@techNmak: For 38 years, computer scientists believed Dijkstra's algorithm was optimal for sparse graphs. The logic seemed airtigh…
Summary
Five researchers from Tsinghua, Stanford, and Max Planck have developed a new shortest path algorithm that beats Dijkstra's for sparse directed graphs, achieving O(m log^(2/3) n) time complexity, the first improvement since 1987.
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Cached at: 06/09/26, 12:47 PM
For 38 years, computer scientists believed Dijkstra’s algorithm was optimal for sparse graphs.
The logic seemed airtight:
Dijkstra sorts vertices by distance. Sorting has a lower bound of O(n log n). Therefore shortest paths can’t be faster.
5 researchers proved the assumption wrong.
The trick: combine Dijkstra’s priority queue with Bellman-Ford’s dynamic programming. Divide and conquer on vertex sets. Shrink the frontier.
Result: O(m log^(2/3) n) First improvement for directed graphs since Fibonacci heap in 1987.
Tsinghua. Stanford. Max Planck. 17 pages.
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