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In computational geometry, the bin data structure allows efficient region queries, i.e., if there are some axis-aligned rectangles on a 2D plane, answer the question Given a query rectangle, return all rectangles intersecting it. kd-tree is another data structure that can answer this question efficiently. In the example in the figure, A, B, C, D, E, and F are existing rectangles, the query with the rectangle Q should return C, D, E and F, if we define all rectangles as closed intervals.

The data structure partitions a region of the 2D plane into uniform-sized bins. The bounding box of the bins encloses all candidate rectangles to be queried. All the bins are arranged in a 2D array. All the candidates are represented also as 2D arrays. The size of a candidate's array is the number of bins it intersects. For example, in the figure, candidate B has 6 elements arranged in a 3 row by 2 column array because it intersects 6 bins in such an arrangement. Each bin contains the head of a singly-linked list. If a candidate intersects a bin, it is chained to the bin's linked list. Each element in a candidate's array is a link node in the corresponding bin's linked list.

In a multithread environment, insert, delete and query are mutually exclusive. However, instead of locking the whole data structure, a sub-range of bins may be locked. Detailed performance analysis should be done to justify the overhead.

Like a hash table, bin's efficiency depends a lot on the distribution of both location and size of candidates and queries. In general, the smaller the query rectangle, the more efficient the query. The bin's size should be such that it contains as few candidates as possible but large enough so that candidates do not span too many bins. If a candidate span many bins, a query has to skip this candidate over and over again after it is reported at the first bin of intersection. For example, in the figure, E is visited 4 times in the query of Q and so has to be skipped 3 times.

To further speed up the query, divisions can be replaced by right shifts. This requires the number of bins along an axis direction to be an exponent of 2.

Against kd-tree, the bin structure allows efficient insertion and deletion without the complexity of rebalancing. This can be very useful in algorithms that need to incrementally add shapes to the search data structure.

- kd-tree is another efficient range query data structure.
- Space partitioning

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Last updated on Friday July 25, 2008 at 09:51:09 PDT (GMT -0700)

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Last updated on Friday July 25, 2008 at 09:51:09 PDT (GMT -0700)

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