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Optimization of Graph Traversal

#algorithms #computer-science #optimization

Analyze the time and space complexity of a modified Dijkstra's algorithm and propose optimizations for dynamic graphs.

Provide a theoretical analysis of a modified Dijkstra's algorithm that supports edge weight updates dynamically. Derive the Time Complexity for the update operation and the shortest path query operation using a Fibonacci Heap. Compare this to the standard static implementation and propose a heuristic optimization that could reduce average-case runtime for spatially clustered graphs.