An O(n^lg k . 2^n/2) Time and O(k . 2^n/k) Space Algorithm for Certain NP-Complete Problems

For a subset of NP-complete problems Schroeppel and Shamir (1981) described a general-purpose algorithm with O(2n2) time and O(2n4) space complexity. In this note we try to combine their idea with the “selection in X+Y” problem. This approach yields a family of algorithms solving a subset of NP-complete problems in O(nlg k · 2n2) time and O(k · 2nk) space.