This preview shows pages 1–3. Sign up to view the full content.
Biconnectivity
3/13/2006 1:49 AM
1
3/13/2006 1:49 AM
Biconnectivity
1
Biconnectivity
SEA
PVD
MIA
SNA
ORD
FCO
3/13/2006 1:49 AM
Biconnectivity
2
Outline and Reading
Definitions (§6.3.2)
±
Separation vertices and edges
±
Biconnected graph
±
Biconnected components
±
Equivalence classes
±
Linked edges and link components
Algorithms (§6.3.2)
±
Auxiliary graph
±
Proxy graph
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentBiconnectivity
3/13/2006 1:49 AM
2
3/13/2006 1:49 AM
Biconnectivity
3
Separation Edges and Vertices
Definitions
±
Let
G
be a connected graph
±
A separation edge of
G
is an edge whose removal disconnects
G
±
A separation vertex of
G
is a vertex whose removal disconnects
G
Applications
±
Separation edges and vertices represent single points of failure in a
network and are critical to the operation of the network
Example
±
DFW, LGA and LAX are separation vertices
±
(DFW,LAX) is a separation edge
ORD
PVD
MIA
DFW
SFO
LAX
LGA
HNL
3/13/2006 1:49 AM
Biconnectivity
4
Biconnected Graph
Equivalent definitions of a biconnected graph
G
±
Graph
G
has no separation edges and no separation vertices
±
For any two vertices
u
and
v
of
G
, there are two disjoint
simple paths between
u
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 cs401
 Algorithms

Click to edit the document details