Dynamic DFS in Undirected Graph using Segment Tree

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 : Numberof Edges n : Number of Vertices
• 4.
  DB A C E Graph G DB A C E DFS treeT
• 5.
  5 2 5 1 25 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 Failureof 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 eg 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 xz 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 ws 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
• 11.
  Overall Complexity: O(log3n)
• 12.
  x u v z yw s t Path Vector Tree Vector xz w s t y u v List L Query (T (w), x, y) Time Complexity : O(log m * log n)
• 14.
  BUIDLING DATA STRUCTURE
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  QUERY OPERATION
• 17.
  m : Numberof Edges n : Number of Vertices https://github.com/simemon/DAA
• 19.
  THANK YOU