BFS Extensions

Multi-Source BFS

Find the shortest distance from any source node to all other vertices. By initializing the queue with multiple sources simultaneously, we simulate concurrent propagation fronts across the graph.

Time ComplexityO(V + E)

Space ComplexityO(V)

Try Interactive Simulator

Concurrent Fronts

Instead of running BFS multiple times, we inject all sources at once. The first front to reach a node defines its shortest distance.

Virtual Source

Conceptually, this is equivalent to adding a "super source" node connected to all real sources with edge weight 0.

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join • 🔘 Double-Click to Toggle Source

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BFS Extensions

Multi-Source BFS

Find the shortest distance from any source node to all other vertices. By initializing the queue with multiple sources simultaneously, we simulate concurrent propagation fronts across the graph.

Time ComplexityO(V + E)

Space ComplexityO(V)

Try Interactive Simulator

Concurrent Fronts

Instead of running BFS multiple times, we inject all sources at once. The first front to reach a node defines its shortest distance.

Virtual Source

Conceptually, this is equivalent to adding a "super source" node connected to all real sources with edge weight 0.

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join • 🔘 Double-Click to Toggle Source

Multi Source Bfs

Multi Source Bfs

Multi-Source BFS

Concurrent Fronts

Virtual Source

Multi-Source BFS

Concurrent Fronts

Virtual Source