Hypergraph Modeling and Approximation Algorithms for the Minimum Length Link Scheduling in Multiuser MIMO Networks

Algorithm 1

Algorithm 𝐏-𝐆(𝐆_𝐇): Providing a coloring solution for hypergraph 𝐺_𝐻=(𝑉_𝐻,𝐸_𝐻).

Input: A 𝑟-uniform hypergraph 𝐺_𝐻=(𝑉_𝐻,𝐸_𝐻).

Output: A coloring solution of 𝐺_𝐻.

(1)  𝑘=2;

(2)  𝑖=1; 𝑊=𝑉_𝐻;

(3)  while  𝑊≠∅

(4)  𝑈=𝐵(𝐺^𝑊_𝐻,𝑘);

(5)  if  𝑈 is not independent

(6)     𝑘=𝑘+1;

(7)  else

(8)     𝐶_𝑖=𝑈;  % color 𝑈 by color 𝑖 %

(9)     𝑖=𝑖+1; 𝑘=2;

(10)   𝑊=𝑊⧵𝑈;

(11)   endif

(12) endwhile;

(13) return a coloring 𝐶={𝐶₁,𝐶₂,…,𝐶_𝑖−1};