A Linear Approximate Algorithm for Earth Mover's Distance with Thresholded Ground Distance

Algorithm 2

Recursive function getBins, Enumerate all possible qualified bins.

   Input: 𝑏: one qualified bin; 𝐵: qualified bin set;

     𝜇: threshold; 𝑑: dimensionality;

     curr: current dimension.

   Output: Qualified bin set 𝐵

(1)  for  𝑖=curr to 𝑑  do

(2)     𝑏^′←𝑏;

(3)    if  𝑏^′[𝑖]=0  then

(4)       𝑏^′[𝑖]←𝑏^′[𝑖]−1;

(5)      if  𝑏^′_𝑝<𝜇  then

(6)       𝐵.𝑎𝑑𝑑(𝑏^′);

(7)        getBins(𝑏^′,𝐵,𝜇,𝑑,𝑖);

(8)       𝑏^′←𝑏, 𝑏^′[𝑖]←𝑏^′[𝑖]+1;

(9)       if  𝑏^′_𝑝<𝜇  then

(10)      𝐵.𝑎𝑑𝑑(𝑏^′);

(11)       getBins(𝑏^′,𝐵,𝜇,𝑑,𝑖);

(12)  else

(13)      if  𝑏^′[𝑖]<0  then

(14)       𝑏^′[𝑖]←𝑏^′[𝑖]−1;

(15)      else

(16)       𝑏^′[𝑖]←𝑏^′[𝑖]+1;

(17)      if  𝑏^′_𝑝<𝜇  then

(18)       𝐵.𝑎𝑑𝑑(𝑏^′);

(19)       getBins(𝑏^′,𝐵,𝜇,𝑑,𝑖);