A Graph Based Backtracking Algorithm for Solving General CSPs

Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches

Quantified weighted constraint satisfaction problems.

Mak, Wai Keung Terrence.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 100-104).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Weighted Constraint Satisfaction Problems --- p.2Chapter 1.3 --- Quantified Constraint Satisfaction Problems --- p.3Chapter 1.4 --- Motivation and Goal --- p.4Chapter 1.5 --- Outline of the Thesis --- p.6Chapter 2 --- Background --- p.7Chapter 2.1 --- Constraint Satisfaction Problems --- p.7Chapter 2.1.1 --- Backtracking Tree Search --- p.9Chapter 2.1.2 --- Local Consistencies for solving CSPs --- p.11Node Consistency (NC) --- p.13Arc Consistency (AC) --- p.14Searching by Maintaining Arc Consistency --- p.16Chapter 2.1.3 --- Constraint Optimization Problems --- p.17Chapter 2.2 --- Weighted Constraint Satisfaction Problems --- p.19Chapter 2.2.1 --- Branch and Bound Search (B&B) --- p.23Chapter 2.2.2 --- Local Consistencies for WCSPs --- p.25Node Consistency --- p.26Arc Consistency --- p.28Chapter 2.3 --- Quantified Constraint Satisfaction Problems --- p.32Chapter 2.3.1 --- Backtracking Free search --- p.37Chapter 2.3.2 --- Consistencies for QCSPs --- p.38Chapter 2.3.3 --- Look Ahead for QCSPs --- p.45Chapter 3 --- Quantified Weighted CSPs --- p.48Chapter 4 --- Branch & Bound with Consistency Techniques --- p.54Chapter 4.1 --- Alpha-Beta Pruning --- p.54Chapter 4.2 --- Consistency Techniques --- p.57Chapter 4.2.1 --- Node Consistency --- p.62Overview --- p.62Lower Bound of A-Cost --- p.62Upper Bound of A-Cost --- p.66Projecting Unary Costs to Cθ --- p.67Chapter 4.2.2 --- Enforcing Algorithm for NC --- p.68Projection Phase --- p.69Pruning Phase --- p.69Time Complexity --- p.71Chapter 4.2.3 --- Arc Consistency --- p.73Overview --- p.73Lower Bound of A-Cost --- p.73Upper Bound of A-Cost --- p.75Projecting Binary Costs to Unary Constraint --- p.75Chapter 4.2.4 --- Enforcing Algorithm for AC --- p.76Projection Phase --- p.77Pruning Phase --- p.77Time complexity --- p.79Chapter 5 --- Performance Evaluation --- p.83Chapter 5.1 --- Definitions of QCOP/QCOP+ --- p.83Chapter 5.2 --- Transforming QWCSPs into QCOPs --- p.90Chapter 5.3 --- Empirical Evaluation --- p.91Chapter 5.3.1 --- Random Generated Problems --- p.92Chapter 5.3.2 --- Graph Coloring Game --- p.92Chapter 5.3.3 --- Min-Max Resource Allocation Problem --- p.93Chapter 5.3.4 --- Value Ordering Heuristics --- p.94Chapter 6 --- Concluding Remarks --- p.96Chapter 6.1 --- Contributions --- p.96Chapter 6.2 --- Limitations and Related Works --- p.97Chapter 6.3 --- Future Works --- p.99Bibliography --- p.10