in a sparse graph with at most 5n edges and a maximum node degree of 10. Existing algorithms with the same promises further require neighbor distance and/or direction information at each node.