Bidirectional Search (graph theory)

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SUMMARY

The discussion centers on the concept of Bidirectional Search in graph theory, specifically addressing an old exam question regarding the shortest path through a node M. The participants confirm that if node M lies on both paths d(O,M) and d(D,M), it is indeed part of the shortest path. They emphasize the necessity of a search algorithm that does not overlook nodes with smaller costs to validate this conclusion, asserting that the absence of shorter paths is a trivial outcome under these conditions.

PREREQUISITES
  • Understanding of graph theory concepts, particularly shortest path algorithms.
  • Familiarity with Bidirectional Search techniques.
  • Knowledge of cost functions in search algorithms.
  • Experience with algorithmic proof techniques.
NEXT STEPS
  • Study the principles of Bidirectional Search in detail.
  • Explore Dijkstra's algorithm and its application in finding shortest paths.
  • Investigate the role of cost functions in search algorithms.
  • Learn about algorithmic proof methods to validate search outcomes.
USEFUL FOR

Students preparing for exams in algorithms, computer scientists focusing on graph theory, and software developers implementing search algorithms in applications.

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Attempt at solution
This is an old exam question. Am I correct to say the shortest path goes through M since M is in d(O,M) and d(D,M)?
I don't know how to prove this and answer the question about the cost
 
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With some assumption about the search algorithm (i. e. one that does not miss nodes with smaller costs - check this), you are right.
The fact that there are no shorter paths looks trivial then.
 

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