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The current status of the CSP during the algorithm can be viewed as a directed graph, where the nodes are the variables of the problem, with edges or arcs between variables that are related by symmetric constraints, where each arc in the worklist represents a constraint that needs to be checked for consistency.
Two other methods involving arc consistency are full and partial look ahead. They enforce arc consistency, but not for every pair of variables. In particular, full look considers every pair of unassigned variables ,, and enforces arc consistency between them. This is different than enforcing global arc consistency, which may possibly require a ...
Directional arc consistency guarantees that every consistent assignment to a variable can be extended to higher nodes, and width 1 guarantees that a node is not joined to more than one lower node. As a result, once the lower variable is assigned, its value can be consistently extended to every higher variable it is joined with.
State-based CRDTs (also called convergent replicated data types, or CvRDTs) are defined by two types, a type for local states and a type for actions on the state, together with three functions: A function to produce an initial state, a merge function of states, and a function to apply an action to update a state.
The most known and used forms of local consistency are arc consistency, hyper-arc consistency, and path consistency. The most popular constraint propagation method is the AC-3 algorithm, which enforces arc consistency. Local search methods are incomplete satisfiability algorithms. They may find a solution of a problem, but they may fail even if ...
Various kinds of local consistency conditions are leveraged, including node consistency, arc consistency, and path consistency. Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions.
Modifying the consistency condition to h(N)−h(P) ≤ c(N,P) establishes a connection to local admissibility, where the heuristic estimate to a specific node remains less than or equal to the actual step cost. This ensures optimality when selecting local nodes, akin to how admissible heuristics ensure global optimality.
The algorithm with the fastest known query time is called hub labeling and is able to compute shortest path on the road networks of Europe or the US in a fraction of a microsecond. [14] Other techniques that have been used are: ALT (A* search, landmarks, and triangle inequality) Arc flags; Contraction hierarchies; Transit node routing; Reach ...