Detection and Optimization of Traffic Networks Based on Voronoi Diagram

Algorithm 1

Compute prominence of VoronoiEdges (f, T).

 Input: a function f and its Voronoi tree T

 Output: the left valley site of each Voronoi edge, represented by Valley^L (•), the right valley site of each Voronoi edge, represented by Valley^R (•), the peak site of each Voronoi edge, represented by Peak (•), and the prominence of each Voronoi edge, represented by Prominence (•)

 Begin

(1)for each Voronoi edge e in T do //T is visited in a bottom-up order.

(2) Let the two input sites be p_i and p_j with i ≤ j.

(3) if j = i then //in this case e is a leaf node.

(4)  Peak(e) = Valley^L(e) = Valley^R(e) = p_i

(5) else

(6)  let the first and second child nodes of e be, respectively, e₁ and e₂

(7)  if y(Peak (e₁)) < y(Peak (e₂)) then

(8)   Peak (e) = Peak (e₂)

(9)   Valley^L (e) = the lowest of Valley^L (e₁), Valley^R (e₁), and Valley^L (e₂)

(10)   Valley^R (e) = Valley^R (e₂)

(11)  else

(12)   Peak (e) = Peak (e₁)

(13)   Valley^L (e) = Valley^L (e₁)

(14)   Valley^R (e) = the lowest of Valley^R (e₁), Valley^L (e₂), and Valley^R (e₂)

(15) Prominence(e) = y(Peak (e))−max(y(Valley^L (e)), y(Valley^R (e)))

(16)return Valley^L (•), Valley^R (•), Peak (•), and Prominence (•).

 End