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A particular instance of the shortest vector problem (SVP) appears in the context of compute-and-forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order O(n&#x03C8; log(n&#x03C8;)), where &#x03C8; = &#x221A;P&#x2225;h&#x2225;<sup>2</sup> + 1 depends on the transmission power and the norm of the channel vector. We will then extend our results to integer-forcing and finally introduce a more general class of lattices for which the SVP and the closest vector problem can be approximated within a constant factor.

Polynomially Solvable Instances of the Shortest and Closest Vector Problems With Applications to Compute-and-Forward