Improved Approximation Guarantees for Power Scheduling Problems With Sum-of-Squares Constraints

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum of squares of linear functions. Its nonlinear nature adds complexity to the scheduling problem, rendering it notably challenging, even in the case of a linear objective. In fact, exact polynomial time algorithms are unlikely to exist, and thus, prior works have focused on designing approximation algorithms with polynomial running time and provable guarantees on the solution quality. In an effort to advance this line of research, we present novel approximation algorithms yielding significant improvements over the existing state-of-the-art results for these problems.