Optimal frequency assignments of cycles and powers of cycles
by Hsun-Wen Chang, Hao-Wen Chen
International Journal of Mobile Network Design and Innovation (IJMNDI), Vol. 1, No. 2, 2006

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.

Online publication date: Tue, 05-Sep-2006

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