A wireless network can achieve maximum throughput without each node meeting all others

We study throughput scaling of an ad-hoc network where the nodes are restricted to move on vertical or horizontal lines on a square. A constant throughput is asymptotically achievable by the proposed scheduling algorithm, using in certain cases more than two hops strategies, without requiring each node to become the nearest neighbor of every other node. Hence the throughput result for one-dimensional mobility obtained by Diggavi et al. in Proc. IEEE ISIT, 2002 still holds under stricter mobility constraints