Trees & Routing (1) BFS
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1 Tees & Routing (1) BFS
2 Why (spanning) tees?
3 Spanning Tee Given a gaph G=(V,E), a Spanning Tee of G is an acyclic subgaph, spanning all the nodes in V.
4 Spanning Tee Given a gaph G=(V,E), a Spanning Tee of G is an acyclic subgaph, spanning all the nodes in V.
5 Beadth-fist Spanning Tee (BFS) Given a gaph G=(V,E) and a node in V, a BFS tee of G ooted at is a spanning tee of G such that fo any node v the path leading fom the oot to v in the tee is of the minimum lenght possible.
6 Beadth-fist Spanning Tee (BFS) Given a gaph G=(V,E) and a node in V, a BFS tee of G ooted at is a spanning tee of G such that fo any node v the path leading fom the oot to v in the tee is of the minimum lenght possible.
7 BFS Constuction
8 BFS - stategies «link state» (Dijksta) gow on the bode «distance vecto» (Bellman-Fod) compute shotest paths
9 Dijksta BFS
10 Dijksta BFS oot,, boadcasts in the cuent tee, T, «pulse»
11 Dijksta-like BFS
12 Dijksta-like BFS upon eception of «pulse», leafs of the cuent tee send «laye» to neighbos (except to paents)
13 Dijksta-like BFS
14 Dijksta-like BFS upon eception of the fist «laye» a node choses the sende as paent and sends back an «ack»
15 Dijksta-like BFS upon eception of an «ack» a node egiste the sende as its child
16 Dijksta-like BFS upon eception of an «ack» a node egiste the sende as its child
17 Dijksta-like BFS
18 Dijksta-like BFS oot,, boadcasts in the cuent tee, T, «pulse»
19 Dijksta-like BFS
20 Dijksta-like BFS upon eception of «pulse», leafs of the cuent tee send «laye» to neighbos (except paent)
21 Dijksta-like BFS upon eception of the fist «laye» a node choses the sende as paent and sends back an «ack»
22 Dijksta-like BFS upon eception of the fist «laye» a node choses the sende as paent and sends back an «ack»
23 Dijksta-like BFS upon eception of the fist «laye» a node choses the sende as paent and sends back an «ack»
24 Dijksta-like BFS upon eception of the fist «laye» a node choses the sende as paent and sends back an «ack»
25 Dijksta-like BFS?
26 Dijksta-like BFS?
27 Dijksta-like BFS - Complexity Time Complexity: O(Diam 2 (G)) Message Complexity: O(nDiam(G)+ E )
28 Bellman-Fod-like BFS each node maintains : its shotes distance to the oot d (initially d=infinity) its paent to the oot on the shotest distance
29 Bellman-Fod-like BFS d= paent= d= paent= d= paent= d= paent= d=0 d= paent=
30 Bellman-Fod-like BFS oot,, boadcasts d=0 to all its neighbos d= paent= d= paent= d= paent= d= paent= d=0 d= paent=
31 Bellman-Fod-like BFS d= paent= d=1 d=1 d=1 d=0 d=1
32 Bellman-Fod-like BFS each node boadcasts its d to all its neighbos except paent d=1 d= paent= d=1 d=0 d=1 d=1
33 Bellman-Fod-like BFS d=2 paent=n2 n4 n2 d=1 n1 d=1 d=1 n3 d=0 d=1 n3
34 Bellman-Fod-like BFS d=2 paent=n2 n4 n2 d=1 n1 d=1 d=1 n3 d=0 d=1 n3
35 Bellman-Fod-like BFS - Complexity Time Complexity: O(Diam(G)) Message Complexity: O( E )
36 BFS - Complexity Time Messages Dijksta-like D 2 E+nD Bellman-Fodlike D ne Awebuch-Peleg Dlog 3 n E+nlog 3 n Lowe Bound D E
37 Spanning Tee and Routing
38 Routing «link state» (Dijksta like) Open Shotest Path Fist (OSPF) «distance vecto» (Bellman-Fod like) Bode Gateway Potocol (BGP) Inteio Gateway Routing Potocol (IGRP, CISCO popety)
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