Abstract
In this paper, we study a variant of the problem of computing a minimum-width parallelogram annulus that encloses a given set of n points in the plane. A parallelogram annulus is a closed region between a parallelogram and its inward offset. Specifically, we present the first algorithm that computes a minimum-width parallelogram annulus with inner angles fixed by the input that encloses n input points. The running time is O(n² log n). To the best of our knowledge, there exists no known algorithm in the literature for the stated problem, and our algorithm generalizes the existing O(n² log n)-time algorithm for the rectangular annulus in arbitrary orientation in the same running time-bound.
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