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Considering a finite intersection of balls and a finite union of other ballsin an Euclidean space, we propose an exact method to test whether theintersection is covered by the union. We reformulate this problem intoquadratic programming problems. For each problem, we study the intersectionbetween a sphere and a Voronoi-like polyhedron. That way we get informationabout a possible overlap between the frontier of the union and the intersectionof balls. If the polyhedra are non-degenerate, the initial nonconvex geometricproblem, which is NP-hard in general, is tractable in polynomial time by convexoptimization tools and vertex enumeration. Under some mild conditions thevertex enumeration can be skipped. Simulations highlight the accuracy andefficiency of our approach compared with competing algorithms in Python fornonconvex quadratically constrained quadratic programming. This work ismotivated by an application in statistics to the problem of multidimensionalchangepoint detection using pruned dynamic programming algorithms.

Is a Finite Intersection of Balls Covered by a Finite Union of Balls in Euclidean Spaces ?