Generating binary trees of bounded height

Lee, C. C.; Lee, D. T.; Wong, Carmen

doi:10.1007/bf00288468

Cited by 19 publications

(5 citation statements)

References 16 publications

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“…The NN algorithm is easy to implement by computing and sorting the distances from any point to every other point, however, this "naive" approach scales with (n − 1) 2 and is therefore computationally expensive for large n. More sophisticated algorithms have been developed to overcome this by seeking to reduce the number of distance determinations required (e.g. Lee & Wong 1977;Aghbari 2005).…”

Section: Nearest Neighbour Densitymentioning

confidence: 99%

Identifying star clusters in a field: A comparison of different algorithms

Schmeja

2011

Astron Nachr

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Key words open clusters and associations: general -methods: statisticalStar clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four algorithms that have been developed to identify clusters as stellar density enhancements in a field, namely stellar density maps from star counts, the nearest neighbour method and the Voronoi tessellation, and the separation of minimum spanning trees. These methods are tested and compared to each other by applying them to artificial clusters of different sizes and morphologies. While distinct centrally concentrated clusters are detected by all methods, clusters with low overdensity or highly hierarchical structure are only reliably detected by methods with inherent smoothing (star counts and nearest neighbour method). Furthermore, the algorithms differ strongly in computation time and additional parameters they provide. Therefore, the method to choose primarily depends on the size and character of the investigated area and the purpose of the study.

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Section: Nearest Neighbour Densitymentioning

confidence: 99%

Identifying star clusters in a field: A comparison of different algorithms

Schmeja

2011

Astron Nachr

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“…Succinct Data Structures. The space efficiency of TEBs is founded on the idea of mapping tree nodes to integer values [30] and the foundational work on succinctly encoded binary trees [24] that efficiently support the necessary navigational operations using the rank and select primitives. Both primitives require a helper structure to lower the time complexity of tree navigations from linear to constant time.…”

Section: Related Workmentioning

confidence: 99%

Tree-Encoded Bitmaps

Lang

Beischl

Leis

et al. 2020

Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data

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We propose a novel method to represent compressed bitmaps. Similarly to existing bitmap compression schemes, we exploit the compression potential of bitmaps populated with consecutive identical bits, i.e., 0-runs and 1-runs. But in contrast to prior work, our approach employs a binary tree structure to represent runs of various lengths. Leaf nodes in the upper tree levels thereby represent longer runs, and vice versa. The tree-based representation results in high compression ratios and enables efficient random access, which in turn allows for the fast intersection of bitmaps. Our experimental analysis with randomly generated bitmaps shows that our approach significantly improves over state-of-the-art compression techniques when bitmaps are dense and/or only barely clustered. Further, we evaluate our approach with real-world data sets, showing that our tree-encoded bitmaps can save up to one third of the space over existing techniques.

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“…In the above methods we traverse the trees in preorder. Lee et al [23] have used level-by-level order, i.e. first the root, then the children of the root from left to right, then their children from left to right, and so on.…”

Section: Encoding With Fixed Length Codewordsmentioning

confidence: 99%

“…The length of these level-to-level sequences naturally equals the length of the codewords obtained by the the methods described above. Lee et al [23] have found the codewords so obtained useful for some special purposes. Moreover, in chapter 7 we shall see that the level-by-level sequence allows tree traversal in compressed trees.…”

Section: Encoding With Fixed Length Codewordsmentioning

confidence: 99%

Tree Compression and Optimization With Applications

Katajainen

Mäkinen

1990

Int. J. Found. Comput. Sci.

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Different methods for compressing trees are surveyed and developed. Tree compression can be seen as a trade-off problem between time and space in which we can choose different strategies depending on whether we prefer better compression results or more efficient operations in the compressed structure. Of special interest is the case where space can be saved while preserving the functionality of the operations; this is called data optimization. The general compression scheme employed here consists of separate linearization of the tree structure and the data stored in the tree. Also some applications of the tree compression methods are explored. These include the syntax-directed compression of program files, the compression of pixel trees, trie compaction and dictionaries maintained as implicit data structures.

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Generating binary trees of bounded height

Cited by 19 publications

References 16 publications

Identifying star clusters in a field: A comparison of different algorithms

Identifying star clusters in a field: A comparison of different algorithms

Tree-Encoded Bitmaps

Tree Compression and Optimization With Applications

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