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.

Given a set of n points in d-dimensional space, each assigned a positive weight, we study the problem of finding k axis-parallel unit hypercubes that maximize the total weight of the points contained in their union. In this paper, we present both exact and (1 - ε)-approximation algorithms for the case of k = 2. We present an exact algorithm that runs in O(n²) time in the plane, improving the previous O(n² log² n)-time result. This algorithm generalizes to higher dimensions and larger k in O(n^{dk/2}) time for fixed d and k. We also present a (1 - ε)-approximation algorithm that runs in O(n log min{n, 1/ε} + 1/ε³) time for k = 2 in the plane, improving the best known result. Our approximation algorithm also extends to higher dimensions.