Given a finite set S of nodes in a rectangular grid, we consider the problem of finding the maximum size subset of S such that the nodes in the subset can be connected to the boundary of the grid by means of nonintersecting line segments parallel to the grid axes. The work is motivated from the VLSIrWSI array processor technology, and in particular, the single-track switch model for config-Ε½ urable array processors S. Y. King et al., Fault-tolerant array processors using Ε½ . . single-track switches, IEEE Trans. Comput. 38 1989 , 501α514 . The problem has been investigated by Bruck and Roychowdhury, who described an algorithm to find the maximum number of compatible connections of n given nodes in the grid in Ε½ 3 . Ε½ 2 . Ε½ O n time and O n space J. Bruck and V. P. Roychowdhury, How to play Ε½ . . bowling in parallel on the grid, J. Algorithms 12 1991 , 516α529 . In this paper, we Ε½ 2 . Ε½ 2 . improve their result by describing an O n log n time and O n space algorithm; instrumental in this improvement is the introduction of a new type of priority search trees which is of interest in its own right. Finally, we extend the algorithm to handle the additional constraint that near-misses are disallowed; this is the first Ε½ 2 . algorithm to resolve this case, and, like the general algorithm, it runs in O n log n Ε½ 2 . time and requires O n space.