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**1 - 2**of**2**### Indexed Geometric Jumbled Pattern Matching

"... Abstract. We consider how to preprocess n colored points in the plane such that later, given a multiset of colors, we can quickly find an axis-aligned rectangle containing a subset of the points with exactly those colors, if one exists. We first give an index that uses o(n4) space and o(n) query tim ..."

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Abstract. We consider how to preprocess n colored points in the plane such that later, given a multiset of colors, we can quickly find an axis-aligned rectangle containing a subset of the points with exactly those colors, if one exists. We first give an index that uses o(n4) space and o(n) query time when there are O(1) distinct colors. We then restrict our attention to the case in which there are only two distinct colors. We give an index that uses O(n) bits and O(1) query time to detect whether there exists a matching rectangle. Finally, we give a O(n)-space index that returns a matching rectangle, if one exists, in O(lg2 n / lg lgn) time. 1

### Mexican Conference on Discrete Mathematics and Computational Geometry Stabbing Segments with Rectilinear Objects

"... Given a set of n line segments in the plane, we say that a region R ⊆ R2 is a stabber if R contains exactly one endpoint of each segment of the set. In this paper we provide efficient algorithms for determining whether or not a stabber exists for several shapes of stabbers. Specifically, we consider ..."

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Given a set of n line segments in the plane, we say that a region R ⊆ R2 is a stabber if R contains exactly one endpoint of each segment of the set. In this paper we provide efficient algorithms for determining whether or not a stabber exists for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of isothetic halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). We provide efficient algorithms reporting all combinatorially different stabbers of that shape. The algorithms run in O(n) time (for the halfplane case), O(n logn) time (for strips and quadrants), O(n2) (for 3-sided rectangles), or O(n3) time (for rectangles). 1