35,334 research outputs found
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
Tractable Optimization Problems through Hypergraph-Based Structural Restrictions
Several variants of the Constraint Satisfaction Problem have been proposed
and investigated in the literature for modelling those scenarios where
solutions are associated with some given costs. Within these frameworks
computing an optimal solution is an NP-hard problem in general; yet, when
restricted over classes of instances whose constraint interactions can be
modelled via (nearly-)acyclic graphs, this problem is known to be solvable in
polynomial time. In this paper, larger classes of tractable instances are
singled out, by discussing solution approaches based on exploiting hypergraph
acyclicity and, more generally, structural decomposition methods, such as
(hyper)tree decompositions
A CHR-based Implementation of Known Arc-Consistency
In classical CLP(FD) systems, domains of variables are completely known at
the beginning of the constraint propagation process. However, in systems
interacting with an external environment, acquiring the whole domains of
variables before the beginning of constraint propagation may cause waste of
computation time, or even obsolescence of the acquired data at the time of use.
For such cases, the Interactive Constraint Satisfaction Problem (ICSP) model
has been proposed as an extension of the CSP model, to make it possible to
start constraint propagation even when domains are not fully known, performing
acquisition of domain elements only when necessary, and without the need for
restarting the propagation after every acquisition.
In this paper, we show how a solver for the two sorted CLP language, defined
in previous work, to express ICSPs, has been implemented in the Constraint
Handling Rules (CHR) language, a declarative language particularly suitable for
high level implementation of constraint solvers.Comment: 22 pages, 2 figures, 1 table To appear in Theory and Practice of
Logic Programming (TPLP
Constraint Design Rewriting
We propose an algebraic approach to the design and transformation of constraint networks, inspired by Architectural Design Rewriting. The approach can be understood as (i) an extension of ADR with constraints, and (ii) an application of ADR to the design of reconfigurable constraint networks. The main idea is to consider classes of constraint networks as algebras whose operators are used to denote constraint networks with terms. Constraint network transformations such as constraint propagations are specified with rewrite rules exploiting the network’s structure provided by terms
A Mining-Based Compression Approach for Constraint Satisfaction Problems
In this paper, we propose an extension of our Mining for SAT framework to
Constraint satisfaction Problem (CSP). We consider n-ary extensional
constraints (table constraints). Our approach aims to reduce the size of the
CSP by exploiting the structure of the constraints graph and of its associated
microstructure. More precisely, we apply itemset mining techniques to search
for closed frequent itemsets on these two representation. Using Tseitin
extension, we rewrite the whole CSP to another compressed CSP equivalent with
respect to satisfiability. Our approach contrast with previous proposed
approach by Katsirelos and Walsh, as we do not change the structure of the
constraints.Comment: arXiv admin note: substantial text overlap with arXiv:1304.441
Constraint-based Sequential Pattern Mining with Decision Diagrams
Constrained sequential pattern mining aims at identifying frequent patterns
on a sequential database of items while observing constraints defined over the
item attributes. We introduce novel techniques for constraint-based sequential
pattern mining that rely on a multi-valued decision diagram representation of
the database. Specifically, our representation can accommodate multiple item
attributes and various constraint types, including a number of non-monotone
constraints. To evaluate the applicability of our approach, we develop an
MDD-based prefix-projection algorithm and compare its performance against a
typical generate-and-check variant, as well as a state-of-the-art
constraint-based sequential pattern mining algorithm. Results show that our
approach is competitive with or superior to these other methods in terms of
scalability and efficiency.Comment: AAAI201
A Partial Taxonomy of Substitutability and Interchangeability
Substitutability, interchangeability and related concepts in Constraint
Programming were introduced approximately twenty years ago and have given rise
to considerable subsequent research. We survey this work, classify, and relate
the different concepts, and indicate directions for future work, in particular
with respect to making connections with research into symmetry breaking. This
paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint
Satisfaction Problems (SymCon'10
Symmetries in planning problems
Symmetries arise in planning in a variety of ways. This paper describes the ways that symmetry aises most naturally in planning problems and reviews the approaches that have been applied to exploitation of symmetry in order to reduce search for plans. It then introduces some extensions to the use of symmetry in planning before moving on to consider how the exploitation of symmetry in planning might be generalised to offer new approaches to exploitation of symmetry in other combinatorial search problems
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