  We consider ad-hoc networks consisting of $n$ wireless nodes that are located
on the plane. Any two given nodes are called neighbors if they are located
within a certain distance (communication range) 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 (unique identification
numbers) of its one- and 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. We also evaluate the performance of our algorithm for random networks. In
this case, our algorithm provides an asymptotically connected network with
$n(1+o(1))$ edges with a degree less than or equal to $6$ for $1-o(1)$ fraction
of the nodes. We also introduce another asynchronous connectivity-preserving
algorithm that can provide an upper bound as well as a lower bound on node
degrees.
