Shortest Paths in Graphs Quiz

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Question 1

Let G(V, E) an undirected graph with positive edge weights. Dijkstra's single-source shortest path algorithm can be implemented using the binary heap data structure with time complexity:

A
O(| V |²)
B
O (| E | + | V | log | V |)
C
O (| V | log | V |)
D
O ((| E | + | V |) log | V |)

Question 2

Given a directed graph where weight of every edge is same, we can efficiently find shortest path from a given source to destination using?

A
Breadth First Traversal
B
Dijkstra\'s Shortest Path Algorithm
C
Neither Breadth First Traversal nor Dijkstra\'s algorithm can be used
D
Depth First Search

Question 3

Let G=(V,E) be a directed, weighted graph with weight function w:E→R. For some function f:V→R, for each edge (u,v)∈E, define w′(u,v) as w(u,v)+f(u)−f(v). Which one of the options completes the following sentence so that it is TRUE ? “The shortest paths in G under w are shortest paths under w′ too, _________”.

A
for every f:V→R
B
if and only if ∀u∈V, f(u) is positive
C
if and only if ∀u∈V, f(u) is negative
D
if and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G

Question 4

Which of the following is application of Breath First Search on the graph?

A
Finding diameter of the graph
B
Finding bipartite graph
C
Both (a) and (b)
D
None of the above

Question 5

Which one of the following algorithm design techniques is used in finding all pairs of shortest distances in a graph?

A
Dynamic programming
B
Backtracking
C
Greedy
D
Divide and Conquer

Question 6

Which of the following algorithm solves the all-pair shortest path problem?

A
Prim’s algorithm
B
Dijikstra’s algorithm
C
Bellman-Ford’s algorithm
D
Floyd-Warshall’s algorithm

Question 7

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?

A
weight (u, v) < 12
B
weight (u, v) ≤ 12
C
weight (u, v) > 12
D
weight (u, v) ≥ 12

Question 8

The Floyd-Warshall algorithm for all-pair shortest paths computation is based on:

A
Greedy paradigm.
B
Divide-and-Conquer paradigm.
C
Dynamic Programming paradigm.
D
neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.

Question 9

Consider the weighted undirected graph with 4 vertices, where the weight of edge {i, j} g is given by the entry
W_ij in the matrix W

gt164

The largest possible integer value of x, for which at least one shortest path between some pair of vertices will contain the edge with weight x is ________

Note : This question was asked as Numerical Answer Type.

A
8
B
12
C
10
D
11

Question 10

Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is

A
4
B
7
C
23
D
99

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