Design an algorithm to detect the shortest path in a dynamically changing graph where edge weights update in real-time (e.g., a network routing table with fluctuating latency). You are strictly limited to O(V log V) time complexity per update and O(V) space complexity. Explain your choice of data structures (e.g., Fibonacci heaps, splay trees) and prove the time complexity bounds. Additionally, discuss how you would handle negative edge-weight cycles if they appear temporarily due to network anomalies.