Shortest Paths in Graphs Quiz (original) (raw)

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:

• O (| E | + | V | log | V |)
• O ((| E | + | V |) log | V |)

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

• Dijkstra\'s Shortest Path Algorithm
• Neither Breadth First Traversal nor Dijkstra\'s algorithm can be used

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, _________”.

• if and only if ∀u∈V, f(u) is positive
• if and only if ∀u∈V, f(u) is negative
• 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

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

• Finding diameter of the graph

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

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

• Floyd-Warshall’s algorithm

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?

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

• Divide-and-Conquer paradigm.
• Dynamic Programming paradigm.
• neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.

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

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.

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

There are 28 questions to complete.

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