1 / 6

Efficient Implementation of Dijkstra's Shortest Path Algorithm in Link-State Routing

Learn about Dijkstra's shortest path algorithm for link-state routing, with examples and spanning tree computation, offering insights into routing table generation and algorithm complexity.

bmercer
Download Presentation

Efficient Implementation of Dijkstra's Shortest Path Algorithm in Link-State Routing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dijkstra’s Shortest Path Algorithm Gordon College

  2. Notation: c(i,j): link cost from node i to j. cost infinite if not direct neighbors D(v): current value of cost of path from source to dest. V p(v): predecessor node along path from source to v, that is next v N: set of nodes already in spanning tree (least cost path known) A D E B F C A Link-State Routing Algorithm Examples: • c(B,C) = 3 • D(E) = 2 • p(B) = A • N = { A, B, D, E } 5 3 5 2 2 1 3 1 2 1

  3. Dijsktra’s Algorithm 1 Initialization: 2 N = {A} 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v) 6 else D(v) = infinity 7 8 Loop 9 find w not in N such that D(w) is a minimum 10 add w to N 11 update D(v) for all v adjacent to w and not in N: 12 D(v) = min( D(v), D(w) + c(w,v) ) 13 /* new cost to v is either old cost to v or known 14 shortest path cost to w plus cost from w to v */ 15 until all nodes in N

  4. 2,A 5,A 1,A infinity,- infinity,- A 2,A 4,D1,A2,D infinity,- AD 2,A 3,E1,A2,D4,E ADE 2,A 3,E 1,A2,D 4,E ADEB 2,A3,E1,A2,D 4,E ADEBC 2,A3,E1,A2,D4,E ADEBCF A D B E F C Dijkstra’s algorithm: example D(B),p(B) D(D),p(D) D(C),p(C) D(E),p(E) Step 0 1 2 3 4 5 N D(F),p(F) 5 3 5 2 2 1 3 1 2 1

  5. 2,A3,E1,A2,D4,E ADEBCF A D B E F C Spanning tree gives routing table D(B),p(B) D(D),p(D) D(C),p(C) D(E),p(E) Step N D(F),p(F) Result fromDijkstra’s algorithm B,2 D,3 D,1 D,2 D,4 B C D E F Outgoing link to use, cost Routing table: 5 3 5 2 2 1 3 1 2 1 destination

  6. Algorithm complexity (n nodes and l links) Computation n iterations each iteration: need to check all nodes, w, not in N n*(n+1)/2 comparisons: O(n2) more efficient implementations possible: O(n log n) Messages network topology and link cost known to all nodes each node broadcasts its direct link cost O(l) messages per broadcast announcement O(n l) Dijkstra’s algorithm performance

More Related