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A polygonP is said to be apalm polygon if there exists a pointx∈P such that the Euclidean shortest path fromx to any pointy∈P makes only left turns or only right turns. The set of all such pointsx is called thepalm kernel. In this paper we propose an O(E) time algorithm for recognizing a palm polygonP, whereE is the size of the visibility graph ofP. The algorithm recognizes the given polygonP as a palm polygon by computing the palm kernel ofP. If the palm kernel is not empty,P is a palm polygon.

Let M be an m-sided simple polygon and N be an n-sided polygon with holes. In this paper we consider the problem of computing the feasible region, i.e., the set of all placements by translation of M so that M lies inside N without intersecting any hole. First we propose an 0(mn2) time algorithm for computing the feasible region for the case when M is a monotone polygon. Then we consider the general case when M is a simple polygon and propose an 0(m2n2) time algorithm for computing the feasible region. Both algorithms are optimal upto a constant factor.