6,294 research outputs found
The complexity of global cardinality constraints
In a constraint satisfaction problem (CSP) the goal is to find an assignment
of a given set of variables subject to specified constraints. A global
cardinality constraint is an additional requirement that prescribes how many
variables must be assigned a certain value. We study the complexity of the
problem CCSP(G), the constraint satisfaction problem with global cardinality
constraints that allows only relations from the set G. The main result of this
paper characterizes sets G that give rise to problems solvable in polynomial
time, and states that the remaining such problems are NP-complete
Constraint satisfaction parameterized by solution size
In the constraint satisfaction problem (CSP) corresponding to a constraint
language (i.e., a set of relations) , the goal is to find an assignment
of values to variables so that a given set of constraints specified by
relations from is satisfied. The complexity of this problem has
received substantial amount of attention in the past decade. In this paper we
study the fixed-parameter tractability of constraint satisfaction problems
parameterized by the size of the solution in the following sense: one of the
possible values, say 0, is "free," and the number of variables allowed to take
other, "expensive," values is restricted. A size constraint requires that
exactly variables take nonzero values. We also study a more refined version
of this restriction: a global cardinality constraint prescribes how many
variables have to be assigned each particular value. We study the parameterized
complexity of these types of CSPs where the parameter is the required number
of nonzero variables. As special cases, we can obtain natural and
well-studied parameterized problems such as Independent Set, Vertex Cover,
d-Hitting Set, Biclique, etc.
In the case of constraint languages closed under substitution of constants,
we give a complete characterization of the fixed-parameter tractable cases of
CSPs with size constraints, and we show that all the remaining problems are
W[1]-hard. For CSPs with cardinality constraints, we obtain a similar
classification, but for some of the problems we are only able to show that they
are Biclique-hard. The exact parameterized complexity of the Biclique problem
is a notorious open problem, although it is believed to be W[1]-hard.Comment: To appear in SICOMP. Conference version in ICALP 201
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
Tractable Combinations of Global Constraints
We study the complexity of constraint satisfaction problems involving global
constraints, i.e., special-purpose constraints provided by a solver and
represented implicitly by a parametrised algorithm. Such constraints are widely
used; indeed, they are one of the key reasons for the success of constraint
programming in solving real-world problems.
Previous work has focused on the development of efficient propagators for
individual constraints. In this paper, we identify a new tractable class of
constraint problems involving global constraints of unbounded arity. To do so,
we combine structural restrictions with the observation that some important
types of global constraint do not distinguish between large classes of
equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text
overlap with arXiv:1307.179
On Global Warming (Softening Global Constraints)
We describe soft versions of the global cardinality constraint and the
regular constraint, with efficient filtering algorithms maintaining domain
consistency. For both constraints, the softening is achieved by augmenting the
underlying graph. The softened constraints can be used to extend the
meta-constraint framework for over-constrained problems proposed by Petit,
Regin and Bessiere.Comment: 15 pages, 7 figures. Accepted at the 6th International Workshop on
Preferences and Soft Constraint
Assigning Satisfaction Values to Constraints: An Algorithm to Solve Dynamic Meta-Constraints
The model of Dynamic Meta-Constraints has special activity constraints which
can activate other constraints. It also has meta-constraints which range over
other constraints. An algorithm is presented in which constraints can be
assigned one of five different satisfaction values, which leads to the
assignment of domain values to the variables in the CSP. An outline of the
model and the algorithm is presented, followed by some initial results for two
problems: a simple classic CSP and the Car Configuration Problem. The algorithm
is shown to perform few backtracks per solution, but to have overheads in the
form of historical records required for the implementation of state.Comment: 11 pages. Proceedings ERCIM WG on Constraints (Prague, June 2001
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