What are common examiner traps in Graph Algorithms?

Confusing Bellman-Ford's complexity (|V||E|) with Dijkstra's algorithm time complexity using heaps (e.g., O(|E| |V|)). Assuming linear number of edges |E| = (n) instead of quadratic |E| = (n2) for dense/complete graphs. Selecting options with logarithmic factors like (n2 n) or (n3 n) by mixing heap-based implementations into Bellman-Ford.

Graph Algorithms

1 Qs · 2013 · 1 marks · 0 marks/paperStandard yield

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GATE tests fundamental graph algorithms by evaluating their asymptotic time complexity on specific graph structures. In this topic, questions require candidates to combine the stan… Guide

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GATE CSE 2013Q19MCQ1 markEasyWhat is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of $n$ vertices?

Topic guide

What does GATE test in Graph Algorithms?

GATE tests fundamental graph algorithms by evaluating their asymptotic time complexity on specific graph structures. In this topic, questions require candidates to combine the standard algorithmic complexity bounds (expressed in terms of vertices $|V|$ and edges $|E|$ ) with the structural edge-density properties of particular graph classes, such as complete graphs.

Core concepts

Bellman-Ford single-source shortest path algorithm
Edge count of complete graphs
Asymptotic time complexity analysis (\ -notation)

Recurring question patterns

Algorithm Time Complexity on Graph Topologies
rare · MCQ · 1 marks · 2013
Evaluating the worst-case/tight asymptotic runtime bound of a shortest-path algorithm (e.g., Bellman-Ford) applied to a special graph family (e.g., complete graph $K_n$ ).

Formulas GATE uses

Bellman-Ford Time Complexity

T(|V|, |E|) = \Theta(|V| \cdot |E|)

Used to compute runtime where $|V|-1$ passes are made over all $|E|$ edges.

Complete Graph Edge Count

|E| = \binom{n}{2} = \frac{n(n-1)}{2} = \Theta(n^2)

Used when an algorithm is executed on a complete graph with $n$ vertices.

Examiner traps in Graph Algorithms

Confusing Bellman-Ford's complexity (|V||E|) with Dijkstra's algorithm time complexity using heaps (e.g., O(|E| |V|)).
Assuming linear number of edges |E| = (n) instead of quadratic |E| = (n2) for dense/complete graphs.
Selecting options with logarithmic factors like (n2 n) or (n3 n) by mixing heap-based implementations into Bellman-Ford.

How questions are asked

Direct asymptotic complexity determination on a specific graph class

Paper trends

Direct 1-mark conceptual question assessing the exact parameter substitution of $|E| = \Theta(n^2)$ into the Bellman-Ford runtime $\Theta(|V| \cdot |E|)$ .
2013

Difficulty notes

Easy: Direct substitution of standard graph parameters (e.g., $|V|=n, |E|=\Theta(n^2)$ ) into the well-known time complexity of standard graph algorithms. Medium/Hard: Introducing algorithmic optimizations, custom stopping conditions, or non-trivial graph topologies (e.g., hypercubes, grid graphs).