Route Lookup - Routing is a Shortest Path

A route lookup uses the shortest-path tree to choose the next hop toward a destination. For F, A forwards toward C.

highlighted = computed this step

Follow predecessors backward

For destination F, the recomputed path from A is A to C to D to F.

\text{A}\to\text{C}\to\text{D}\to\text{F}

The predecessor chain reads backward as F to D to C to A. Reversing that chain gives the forwarding path from A.

\text{F}\to\text{D}\to\text{C}\to\text{A}

From A, the next hop toward F is C.

\text{next hop}=\text{C}

The route cost is A-C weight 2 plus C-D weight 3 plus D-F weight 5, totaling 10.

2+3+5=10

The total path cost to F is 10.

d(F)=10

Routing here is exact shortest-path arithmetic only; timing, throughput, and policy behavior are outside this model.

\text{route selected by shortest path}