1
GATE CSE 2007
+2
-0.6
In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by
A
Dijkstra’s algorithm starting from S.
B
Warshall’s algorithm
C
Performing a DFS starting from S.
D
Performing a BFS starting from S.
2
GATE CSE 2006
+2
-0.6
Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal’s algorithm?
A
$$(a-b),(d-f),(b-f),(d-c),(d-e)$$
B
$$(a-b),(d-f),(d-c),(b-f),(d-e)$$
C
$$(d-f),(a-b),(d-c),(b-f),(d-e)$$
D
$$(d-f),(a-b),(b-f),(d-e),(d-c)$$
3
GATE CSE 2004
+2
-0.6
Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge-weighted directed graph with vertex P as the source.
In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized?
A
$$P,Q,R,S,T,U$$
B
$$P,Q,R,U,S,T$$
C
$$P,Q,R,U,T,S$$
D
$$P,Q,T,R,U,S$$
4
GATE CSE 2003
+2
-0.6
Let G=(V,E) be an undirected graph with a subgraph G1=(V1,E1). Weights are assigned to edges of G as follows. $$w(e) = \begin{cases} 0 \text{, if } e \in E_1 \\1 \text{, otherwise} \end{cases}$$\$ A single-source shortest path algorithm is executed on the weighted graph (V,E,w) with an arbitrary vertex v1 of V1 as the source. Which of the following can always be inferred from the path costs computed?
A
The number of edges in the shortest paths from v1 to all vertices of G
B
G1 is connected
C
V1 forms a clique in G
D
G1 is a tree
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