We describe the methods used by Team Shadoks to win the CG:SHOP 2026 Challenge on parallel reconfiguration of planar triangulations. Our approach combines exact methods based on SAT with several greedy heuristics, and also makes use of SAT and MaxSAT for solution improvement.

Description of the solvers used by the Shadoks team in the PACE 2025 challenge. The challenge considers solvers for the minimum dominating set and hitting set problems. For the heuristic challenge, we respectively won third and fourth place for hitting set and dominating set. For the exact challenge, we won fifth place on both problems.

The 2024 edition of the CG:SHOP Challenge focused on the knapsack polygonal packing problem. Each instance consists of a convex polygon known as the container and a multiset of items, where each item is a simple polygon with an associated integer value. A feasible packing solution places a selection of the items inside the container without overlapping and using only translations. The goal is to achieve a packing that maximizes the total value of the items in the solution. Our approach to win first place is divided into two main steps. First, we generate promising initial solutions using two strategies: one based on integer linear programming and the other on employing a combination of geometric greedy heuristics. In the second step, we enhance these solutions through local search techniques, which involve repositioning items and exploring potential replacements to improve the total value of the packing.

International audience

International audience

We consider a class of problems of Discrete Tomography which has been deeply investigated in the past: the reconstruction of convex lattice sets from their horizontal and/or vertical X-rays, i.e. from the number of points in a sequence of consecutive horizontal and vertical lines. The reconstruction of the HV-convex polyominoes works usually in two steps, first the filling step consisting in filling operations, second the convex aggregation of the switching components. We prove three results about the convex aggregation step: (1) The convex aggregation step used for the reconstruction of HV-convex polyominoes does not always provide a solution. The example yielding to this result is called the bad guy and disproves a conjecture of the domain. (2) The reconstruction of a digital convex lattice set from only one X-ray can be performed in polynomial time. We prove it by encoding the convex aggregation problem in a Directed Acyclic Graph. (3) With the same strategy, we prove that the reconstruction of fat digital convex sets from their horizontal and vertical X-rays can be solved in polynomial time. Fatness is a property of the digital convex sets regarding the relative position of the left, right, top and bottom points of the set. The complexity of the reconstruction of the digital convex sets which are not fat remains an open question.

This paper describes the heuristics used by the Shadoks team for the CG:SHOP 2021 challenge on motion planning. Using the heuristics outlined in this paper, our team won first place with the best solution to 202 out of 203 instances and optimal solutions to at least 105 of them.

We study a problem that we call Shape-from-Template, which is the problem of reconstructing the shape of a deformable surface from a single image and a 3D template. Current methods in the literature address the case of isometric deformations, and relax the isometry constraint to the convex inextensibility constraint, solved using the so-called maximum depth heuristic. We call these methods zeroth-order since they use image point locations (the zeroth-order differential structure) to solve the shape inference problem from a perspective image. We propose a novel class of methods that we call first-order. The key idea is to use both image point locations and their first-order differential structure. The latter can be easily extracted from a warp between the template and the input image. We give a unified problem formulation as a system of PDEs for isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our isometric methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy, while our conformal methods largely outperform all isometric methods for extensible deformations.

Recovering a deformable surface's 3D shape from a single view registered to a 3D template requires one to provide additional constraints. A recent approach has been to constrain the surface to deform quasi-isometrically. This is applicable to surfaces of materials such as paper and cloth. Current `closed-form' solutions solve a convex approximation of the original problem whereby the surface's depth is maximized under the isometry constraints (this is known as the maximum depth heuristic). No such convex approximation has yet been proposed for the conformal case. We give a unified problem formulation as a system of PDEs for developable, isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy.