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 P of n points in the plane, the two-line center problem asks to find two lines that minimize the maximum distance from each point in P to its closer one of the two resulting lines. The currently best algorithm for the problem takes $O(n^2\log^2n)$ time by Jaromczyk and Kowaluk in 1995. In this paper, we present faster algorithms for three variants of the two-line center problem in which the orientations of the resulting lines are constrained. Specifically, our algorithms solve the problem in $O(n \log n)$ time when the orientations of both lines are fixed; in $O(n \log^3 n)$ time when the orientation of one line is fixed; and in $O(n^2 α(n) \log n)$ time when the angle between the two lines is fixed, where $α(n)$ denotes the inverse Ackermann function.

We present an algorithm to compute the geodesic $L_1$ farthest-point Voronoi diagram of $m$ point sites in the presence of $n$ rectangular obstacles in the plane. It takes $O(nm+n \log n + m\log m)$ construction time using $O(nm)$ space. This is the first optimal algorithm for constructing the farthest-point Voronoi diagram in the presence of obstacles. We can construct a data structure in the same construction time and space that answers a farthest-neighbor query in $O(\log(n+m))$ time.