. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Physically-based modeling has been used in the past to support a variety of interactive modeling tasks including free-form surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which the system responds subject to the active constraints. In the past, this kind of interaction has been applicable only to models that are governed by continuous parameters. In this paper we present an extension to mixed continuous /discrete models, emphasizing constrained layout problems that arise in architecture and other domains. When the object being dragged is blocked from further motion by geometric constraints, a local discrete search is triggered, during which transformations such as swapping of adjacent objects may be performed. The result of the search is a "nearby" state in which the target object has been moved in the indicated direction and in which all constraints are satisfied. ...