CS 6515 Exam 2 ACTUAL EXAM
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,Terms in this set (71)
Tree's are undirected, connected
and acyclic that connect all nodes.
1. Tree on n vertices has (n-1) edges -
> would have a cycle otherwise
(more than n-1 edges means cycle)
Basic Properties 2. In tree exactly one path between
of Trees every pair of vertices (otherwise it's
not connected)
- More than 1 path implies cycle
- less than 1 path implies not
connected
3. Any connected G(V, E) with |E| =
|V| - 1 is a tree
1. Sort E by increasing weigt
2. Go through edges in order and
add an edge to our current tree if it
Kruskal's
doesn't create a cycle
Algorithm
Running Time: O(m log n), m = |E|, n =
|V|
, Is there ever a No
reason to use
cycles in a flow
graph?
Flow Network For all edges, the flow must be
Constraints: larger than zero, but less than the
Capacity capacity of that edge
Constraint
Maximize the flow out of the source
Goal of Flow (or into the sink) of maximum size
Problem while satisfying the capacity and
conservation of flow constraints.
Flow Network For all vertices (other than the
Constraints: starting (source) and ending (sink)
Conservation of vertices), the flow into v must equal
Flow the flow out of v.
QUESTIONS WITH COMPLETE
SOLUTION GUIDE (A+ GRADED
100% VERIFIED) LATEST VERSION
2025!!
Save
Get a taste for our practice questions
Learn
Studied 7 terms
Nice work, you're crushing it
Continue studying in Learn
,Terms in this set (71)
Tree's are undirected, connected
and acyclic that connect all nodes.
1. Tree on n vertices has (n-1) edges -
> would have a cycle otherwise
(more than n-1 edges means cycle)
Basic Properties 2. In tree exactly one path between
of Trees every pair of vertices (otherwise it's
not connected)
- More than 1 path implies cycle
- less than 1 path implies not
connected
3. Any connected G(V, E) with |E| =
|V| - 1 is a tree
1. Sort E by increasing weigt
2. Go through edges in order and
add an edge to our current tree if it
Kruskal's
doesn't create a cycle
Algorithm
Running Time: O(m log n), m = |E|, n =
|V|
, Is there ever a No
reason to use
cycles in a flow
graph?
Flow Network For all edges, the flow must be
Constraints: larger than zero, but less than the
Capacity capacity of that edge
Constraint
Maximize the flow out of the source
Goal of Flow (or into the sink) of maximum size
Problem while satisfying the capacity and
conservation of flow constraints.
Flow Network For all vertices (other than the
Constraints: starting (source) and ending (sink)
Conservation of vertices), the flow into v must equal
Flow the flow out of v.
