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This algorithm, which runs in [formula] time where g is the maximum number of data items included in a test (check) and l is the number of tests, is suitable for systems with a small value of l."

Abstract: "The bit (or width) minimization problem for microprograms is known to be NP-complete. Motivated by its practical importance, we address the question of obtaining near-optimal solutions. Two main results are presented. First, we establish a tight bound on the quality of solutions produced by algorithms which minimize the number of compatibility classes. Second, we show that the bit minimization problem has a polynomial time relative approximation algorithm only if the vertex coloring problem for graphs with n nodes can be approximated to within a factor of O(logn) in polynomial time."

This algorithm can also be extended to obtain a rectilinear minimum spanning tree for a set of non-intersecting simple polygons."

For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX- AVG criteria. Using the latter algorithm, we obtain a heuristic which provides an asymptotic performance guarantee of [formula] for the 2- dimensional dispersion problem under the MAX-AVG criterion."