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In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.
  • a)
    Yes
  • b)
    No
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a weighted graph, assume that the shortest path from a source s to ...
See the following counterexample. There are 4 edges s-a, a-b, b-t and s-t of wights 1, 1, 1 and 4 respectively. The shortest path from s to t is s-a, a-b, b-t. IF we increase weight of every edge by 1, the shortest path changes to s-t.
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Most Upvoted Answer
In a weighted graph, assume that the shortest path from a source s to ...
See the following counterexample. There are 4 edges s-a, a-b, b-t and s-t of wights 1, 1, 1 and 4 respectively. The shortest path from s to t is s-a, a-b, b-t. IF we increase weight of every edge by 1, the shortest path changes to s-t.
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Community Answer
In a weighted graph, assume that the shortest path from a source s to ...
Explanation:
Increasing the weight of every edge in a weighted graph by 1 does not guarantee that the shortest path will remain the same. The reason for this is explained below:
- Effect on Path Selection:
- When the weights of all edges are increased by 1, the overall path cost for each path in the graph increases by the same amount. This increase in path cost can potentially change the selection of the shortest path from source s to destination t.
- Example:
- Consider a simple graph with two paths from source s to destination t: Path 1 with a total weight of 5 and Path 2 with a total weight of 6. Path 1 is currently the shortest path.
- If we increase the weight of every edge by 1, Path 1 now has a total weight of 6 and Path 2 has a total weight of 7. In this case, the shortest path changes from Path 1 to Path 2.
- Conclusion:
- Therefore, it is not always true that increasing the weight of every edge by 1 will keep the shortest path the same. It depends on the specific weights of the edges and the initial shortest path calculated by the algorithm.
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In a weighted graph, assume that the shortest path from a source s to a destination t is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer?
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