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

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Problems in Finding a Leaf • The straight-forward idea is to maintain a leaf collection • Each node should have some kind of a link to the leaf collection • The problem is how to handle those links during updates • The straight-forward ideas don’t work in constant time
Previous Work • H. Kaplan, N. Shafrir, R.E. Tarjan: Union-Find with deletions. SODA 2002 • S. Alstrup, I.L. Gørtz, T. Rauhe, M. Thorup, U. Zwick: Union-Find with Constant Time Deletions, ICALP 2005
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 and 10: To increase the amortized efficienc
Page 11 and 12: Purpose of this talk: Describe a si
Page 13 and 14: Delete operation Deleting a leaf no
Page 15 and 16: Possible Solution Find a leaf, swit
Page 17: Possible Solution Find a leaf, swit
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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