- #1
Huumah
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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
Bidirectional Search (graph theory)
- Thread starter Huumah
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- Graph theory Search Theory
In summary, Bidirectional search is a graph traversal algorithm that combines the advantages of breadth-first search and depth-first search to efficiently find the shortest path between two nodes in a graph. It works by simultaneously exploring nodes from both the source and destination, gradually expanding the search until they meet at the shortest path. This algorithm is more efficient than traditional graph search methods and is commonly used in GPS navigation systems, robotics, and database optimization. However, it can only be used when the source and destination nodes are known, and it requires additional memory. Additionally, if the two searches do not meet, it does not guarantee to find the shortest path.
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
- #2
mfb
Mentor
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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.
The fact that there are no shorter paths looks trivial then.
1. What is bidirectional search in graph theory?
Bidirectional search is a graph traversal algorithm that starts from both the source and destination nodes and works towards each other to find the shortest path between them. It combines the advantages of both breadth-first search and depth-first search to improve the efficiency of finding a solution in a graph.
2. How does bidirectional search work?
Bidirectional search starts by exploring the nodes adjacent to the source and destination nodes simultaneously. It then expands the search to the next layer of nodes and continues until the two searches meet. This meeting point is the shortest path between the source and destination nodes.
3. What are the advantages of bidirectional search?
Bidirectional search is more efficient than traditional graph search algorithms because it reduces the search space by exploring from both ends rather than searching the entire graph. It also guarantees to find the shortest path between two nodes if it exists in the graph.
4. What are the limitations of bidirectional search?
Bidirectional search can only be used in graphs where the source and destination nodes are known. It also requires additional memory to keep track of the explored nodes from both ends. Furthermore, if the two searches do not meet, it does not guarantee to find the shortest path.
5. In which real-world applications is bidirectional search useful?
Bidirectional search is commonly used in GPS navigation systems, where the source and destination are known, and finding the shortest route is crucial. It is also used in robotics for path planning and in database optimization for query processing.
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