3.5.1. Rank Comparison (DAGRank())

Rank may be thought of as a fixed-point number, where the position of the radix point between the integer part and the fractional part is determined by MinHopRankIncrease. MinHopRankIncrease is the minimum increase in Rank between a node and any of its DODAG parents. A DODAG root provisions MinHopRankIncrease. MinHopRankIncrease creates a trade-off between hop cost precision and the maximum number of hops a network can support. A very large MinHopRankIncrease, for example, allows precise characterization of a given hop's effect on Rank but cannot support many hops.

When an Objective Function computes Rank, the Objective Function operates on the entire (i.e., 16-bit) Rank quantity. When Rank is compared, e.g., for determination of parent relationships or loop detection, the integer portion of the Rank is to be used. The integer portion of the Rank is computed by the DAGRank() macro as follows, where floor(x) is the function that evaluates to the greatest integer less than or equal to x:

           DAGRank(rank) = floor(rank/MinHopRankIncrease)

For example, if a 16-bit Rank quantity is decimal 27, and the MinHopRankIncrease is decimal 16, then DAGRank(27) = floor(1.6875) = 1. The integer part of the Rank is 1 and the fractional part is 11/16.

Following the conventions in this document, using the macro DAGRank(node) may be interpreted as DAGRank(node.rank), where node.rank is the Rank value as maintained by the node.

A Node A has a Rank less than the Rank of a Node B if DAGRank(A) is less than DAGRank(B).

A Node A has a Rank equal to the Rank of a Node B if DAGRank(A) is equal to DAGRank(B).

A Node A has a Rank greater than the Rank of a Node B if DAGRank(A) is greater than DAGRank(B).