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Shortest Path in Sparse Graphs

#algorithms #computer-science #optimization #coding

Provide an optimized algorithm for finding shortest paths in sparse graphs.

Provide an in-depth technical analysis and optimized pseudocode implementation for finding the single-source shortest paths in a large, sparse graph. Compare the time and space complexity of Dijkstra’s algorithm using a Binary Heap versus a Fibonacci Heap. Furthermore, discuss the feasibility of using the A* algorithm versus Dijkstra for this specific case, assuming geographic coordinates are available for nodes. Provide Python code that implements the most efficient approach discussed, focusing on memory optimization for graphs with millions of nodes.