We propose polynomial time approximation algorithms for minimum span channel (frequency) assignment problems, which is known to be NP-hard. Let α be the approximation ratio of our algorithm and W ≥2 be the maximum of numbers of channels required in vertices. If an instance is defined on a perfect graph G, then $\alpha \leq 1+(1+\frac{1}{W-1})\text{H}_{\omega(G)}$, where $\text{H}_i$ denotes the i-th harmonic number. For any instance defined on a unit disk graph G, α is less than or equal to $(1+\frac{1}{W-1})(3\text{H}_{\omega(G)}-1)$. If a given graph is 4 or 3 colorable, α is bounded by $(2.5+\frac{1.5}{W-1})$ and $(2+\frac{1}{W-1})$, respectively. We also discuss well-known practical instances called Philadelphia instances and propose an algorithm with α≤12/5.