1

2013 IEEE 9th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

978-1-4799-0428-0/13/$31.00 ©2013 IEEE 578

N

{FBS1, FBS2, . . . , FBSN} M

{U1, U2, . . . , UM}R = 50

gmn

FBSn n ∈ {1, . . . , N} Um m ∈ {1, . . . , M}gmn

α

γmn FBSn

n ∈ {1, . . . , N} Um m ∈ {1, . . . , M}

xmn

xmn =

{1 m n

0

m ∈ {1, . . . , M}n ∈ {1, . . . , N}

SINRmn =γmngmnxmn∑

∀m′ �=m

∑∀n′ �=n γm′n′gmn′xm′n′ + 1

.

Γm m ∈ {1, . . . , M}

FBSn n ∀n ∈ {1, . . . , N}Um m ∀m ∈ {1, . . . , M}

Maximize

N∑n=1

M∑m=1

xmn

M∑m=1

xmn ≤ 1, ∀ n ∈ {1, . . . , N} ,

∑N

n=1 γmngmnxmn∑∀m′ �=m

∑∀n′ �=n γm′n′gmn′xm′n′ + 1

≥ Γm

N∑n=1

xmn,

∀ m ∈ {1, . . . , M} ,N∑

n=1

xmn ≤ 1, ∀ m ∈ {1, . . . , M} ,

xmn ∈ {0, 1} , ∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N} .

n ∈ {1, . . . , N}

m ∈ {1, . . . , M}

579

C(N,M) =

⎛⎝min(N,M)∑

k=1

k!×

(min(N,M)

k

)×

(max(N,M)

k

)⎞⎠ .

N < M

C(N,M) ≤

N∑k=1

N !×

(M

N

)×

(N

N

).

(nk

)k≤

(nk

)≤ nk

k!

C(N,M) ≤ N ×N !×MN

N != N ×MN .

C(N,M) ≤

{M ×NM N > M ,

N ×MN N < M .

OPT-C

O(M2 ×N2

)

OPT-C ∈ O(M2 ×N2 × C(N,M)

)∈⎧⎪⎨

⎪⎩O(M3 ×NM+2

)N > M ,

O(N3 ×MN+2

)N < M ,

O(N3 ×N2 ×N !

)N = M .

γmn ∀ m ∈ {1, . . . , M} , n ∈{1, . . . , N}

γmngmn∑k �=m

γkngkn+1

∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}

n m

N×M

gmn mn Γm

listmn ←γmngmn∑

k �=mγkngkn+1 ∀ m ∈ {1, . . . , M} , ∀n ∈

{1, . . . , N}

iter ≤ size(listmn)m n

m← n m n

iter← iter + 1

m � n m n

iter← iter + 1

O(N2 ×M2

)N ×M

M × N × log(M × N)

MRCGA-C ∈ O(M ×N × log(M ×N) +N3 ×M3

),

MRCGA-C ∈ O(N3 ×M3

).

580

∑M

m=1γmngmn

M∀ n ∈ {1, . . . , N}

gmn mn Γm

n

listn ←∑

M

m=1γmngmn

M∀ n ∈ {1, . . . , N}

n← 1 size(listn)m← 1 M

m n

m← n m n

break

m � n m n

MRCGA-C ∈ O(N3 ×M3

).

γmn n m

∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}

M

N

P = γmn ∀ m ∈ M n ∈ N

gmn mn Γm

I ← {1, 2, . . . ,M}J ← {1, 2, . . . , N}c← 1

c ≤ N ×M

γmn

iter← 1∈ I ∈ J

listmn ←γmngmn∑

k �=nγmkgmk+1 ∀ m ∈ I, n ∈ J

iter ≤ size(listmn)m n

m← n m n

I ← I \{m} m

J ← J \{n} n

γmn

mn = Γm

break

m � n m n

iter← iter + 1

c← c+ 1

M < N M = 10, N =

20

OUA-C O(M3

×NM+2)

MRCGA-C O(N3

×M3)

MACGA-C O(N3

×M3)

JntPUA-C O(N3

×M6)

α = 4R = 50

581

Γm = .5

γmn ∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}γmn ∀ m ∈

{1, . . . , M} , n ∈ {1, . . . , N}

M = 10

Γm = .5 γmn = 20

N = 6

γmn

γmn ∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}

γ

γ

M = 10

Γm = .5

γmn = 10 γmn = 2

Γ

N = 30 M = 10

γmn = 10

γmn ∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}

582

γ

N = 30 M = 10

Γm = .5

γ

N = 6

M = 10 Γm = .5

γmn ∀ m ∈ {1, . . . , M} , n ∈ {1, . . . , N}

583