This chapter surveys counting Constraint Satisfaction Problems (counting CSPs, or #CSPs) and their computational complexity. It aims to provide an introduction to the main concepts and techniques, and present a representative selection of results and open problems. It does not cover holants, which are the subject of a separate chapter. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorith...

Abstract Recent work in economics has rediscovered the importance of belief-based utility for understanding human behaviour. Belief ‘choice’ is subject to an important constraint, however: people can only bring themselves believe things which they find rationalizations. When preferences similar beliefs are widespread, this constraint generates rationalization markets, social structures agents c...

We investigate methods of coding for a channel subject to a large dead-time constraint, i.e., a constraint on the minimum spacing between transmitted pulses, with the deep-space optical channel as the motivating example. Several constrained codes designed to satisfy the dead-time constraint are considered and compared on the basis of throughput, complexity, and decoded error rate. The performan...

The Job-Shop Scheduling Problem (JSSP) deals with the allocation of resources over time to factory operations. Allocations are subject to various constraints (e.g., production precedence relationships, factory capacity constraints, and limits on the allowable number of machine setups) which must be satisfied for a schedule to be valid. The identification of constraint violations and the monitor...

A signal restoration problem can be formulated as a leastsquares inversion subject to a constraint that the signal has no more than k piecewise monotonic segments. We refer to the associated constraint as controlled piecewise monotonicity or CPM. We show that this constraint alone is powerful enough to stabilize an ill-posed inversion and enables us to incorporate the knowledge about the wavefo...

We present a method for achieving geometrical constraint stabilization for a linear-complementaritybased time-stepping scheme for rigid multibody dynamics with joints, contact, and friction. The method requires the solution of only one linear complementarity problem per step. We prove that the velocity stays bounded and that the constraint infeasibility is uniformly bounded in terms of the size...

Variable-radius circles are common constructs in planar constraint solving and are usually not handled fully by algebraic constraint solvers. We give a complete treatment of variable-radius circles when such a circle must be determined simultaneously with placing two groups of geometric entities. The problem arises for instance in solvers using triangle decomposition to reduce the complexity of...

Many problems in multi-agent systems can be represented as a Distributed Constraint Optimization Problem (DCOP) where the goal is to find the best assignment to variables in order to minimize the cost. More complex problems including several criteria can be represented as a Multi-Objective Distributed Constraint Optimization Problem (MODCOP) where the goal is to optimize several criteria at the...