Related papers: Exploring Properties of Icosoku by Constraint Sati…
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
Despite their proficiency in various language tasks, Large Language Models (LLMs) struggle with combinatorial problems like Satisfiability, Traveling Salesman Problem, or even basic arithmetic. We address this gap through a novel trial &…
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…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
In eXplainable Constraint Solving (XCS), it is common to extract a Minimal Unsatisfiable Subset (MUS) from a set of unsatisfiable constraints. This helps explain to a user why a constraint specification does not admit a solution. Finding…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…