The procedure stops when the result of a region query

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points than the previous query. The procedure stops when the result of a region query is non-empty. The distance from P to each point within this region is calculated and the set of points at the smallest distance is reported. 25.4 Suppose you want to store line segments in an R-tree. If a line segment is not parallel to the axes, the bounding box for it can be large, containing a large empty area. Describe the effect on performance of having large bounding boxes on queries that ask for line segments intersecting a given region. Briefly describe atechnique toimprove performance for suchqueries and give an example of its benefit. Hint: You can divide segments into smaller pieces. Answer: Large bounding boxes tend to overlap even where the region of overlap does not contain any information. The following figure: R shows a region R within which we have to locate a segment. Note that even though none of the four segments lies in R , due to the large bounding boxes, we have to check each of the four bounding boxes to confirm this. A significant improvement is observed in the follwoing figure:
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Practice Exercises 3 R where each segment is split into multiple pieces, each with its own bounding box. In the second case, the box R is not part of the boxes indexed by the R-tree. In general, dividing a segment into smaller pieces causes the bounding boxes to be smaller and less wasteful of area. 25.5 Give a recursive procedure to efficiently compute the spatial join of two relations with R-tree indices. (Hint: Use bounding boxes to check if leaf entries under a pair of internal nodes may intersect.) Answer: Following is a recursive procedure for computing spatial join of two R-trees. SpJoin (node n 1 , node n 2 ) begin if (the bounding boxes of n 1 and n 2 do not intersect) return ; if (both n 1 and n 2 are leaves) output all pairs of entries ( e 1 , e 2 ) such that e 1 n 1 and e 2 n 2 , and e 1 and e 2 overlap; if ( n 1 is not a leaf) NS 1 = set of children of n 1 ; else NS 1 = { n 1 } ; if ( n 1 is not a leaf) NS 1 = set of children of n 1 ; else NS 1 = { n 1 } ; for each ns 1 in NS 1 and ns 2 in NS 2 ; SpJoin( ns 1 , ns 2 ); end 25.6 Describe how the ideas behind the RAID organization (Section 10.3) can be used in a broadcast-data environment, where there may occasionally be noise that prevents reception of part of the data being transmitted.
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4 Chapter 25 Advanced Data Types and New Applications Answer: The concepts of RAID can be used to improve reliability of the broadcast of data over wireless systems. Each block of data that is
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