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the `identifier` of the root switch (`R`)
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the `cost` of the shortest path between the switch that sent the `BPDU` and the root switch (`c`)
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the `identifier` of the switch that sent the `BPDU` (`T`)
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the number of the switch port over which the `BPDU` was sent (`p`)
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In addition to the `identifier` discussed above, the network administrator can also configure a `cost` to be associated to each switch port. Usually, the `cost` of a port depends on its bandwidth and the [IEEE802.1d]_ standard recommends the values below. Of course, the network administrator may choose other values. We will use the notation `cost[p]` to indicate the cost associated to port `p` in this section.
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Bandwidth
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Cost
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10 Mbps
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2000000
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100 Mbps
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200000
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1 Gbps
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20000
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2000
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100 Gbps
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200
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The `Spanning Tree Protocol` uses its own terminology that we illustrate in the figure above. A switch port can be in three different states : `Root`, `Designated` and `Blocked`. All the ports of the `root` switch are in the `Designated` state. The state of the ports on the other switches is determined based on the `BPDU` received on each port.
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The `Spanning Tree Protocol` uses the ordering relationship to build the spanning tree. Each switch listens to `BPDUs` on its ports. When `BPDU = <R,c,T,p>` is received on port `q`, the switch computes the port's `root priority vector`: `V[q] = <R,c+cost[q],T,p,q>` , where `cost[q]` is the cost associated to the port over which the `BPDU` was received. The switch stores in a table the last `root priority vector` received on each port. The switch then compares its own `identifier` with the smallest `root identifier` stored in this table. If its own `identifier` is smaller, then the switch is the root of the spanning tree and is, by definition, at a distance `0` of the root. The `BPDU` of the switch is then `<R,0,R,p>`, where `R` is the switch `identifier` and `p` will be set to the port number over which the `BPDU` is sent.
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Otherwise, the switch chooses the best priority vector from its table, `bv = <R,c+cost[q'],T,p,q'>`. The port `q'`, over which this best root priority vector was learned, is the switch port that is closest to the `root` switch. This port becomes the `Root` port of the switch. There is only one `Root` port per switch (except for the `Root` switches whose ports are all `Designated`). The switch can then compute its own `BPDU` as `BPDU = <R,c',S,p>` , where `R` is the `root identifier`, `c'` the cost of the best root priority vector, `S` the identifier of the switch and `p` will be replaced by the number of the port over which the `BPDU` will be sent.
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To determine the state of its other ports, the switch compares its own `BPDU` with the last `BPDU` received on each port. Note that the comparison is done by using the `BPDUs` and not the `root priority vectors`. If the switch's `BPDU` is better than the last `BPDU` of this port, the port becomes a `Designated` port. Otherwise, the port becomes a `Blocked` port.
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