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We present a new game, Dots & Polygons, played on a planar point set. Players take turns connecting two points, and when a player closes a (simple) polygon, the player scores its area. We show that deciding whether the game can be won from…
The game of Spot it(R) is based on an order 7 finite projective plane. This article presents a solitaire challenge: extract an order 7 affine plane and arrange those 49 cards into a square such that the symmetries of the affine and…
Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other.…
Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
Our goal is to prove new results in graph theory and combinatorics thanks to the speed of computers, used with smart algorithms. We tackle four problems. The four-colour theorem states that any map whose countries are connected can be…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
Jigsaw puzzle solving is an intriguing problem which has been explored in computer vision for decades. This paper focuses on a specific variant of the problem - solving puzzles with eroded boundaries. Such erosion makes the problem…
We introduce GamePlot, an LLM-powered assistant that supports game designers in crafting immersive narratives for turn-based games, and allows them to test these games through a collaborative game play and refine the plot throughout the…
Automated planning using a symbolic planning language, such as PDDL, is a general approach to producing optimal plans to achieve a stated goal. However, creating suitable machine understandable descriptions of the planning domain, problem,…
In automated planning, the need for explanations arises when there is a mismatch between a proposed plan and the user's expectation. We frame Explainable AI Planning in the context of the plan negotiation problem, in which a succession of…
Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three…
Understanding player strategies is a key question when analyzing player behavior both for academic researchers and industry practitioners. For game designers and game user researchers, it is important to gauge the distance between intended…
PDDL was originally conceived and constructed as a lingua franca for the International Planning Competition. PDDL2.1 embodies a set of extensions intended to support the expression of something closer to real planning problems. This…