If the graph has a cycle, a topological order cannot exist
. Imagine the simplest cycle, consist- ing of two edges: (a, b) and (b, a). A topological ordering , if it existed, would have to satisfy that a must come before b and b must come before a. This is not possible.
When can you not apply topological sort?
Topological Sorting for a graph is not possible
if the graph is not a DAG
. For example, a topological sorting of the following graph is “5 4 2 3 1 0”. There can be more than one topological sorting for a graph. For example, another topological sorting of the following graph is “4 5 2 3 1 0”.
What is topological sort good for?
Scheduling jobs from given dependencies among Jobs
. For example, if some job requires the dependency of some other job, then we can use topological sorting. Determining the order of compilation tasks to perform in makefiles, data serializations and resolving symbol dependencies in linkers.
Can we apply topological sort on directed cyclic graph?
Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering.
Topological Sorting for a graph is not possible if the graph is not a DAG
.
Is topological sort DFS?
Topological sort is a DFS-based algorithm on a directed acyclic graph (DAG)
. Topological ordering is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. A topological ordering is possible if and only if the graph has no directed cycles.
Can BFS detect cycle?
BFS wont work for a directed graph in finding cycles
. Consider A->B and A->C->B as paths from A to B in a graph. BFS will say that after going along one of the path that B is visited. When continuing to travel the next path it will say that marked node B has been again found,hence, a cycle is there.
Can a spanning tree have cycles?
A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges. Hence,
a spanning tree does not have cycles
and it cannot be disconnected..
Is Kahn’s algorithm BFS?
IIRC,
Kahn’s algorithm is effectively a BFS
.
Is topological sort DFS or BFS?
Topological Sorting can be done by both DFS as well as BFS
,this post however is concerned with the BFS approach of topological sorting popularly know as Khan’s Algorithm.
Why do we perform topological sorts only on DAGs?
Since we have a cycle, topological sort is not defined
. We also can’t topologically sort an undirected graph since each edge in an undirected graph creates a cycle. So topological sorts only apply to directed, acyclic (no cycles) graphs – or DAGs.
Is topological sort unique?
In general, the topological sort is
not unique
. For example, if we have v
0
< v
1
, and v
2
< v
3
, any one of the orderings v
1
v
2
v
3
v
4
, v
3
v
4
v
1
v
2
, v
1
v
3
v
2
v
4
is a topological sort.
What is the most efficient time complexity for topological sorting?
The time complexity of topological sort using Kahn’s algorithm is
O(V+E)
, where V = Vertices, E = Edges.
What is topological sorting in DAA?
AlgorithmsData StructureGraph Algorithms. The topological sorting for a directed acyclic graph is
the linear ordering of vertices
. For every edge U-V of a directed graph, the vertex u will come before vertex v in the ordering.
How do you find the topological order on a graph?
Can we apply topological sorting algorithm on the following graph?
Topological Sorting is possible if and only if the graph is a Directed Acyclic Graph
. There may exist multiple different topological orderings for a given directed acyclic graph.
Why is topological sort called topological sort?
Under the understanding that
“topological” means “pertaining to shape”, a “topological sort” simply means “a spacial sort.”
How would you use the topological sorting algorithm for detection of cycles in a graph?
Approach: In Topological Sort, the idea is to
visit the parent node followed by the child node
. If the given graph contains a cycle, then there is at least one node which is a parent as well as a child so this will break Topological Order.
Which of the following is used for topological sorting?
Explanation: We can implement topological sort by both
BFS and DFS
. In BFS, we use queue as data structure and in DFS, we use Linked list (if recursive) or Stack (if not recursive) as data structure.
Why DFS is faster than BFS?
DFS is faster than BFS.
Time Complexity of BFS = O(V+E) where V is vertices and E is edges
. Time Complexity of DFS is also O(V+E) where V is vertices and E is edges.
How do you know if an undirected graph has cycles?
To detect if there is any cycle in the undirected graph or not, we will
use the DFS traversal for the given graph
. For every visited vertex v, when we have found any adjacent vertex u, such that u is already visited, and u is not the parent of vertex v. Then one cycle is detected.
Can DFS detect cycles?
Using a Depth First Search (DFS) traversal algorithm we can detect cycles in a directed graph
. If there is any self-loop in any node, it will be considered as a cycle, otherwise, when the child node has another edge to connect its parent, it will also a cycle.
What is BFS and DFS?
BFS stands for Breadth First Search. DFS stands for Depth First Search
. 2. BFS(Breadth First Search) uses Queue data structure for finding the shortest path. DFS(Depth First Search) uses Stack data structure.
What is Spanning Tree Protocol Cisco?
The Spanning Tree Protocol is
a link management protocol that is designed to support redundant links while at the same time preventing switching loops in the network
. It is quite useful and should be enabled on the switch interfaces.
Which algorithm is used to check the negative cycle in a graph?
The
Bellman-Ford algorithm
is a way to find single source shortest paths in a graph with negative edge weights (but no negative cycles). The second for loop in this algorithm also detects negative cycles.
Can BFS be used for topological sort?
Yes, you can do topological sorting using BFS
.
What is Indegree and Outdegree?
Indegree and outdegree
For a vertex,
the number of head ends adjacent to a vertex is called the indegree of the vertex and the number of tail ends adjacent to a vertex is its outdegree
(called branching factor in trees).
What is Kahn algorithm?
Essentially, Kahn’s algorithm works by
keeping track of the number of incoming edges into each node (indegree)
. It repeatedly: Finds nodes with no incoming edge, that is, nodes with zero indegree (no dependency). Stores the nodes with zero indegree in a stack/queue and deletes them from the original graph.
