A Simple and Efficient Union-Find-Delete Algorithm - Corelab

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These results go back to... • R.E. Tarjan. Efficiency of good but not linear set union algorithm. Journal of the ACM, 22:215-225, 1975 • R.E. Tarjan and Jan van Leeuwen. Worst-case analysis of set union algorithms. Journal of the ACM, 31(2):245-281, 1984 • These works did not consider delete
Purpose of this talk: Describe a simple and efficient way to incorporate the delete operation. Goals: - Delete operation in constant time - Other operations preserve their current efficiency (time and space)
Page 1 and 2: A Simple and Efficient Union-Find-D
Page 3 and 4: Union Find Delete data structure Ma
Page 5 and 6: The classic data structure Represen
Page 7 and 8: Find climbs from the provided eleme
Page 9: To increase the amortized efficienc
Page 13 and 14: Delete operation Deleting a leaf no
Page 15 and 16: Possible Solution Find a leaf, swit
Page 17 and 18: Possible Solution Find a leaf, swit
Page 19 and 20: Previous Work • H. Kaplan, N. Sha
Page 21 and 22: • The solution instead of finding
Page 23 and 24: • The solution instead of finding
Page 25 and 26: Tree Nodes in DFS Order The predece
Page 27 and 28: • The predecessor is a parent or
Page 29 and 30: or • Reduced - a single node of r
Page 31 and 32: Implementing Union One of the trees
Page 33 and 34: Both trees are of size ≥ 4 : Unio
Page 35 and 36: Implementing Find • Instead of pa
Page 37 and 38: Fixing The DFS Order • If node x
Page 39 and 40: Fixing The DFS Order • If node x
Page 41 and 42: • If node x is the leftmost child
Page 43 and 44: Implementing Delete Tree is of size
Page 45 and 46: Local Rebuild If node y is not the
Page 47 and 48: Local Rebuild If node y is not the
Page 49 and 50: If node y is the root and node c is
Page 51 and 52: Analysis Our asymptotic worst case
Page 53: E Thank You

A Simple and Efficient Union-Find-Delete Algorithm - Corelab

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