Complexity of Terminal-Only Manhattan Prim-Dijkstra Routing

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algorithms-optimizationJul 18, 2026Significance 10/100Registry: unreviewed

Complexity of Terminal-Only Manhattan Prim-Dijkstra Routing

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Prim-Dijkstra routing interpolates between a minimum spanning tree and a shortest-path tree, and has been used and improved in VLSI physical design since the early 1990s, but the complexity of the terminal-only Manhattan decision problem was never settled. It is weakly NP-complete. A continuous cost-radius tradeoff with a balanced $(2,2)$ guarantee accompanies the classification.

Source authenticatedComplexity of Terminal-Only Manhattan Prim-Dijkstra Routing →

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Prim-Dijkstra routing interpolates between a minimum spanning tree and a shortest-path tree, and has been used and improved in VLSI physical design since the early 1990s, but the complexity of the terminal-only Manhattan decision problem was never settled. It is weakly NP-complete. A continuous cost-radius tradeoff with a balanced $(2,2)$ guarantee accompanies the classification.

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