390 research outputs found
Constraint Programming Algorithms for Route Planning Exploiting Geometrical Information
Problems affecting the transport of people or goods are plentiful in industry
and commerce and they also appear to be at the origin of much more complex
problems. In recent years, the logistics and transport sector keeps growing
supported by technological progress, i.e. companies to be competitive are
resorting to innovative technologies aimed at efficiency and effectiveness.
This is why companies are increasingly using technologies such as Artificial
Intelligence (AI), Blockchain and Internet of Things (IoT). Artificial
intelligence, in particular, is often used to solve optimization problems in
order to provide users with the most efficient ways to exploit available
resources. In this work we present an overview of our current research
activities concerning the development of new algorithms, based on CLP
techniques, for route planning problems exploiting the geometric information
intrinsically present in many of them or in some of their variants. The
research so far has focused in particular on the Euclidean Traveling
Salesperson Problem (Euclidean TSP) with the aim to exploit the results
obtained also to other problems of the same category, such as the Euclidean
Vehicle Routing Problem (Euclidean VRP), in the future.Comment: In Proceedings ICLP 2020, arXiv:2009.0915
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming
The NP-hard general factor problem asks, given a graph and for each vertex a
list of integers, whether the graph has a spanning subgraph where each vertex
has a degree that belongs to its assigned list. The problem remains NP-hard
even if the given graph is bipartite with partition U+V, and each vertex in U
is assigned the list {1}; this subproblem appears in the context of constraint
programming as the consistency problem for the extended global cardinality
constraint. We show that this subproblem is fixed-parameter tractable when
parameterized by the size of the second partite set V. More generally, we show
that the general factor problem for bipartite graphs, parameterized by |V|, is
fixed-parameter tractable as long as all vertices in U are assigned lists of
length 1, but becomes W[1]-hard if vertices in U are assigned lists of length
at most 2. We establish fixed-parameter tractability by reducing the problem
instance to a bounded number of acyclic instances, each of which can be solved
in polynomial time by dynamic programming.Comment: Full version of a paper that appeared in preliminary form in the
proceedings of IPEC'1
Improved filtering for the Euclidean Traveling Salesperson Problem in CLP(FD)
The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. The Euclidean TSP is a special case in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. Many works in the Constraint Programming (CP) literature addressed the TSP, and use as benchmark Euclidean instances; however the usual approach is to build a distance matrix from the points coordinates, and then address the problem as a TSP, disregarding the information carried by the points coordinates for constraint propagation. In this work, we propose to use geometric information, present in Euclidean TSP instances, to improve the filtering power. In order to have a declarative approach, we implemented the filtering algorithms in Constraint Logic Programming on Finite Domains (CLP(FD))
Quantified Constraints in Twenty Seventeen
I present a survey of recent advances in the algorithmic and computational complexity theory of non-Boolean Quantified Constraint Satisfaction Problems, incorporating some more modern research directions
On the Subexponential Time Complexity of CSP
A CSP with n variables ranging over a domain of d values can be solved by
brute-force in d^n steps (omitting a polynomial factor). With a more careful
approach, this trivial upper bound can be improved for certain natural
restrictions of the CSP. In this paper we establish theoretical limits to such
improvements, and draw a detailed landscape of the subexponential-time
complexity of CSP.
We first establish relations between the subexponential-time complexity of
CSP and that of other problems, including CNF-Sat. We exploit this connection
to provide tight characterizations of the subexponential-time complexity of CSP
under common assumptions in complexity theory. For several natural CSP
parameters, we obtain threshold functions that precisely dictate the
subexponential-time complexity of CSP with respect to the parameters under
consideration.
Our analysis provides fundamental results indicating whether and when one can
significantly improve on the brute-force search approach for solving CSP
Generating Random Logic Programs Using Constraint Programming
Testing algorithms across a wide range of problem instances is crucial to
ensure the validity of any claim about one algorithm's superiority over
another. However, when it comes to inference algorithms for probabilistic logic
programs, experimental evaluations are limited to only a few programs. Existing
methods to generate random logic programs are limited to propositional programs
and often impose stringent syntactic restrictions. We present a novel approach
to generating random logic programs and random probabilistic logic programs
using constraint programming, introducing a new constraint to control the
independence structure of the underlying probability distribution. We also
provide a combinatorial argument for the correctness of the model, show how the
model scales with parameter values, and use the model to compare probabilistic
inference algorithms across a range of synthetic problems. Our model allows
inference algorithm developers to evaluate and compare the algorithms across a
wide range of instances, providing a detailed picture of their (comparative)
strengths and weaknesses.Comment: This is an extended version of the paper published in CP 202
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