  We study the problem of cooperative localization of a large network of nodes
in integer-coordinated unit disk graphs, a simplified but useful version of
general random graph. Exploiting the property that the radius $r$ sets clear
cut on the connectivity of two nodes, we propose an essential philosophy that
"no connectivity is also useful information just like the information being
connected" in unit disk graphs. Exercising this philosophy, we show that the
conventional network localization problem can be re-formulated to significantly
reduce the search space, and that global rigidity, a necessary and sufficient
condition for the existence of unique solution in general graphs, is no longer
necessary. While the problem is still NP-hard, we show that a (depth-first)
tree-search algorithm with memory O(N) ($N$ is the network size) can be
developed, and for practical setups, the search complexity and speed is very
manageable, and is magnitudes less than the conventional problem, especially
when the graph is sparse or when only very limited anchor nodes are available.
