We study an interference network where equally numbered transmitters and receivers lie on two parallel lines, with each transmitter opposite its intended receiver. We consider two short-range interference models: the asymmetric network, where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a symmetric network, where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the t_l transmitters to its left, and the messages of the t_r transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the r_l receive antennas to its left, and at the r_r receive antennas to its right. For such networks, we provide upper and lower bounds on the multiplexing gain, i.e., on the high signal-to-noise ratio asymptotic logarithmic growth of the sum-rate capacity. In some cases, our bounds coincide, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter side-information parameters t_l, t_r and the receiver side-information parameters r_l, r_r in the sense that increasing/decreasing t_l or tr by a positive integer δ has the same effect on the multiplexing gain as increasing/decreasing r_l or r_r by δ. Moreover—even in asymmetric networks—there is an equivalence between the left side-information parameters (t_l,r_l) and the right side-information parameters (t_r,r_r).