. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...

The D-Algorithm (DALG) is shown to be ineffective for the class of combinational logic circuits that is used to implement Error Correction and Translation (ECAT) functions. PODEM (Path-Oriented Decision Making) is a new test generation algorithm for combinational logic circuits. PODEM uses an implicit enumeration approach analogous to that used for solving 0- 1 integer programming problems. It is shown that PODEM is very efficient for ECAT circuits and is significantly more efficient than DALC over the general spectrum of combinational logic circuits. A distinctive feature of PODEM is its simplicity when compared to the D-Algorithm. PODEM is a complete algorithm in that it will generate a test if one exists. Heuristics are used to achieve an efficient implicit search of the space of all possible primary input patterns until either a test is found or the space is exhausted.

. 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...

Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,

Finding optimal solutions for multi-unit combinatorial auctions is a hard problem and nding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from above the value of the best allocation and a good criterion to decide which bids are to be tried rst. Dierent methods for eciently bounding from above the value of the best allocation are considered. Theoretical original results characterize the best approximation ratio and the ordering criterion that provides it. We suggest to use this criterion. Keywords Combinatorial Auctions, Branch and Bound 1. MULTI-UNIT COMBINATORIAL AUCTIONS (MUCAS) Auctions have been used from times immemorial, but the renewed modern interest in auctions stems from: their increased use for selling o government property after WWII and later in extensive denationalizations, and the theoretical breakthroughs started by [14]. A very recent surge of interest in aucti...

The problem of allocating the data of a database to the sites of a communication network is investigated. This problem deviates from the well-known file allocation problem in several aspects. First, the objects to be allocated are not known a priori; second, these objects are accessed by schedules that contain transmissions between objects to produce the result. A model that makes it possible to compare the cost of allocations is presented, the cost can be computed for different cost functions and for processing schedules produced by arbitrary query processing algorithms. For minimizing the total transmission cost, a method is proposed to determine the fragments to be allocated from the relations in the conceptual schema and the queries and updates executed by the users. For the same cost function, the complexity of the data allocation problem is investigated. Methods for obtaining optimal and heuristic solutions under various ways of computing the cost of an allocation are presented and compared. Two different approaches to the allocation management problem are presented and their merits are discussed.

We consider the effects of parallelizing branch-and-bound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branch-and-bound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermore, it is also possible to achieve speedups that are in excess of the ratio n 2 /n 1 . Experimental results with the 0/1-Knapsack and Traveling Salesperson problems are also presented.

This paper presents many different parallel formulations of the A*/Branch-and-Bound search algorithm. The parallel formulations primarily differ in the data structures used. Some formulations are suited only for shared-memory architectures, whereas others are suited for distributedmemory architectures as well. These parallel formulations have been implemented to solve the vertex cover problem and the TSP problem on the BBN Butterfly parallel processor. Using appropriate data structures, we are able to obtain fairly linear speedups for as many as 100 processors. We also discovered problem characteristics that make certain formulations more (or less) suitable for some search problems. Since the bestfirst search paradigm of A*/Branch-and-Bound is very commonly used, we expect these parallel formulations to be effective for a variety of problems. Concurrent and distributed priority queues used in these parallel formulations can be used in many parallel algorithms other than parallel A*/bra...

We consider the joint optimal design of the physical, medium access control (MAC), and routing layers to maximize the lifetime of energy-constrained wireless sensor networks. The problem of computing lifetime-optimal routing flow, link schedule, and link transmission powers for all active time slots is formulated as a non-linear optimization problem. We first restrict the link schedules to the class of interference-free time division multiple access (TDMA) schedules. In this special case, we formulate the optimization problem as a mixed integerconvex program, which can be solved using standard techniques. Moreover, when the slots lengths are variable, the optimization problem is convex and can be solved efficiently and exactly using interior point methods. For general non-orthogonal link schedules, we propose an iterative algorithm that alternates between adaptive link scheduling and computation of optimal link rates and transmission powers for a fixed link schedule. The performance of this algorithm is compared to other design approaches for several network topologies. The results illustrate the advantages of load balancing, multihop routing, frequency reuse, and interference mitigation in increasing the lifetime of energy-constrained networks. We also briefly discuss computational approaches to extend this algorithm to large networks.

This paper reports a Fast Local Search (FLS) algorithm which helps to improve the efficiency of hill climbing and a Guided Local Search (GLS) Algorithm which is developed to help local search to escape local optima and distribute search effort. To illustrate how these algorithms work, this paper describes their application to British Telecom's workforce scheduling problem, which is a hard real life problem. The effectiveness of FLS and GLS are demonstrated by the fact that they both out-perform all the methods applied to this problem so far, which include simulated annealing, genetic algorithms and constraint logic programming. I. Introduction Due to their combinatorial explosion nature, many real life constraint optimization problems are hard to solve using complete methods such as branch & bound [17, 14, 21, 23]. One way to contain the combinatorial explosion problem is to sacrifice completeness. Some of the best known methods which use this strategy are local search methods, the ba...