11 research outputs found
Efficient Operations On MDDs For Building Constraint Programming Models
International audienceWe propose improved algorithms for defining the most common operations on Multi-Valued Decision Diagrams (MDDs): creation, reduction, complement , intersection, union, difference, symmetric difference, complement of union and complement of intersection. Then, we show that with these algorithms and thanks to the recent development of an efficient algorithm establishing arc consistency for MDD based constraints (MDD4R), we can simply solve some problems by modeling them as a set of operations between MDDs. We apply our approach to the regular constraint and obtain competitive results with dedicated algorithms. We also experiment our technique on a large scale problem: the phrase generation problem and we show that our approach gives equivalent results to those of a specific algorithm computing a complex automaton
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
BDD-based heuristics for binary optimization
In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems
Το Πρόβλημα του Περιοδεύοντος Πωλητή: Ανάλυση Ερευνητικού Πεδίου, Αλγόριθμοι Επίλυσης και Επιχειρησιακές Εφαρμογές
Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Τεχνο-Οικονομικά Συστήματα (ΜΒΑ)
A Constraint Store Based on Multivalued Decision Diagrams
The typical constraint store transmits a limited amount of
information because it consists only of variable domains. We propose a
richer constraint store in the form of a limited-width multivalued decision
diagram (MDD). It reduces to a traditional domain store when
the maximum width is one but allows greater pruning of the search tree
for larger widths. MDD propagation algorithms can be developed to
exploit the structure of particular constraints, much as is done for domain
filtering algorithms.We propose specialized propagation algorithms
for alldiff and inequality constraints. Preliminary experiments show that
MDD propagation solves multiple alldiff problems an order of magnitude
more rapidly than traditional domain propagation. It also significantly
reduces the search tree for inequality problems, but additional research
is needed to reduce the computation time