When I search for Dijkstra's algorithm and hypergraphs, I don't get any results discussing it. The Wikipedia page regarding Dijkstra's algorithm doesn't mention hypergraphs and the one regarding hypergraphs doesn't mention Dijkstra's algorithm. When I search for shortest path algorithms for hypergraphs, I only get results with complicated algorithms.
But when I look at Dijkstra's algorithm, I can't seem to see anything in it where it uses the fact that each edge only connects two nodes.
1 function Dijkstra(Graph, source): 2 dist[source] ← 0 // Initialization 3 4 create vertex set Q 5 6 for each vertex v in Graph: 7 if v ≠ source 8 dist[v] ← INFINITY // Unknown distance from source to v 9 prev[v] ← UNDEFINED // Predecessor of v 10 11 Q.add_with_priority(v, dist[v]) 12 13 14 while Q is not empty: // The main loop 15 u ← Q.extract_min() // Remove and return best vertex 16 for each neighbor v of u: // only v that is still in Q 17 alt ← dist[u] + length(u, v) 18 if alt < dist[v] 19 dist[v] ← alt 20 prev[v] ← u 21 Q.decrease_priority(v, alt) 22 23 return dist, prev
The only time this algorithm mentions connections is in line 16, where it says "for each neighbor v of u".
Could I simply use this algorithm for hypergraphs and only get correct results?