In the CG:SHOP 2026 Challenge, the goal is to compute a central triangulation for a given set of triangulations on the same point set while minimizing the sum of parallel flip distances. To address the problem, our team (CG#Hunters) constructs an initial solution by iteratively applying parallel flips to reduce the total number of crossings between the triangulations until none remain. To optimize these solutions, we shorten the paths by using a score-based greedy edge selection and refine the central triangulation via a large scale neighborhood search. Additionally, a representative-set-based approach is utilized to efficiently handle large instances. With these combined approaches, we achieved third place by successfully computing central triangulations with sufficiently short parallel flip paths for all 250 instances.

We study the problem of minimizing the convex hull of two convex polytopes with n vertices in total under translation in d-dimensional space ℝd for any fixed dimension d ≥ 2. For d ≥ 2, we present a deterministic O (n )-time algorithm returning a translation minimizing the area of the convex hull, improving upon the previously best O (n log n )-time algorithm. Our algorithm returns the smallest area of convex hulls under translation in the same time, and thus it is optimal. For d ≥ 3, we present a deterministic algorithm with running time O (n(d +1)/2) for odd d and O (nd /2 logd n ) for even d. This improves substantially upon the previously best algorithm by a factor at least n(d -1)/2 log n. We also consider the variant that two input polytopes are restricted to remain disjoint, and present a deterministic algorithm with running time O (nd+1) for odd d and O (nd logd -1 n) for even d. This improves substantially upon the previously best algorithm for d > 3 by factor nO (d2) We also study the problem of maximizing the overlap of two convex polytopes under translation in d-dimensional space ℝd for d ≥ 3. We give an -time algorithm, improving substantially upon the previously best algorithm by a factor at least n1-3/d logd +1 n.