Dependency Graphs Math Example 5

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Example 5

hard
Given the dependency graph with edges A→CA \to C, A→DA \to D, B→DB \to D, B→EB \to E, C→FC \to F, D→FD \to F, E→FE \to F, determine whether adding the edge F→AF \to A would create a problem, and explain why.

Solution

  1. 1
    Adding F→AF \to A creates the cycle A→C→F→AA \to C \to F \to A (or A→D→F→AA \to D \to F \to A).
  2. 2
    A dependency graph must be a DAG (directed acyclic graph). A cycle means AA depends on FF which depends on CC which depends on AA — a circular dependency that cannot be resolved.

Answer

Yes, it creates a cycle, making the dependencies unsatisfiable.\text{Yes, it creates a cycle, making the dependencies unsatisfiable.}
Dependency graphs must be acyclic (DAGs). Adding an edge that creates a cycle means no valid topological ordering exists, so the tasks cannot be scheduled — each waits for another indefinitely.

About Dependency Graphs

A dependency graph is a directed graph where nodes are variables and arrows show which variables directly influence which others.

Learn more about Dependency Graphs →

More Dependency Graphs Examples

Example 1 easy

Three tasks have the following dependencies: Task B depends on Task A, and Task C depends on Task B.

Example 2 medium

Given the dependencies: [formula] depends on [formula] and [formula]; [formula] depends on [formula]

Example 3 medium

Tasks [formula], [formula], [formula], [formula]. What is the minimum number of stages to complete a

Example 4 medium

A project has tasks with dependencies: [formula] depends on [formula]; [formula] depends on [formula

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Related Concepts

Functional Dependency