Given CSP P = (V; D; C), the dual constraint graph of P is the undirected simple graph whose vertex set is the set of all distinct constraint scopes of the constraints in C, and for which two scopes are adjacent i they have one or more variables in common.

We can draw a constraint graph for this representation where each variable gets a node and constraints between variables are represented with arrows. In this graph, constraint #1 is represented with the red arc, constraint #2 with blue arc,

2022年8月22日 · We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner.

It is helpful to visualize a CSP as a constraint graph, as shown in Figure 5.1(b). The nodes of the graph correspond to variables of the problem and the arcs correspond to constraints. Treating a problem as a CSP confers several important benefits.

What is a CSP? Standard search problem: – state is a “black box”—any old data structure that supports goal test, eval, successor CSP: – state is defined by variables X i with values from domain D i – goal test is a set of constraints specifying allowable combinations of values for subsets of variables

• Constraint graph for binary CSP problem: – Nodes are variables – Links represent the constraints – Same as our canonical graph-coloring problem N-Queens

We propose a universal Graph Neural Network archi-tecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner.

We propose to do so by introducing an encoding consisting in a heterogeneous and undirected graph featuring 5 types of vertices: variables, constraints, values, operators, and model. The core idea is to split each constraint as a sequence of elementary operations, to merge vertices representing the same variable or value, and connect together ...

2024年10月3日 · In this article, we will dive deep into the concept of CSP, its components, methods to solve CSPs, and real-world applications, illustrating how CSPs can be used effectively in AI systems.

The tree_csp_solver function (Figure 6.11 in the book) can be used to solve problems whose constraint graph is a tree. Given a CSP, with neighbors forming a tree, it...