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Table 1 Important notations used in this article

From: Two novel price-based algorithms for spectrum sharing in cognitive radio networks

Notation

Meaning

M l

The number of particles for the leader

M f

The number of particles for followers

x m

The m th particles for the leader, x m  = (xm 1, xm 2, …, x mn )T, m = 1, …, M l

v m

The velocity of x m , v m  = (vm 1, vm 2, …, v mn )T, m = 1, …, M l

y m

The follower's choice for each x m from the leader, y m  = (ym 1, ym 2, …, y mw )T

y mp

The p th particles by the follower for the choice x m from the leader, y mp  = (ymp 1, vmp 2, …, v mpw )T, p = 1, …, M f

v mp

The velocity of y mp , v mp  = (vmp 1, vmp 2, …, v mpw )T, p = 1, …, M f

pb m

The best previously visited solution of x m , pb m  = (pbm 1, pbm 2, …, pb mn )T

pb mp

The best previously visited solution of y mp , pb mp  = (pbmp 1, pbmp 2, …, pb mpw )T

x *

Current best solution for particle x m from the leader

y *

Current best solution for particle y mp from the follower

y mpi

The y mp value of the i th follower, i = 1, …, N

v mpi

The v mp value of the i th follower, i = 1, …, N

y i *

The y*value of the i th follower, i = 1, …, N

g l

Current iteration number for the upper-level problem

g f

Current iteration number for the lower-level problem

max_g l

The predefined max iteration number for g l

max_g f

The predefined max iteration number for g f