Article: Optimal frequency assignments of cycles and powers of cycles Journal: International Journal of Mobile Network Design and Innovation (IJMNDI) 2006 Vol.1 No.2 pp.118 - 123 Abstract: To reduce the interfering among transmitters, any two |close| transmitters, with distance no more than d2, must receive frequencies at least l2 apart, and any two |very close| transmitters, with distance no more than d1, must receive channels at least l1 apart. The assignment problem is to assign a frequency to each transmitter such that total bandwidth of assigned frequencies can be minimised. In this paper, we present upper and lower bounds of the minimum bandwidth of cycles and powers of cycles. We also show the corresponding assignment functions. And then we partially solve the assignment problem of cycles Cn and their powers such as: (i) 3 ≤ n ≤ 2d1+1; (ii) 2d1 + 2 ≤ n ≤ 2d2 + 1, q1 ≠ 0 and l1 ≤ m1l2; (iii) 2d1 + 2 ≤ n ≤ 2d2 + 1, q1 ≡ 1(mod m1) and l1 > m1l2; (iv) 2d1 + 2 ≤ n ≤ 2d2 + 1, q1 = 0 and l1 ≥ (m1 + d1 − 1)l2 or l1 ≤ (m1 − 1)l2; (v) n ≥ 2d2 + 2 and l1 ≤ ⌊(d2 + ⌊q2/m2⌋)/(d1 + 1)⌋l2; and (vi) n ≥ 2d2 + 2, q1 ≡ 1(mod m1), and l1 > m1l2, where n = mi(di + 1) + qi and 0 ≤ qi ≤ di. Inderscience Publishers - linking academia, business and industry through research

Title: Optimal frequency assignments of cycles and powers of cycles

Authors: Hsun-Wen Chang, Hao-Wen Chen

Addresses: Department of Applied Mathematics, Tatung University, Taipei, Taiwan, ROC. ' Department of Applied Mathematics, Tatung University, Taipei, Taiwan, ROC

Abstract: To reduce the interfering among transmitters, any two |close| transmitters, with distance no more than d₂, must receive frequencies at least l₂ apart, and any two |very close| transmitters, with distance no more than d₁, must receive channels at least l₁ apart. The assignment problem is to assign a frequency to each transmitter such that total bandwidth of assigned frequencies can be minimised. In this paper, we present upper and lower bounds of the minimum bandwidth of cycles and powers of cycles. We also show the corresponding assignment functions. And then we partially solve the assignment problem of cycles C_n and their powers such as: (i) 3 ≤ n ≤ 2d₁+1; (ii) 2d₁ + 2 ≤ n ≤ 2d₂ + 1, q₁ ≠ 0 and l₁ ≤ m₁l₂; (iii) 2d₁ + 2 ≤ n ≤ 2d₂ + 1, q₁ ≡ 1(mod m₁) and l₁ > m₁l₂; (iv) 2d₁ + 2 ≤ n ≤ 2d₂ + 1, q₁ = 0 and l₁ ≥ (m₁ + d₁ − 1)l₂ or l₁ ≤ (m₁ − 1)l₂; (v) n ≥ 2d₂ + 2 and l₁ ≤ ⌊(d₂ + ⌊q₂/m₂⌋)/(d₁ + 1)⌋l₂; and (vi) n ≥ 2d₂ + 2, q₁ ≡ 1(mod m₁), and l₁ > m₁l₂, where n = m_i(d_i + 1) + q_i and 0 ≤ q_i ≤ d_i.

Keywords: frequency assignment; bandwidth; assignment number; powers of cycles; mobile networks; interference; mobile communications.

DOI: 10.1504/IJMNDI.2006.010817

International Journal of Mobile Network Design and Innovation, 2006 Vol.1 No.2, pp.118 - 123

Published online: 05 Sep 2006 *

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Title: Optimal frequency assignments of cycles and powers of cycles

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