This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Useful References 1 a Cormen, Leiserson, Rivest & Stein :1 T.C. Hu and MT. Shing
Enlarged Second Edition, Dover paperback
:1 Cook, Cunningham, Pulleyblank, SchrUver
m Korte & Vygen
a Kleinberg & Tardos 0 r1, 042/
CSE 202, April 6, 2006  1 / 11 Useful References 2 :1 Graphs, Networks & Algorithms
by Dieter Jungnickel a Combinatorial Optimization
by Alexander Schrijver
Vol A, B, C
Pages 1 — 1882 03 0,3
CSE 202, April 6, 2006 — 2 / 11 BFS '(G,s) 1 2 3 10 11 12 13 14 15 16 17 18 for each vertex u e V [G] — {3}
do color[u] é— WHITE
d[u] <— co
1t[u] e— NIL
color[s] <— ‘GRAY
d[s] <— 0
1c[s] <— NIL
Q <— {8}
While Q 4i (1)
do u <—' head [Q]
for each 12 E Adj[u]
doifcolor [v] = WHITE
then color[v] (— GRAY
d[v]<—— d[u] + 1
1c[v] <— u
ENQUEUE (Q, v)
DEQUEUE (Q) color[u] <— BLACK DFS (G) 1 for each vertex u E V [G]
do color[u] <— WHITE
7r,[u] (— NIL
time <— 0
for each vertex u E V [G]
do if color[u] = WHITE then DPSVisit (u) DPS—Visit (u) 8 eolor[u] <— GRAY t> White vertex it has just been discovered.
d[u]<— time <— time +1
for each v e Adj[u] l> Explore edge (u,v).‘
do if color[v] = WHITE
then 1t[v] <— u_ DPSVisit (v) color[u] <— BLACK D Blacken u; it is finished. f[u] (— time <— time + 1 f‘xJ Traversing Graphs Visiting all nodes 0f G in some order TWO nodes are neighbors if they share an edge Edge 8/. Arc o edge . Node A and Node B are neighbors 0 arc e A is not a neighbor of B
B is a neighbor of A Mi CSE 202, April 6, 2006  3 / 11 BFS
Let 1, 2, ...i, ...,j, ..., k be
the assigned labels _ & Vi has the smallest label
and unlabeled neighbors. Label the neighbor K+1 BFS
0. Label a vertex V1. I={1}
1. Index I = {1, 2, ..., k} x be a neighbor of the
smallest index vertex 2. Label x with k+l Return to step 1 DFS Let 1, 2, ..., i, ...,j, ..., k
be the assigned labels
& Vj has the largest label and unlabeled neighbors Label the neighbor K+1 ‘ / DFS C7“? Step 0. Same
Step 1. Smallest 6— largest . . Step 2. Same BFS DFS Shortest Path
(Dijkstra) Minimum Spanning Tree
(Prim) . Shortest Paths
Floyd& Warshall 01  path I 2  subpath  02 Subpath of shortest path must
itself be shortest 03 Any shortest path contains at
most n1 arcs P13 P23 P33...SPH_1 Shortest Paths (Dijkstra)
0. Vertex V0 with t5”: 0
Vi get temp labels
6 i = doi (direct are) 61' = °° (if no direct are) 1. Pick BK: min Ei ' EKF£K>k 2. 21 am [61,?“ am] Shortest Path Minimum Spanning Tree (Prim)
0. Same 1. Same 2. 6i <_ min [€i, dKi] In general £1 6 min m, a€K*+BdKi] H3 4'19 2
5 302° Hi Shortest Paths From 0 To All W CSE 202, April 6, 2006  9 / 11 ‘ Minimum Spanning Tree CSE 202, April 6, 2006 — 10 / 11 Minimum Clock Tree than
9
o e
9 o
0913 [,2L CSE 202, April 6, 2006  11 / 11 Other Opt. Paths L (e1, e2: 63! "'J en) : L (L (91, 92, 63, ... s en1)! en) L (91, 625 93, ”5 en! en+1) 2 L (91, 92, es, .. ., en) ...
View
Full Document
 Fall '06
 Hu
 Algorithms

Click to edit the document details