Dynamic DFS in Undirected Graph using Segment Tree
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The document discusses a research project on dynamic depth-first search (DFS) in undirected graphs, presenting methods to break the O(m) complexity barrier. It introduces new data structures and algorithms to improve efficiency in handling graph queries. Key findings and the overall complexity of the approach are highlighted, demonstrating significant advancements in the field.
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Dynamic DFS in Undirected Graph using Segment Tree
- 1. CMSC 641 – Research Project (Team 10) Original Paper: Dynamic DFS in Undirected Graphs: breaking the O(m) barrier (SODA’16 Page: 730-739) Authors: Baswana, Surender ; Chaudhury, Shreejit ; Choudhary, Keerti ; Khan, Shahbaz
- 3. m : Number of Edges n : Number of Vertices
- 5. 5 2 5 1 2 5 6 0 1 2 3 4 5 18 17 13 19 15 11 20 [0,6] [4,6] [4,5] [6,6] [0,0] [1,1] [2,2] [3,3] [4,4] [5,5] [0,3] [0,1] [2,3] 0 1 2 3 4 5 6 Array
- 6. r w v T* e1’ e1 e2’ e2 C1 C2 C1 & C2 - Connected Components
- 7. r ma b f c d e g k l h i j r ma b f c d e g k l h i j Failure of edge (b, f). Partial DFS tree T with unvisited graph T(f), components property allows us to neglect (a, l).
- 8. r m a b k c d e g f lh i j r m a b k c d e g f lh i j Augmented path(k, f) to T, components property allows us to neglect (l, k). Final DFS tree of G{(b, f)}.
- 9. DFS Tree x u v z y w s t x z w s t y u v List L x z w s t y u v (x,s) (z,w) (w,s) (s,w) (t,w) (z,t) (w,t) Segment Tree TB
- 10. x z w s t y u v Segment Tree TB [w-s] (s,w) (t,w)(w,s) (z,w) (x,s) BST stored at segment tree node [w-s] (x,s) (z,w) (w,s) (s,w) (t,w) Edge-list sorted according to List L x z w s t y u v List L
- 12. x u v z yw s t Path Vector Tree Vector x z w s t y u v List L Query (T (w), x, y) Time Complexity : O(log m * log n)
- 15. QUERY OPERATION
- 17. m : Number of Edges n : Number of Vertices https://github.com/simemon/DAA
- 19. THANK YOU