On Matrices, Automata, and Double Counting

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances

Revisiting the tree Constraint

International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning

Estimating the Number of Solutions of Cardinality Constraints through range and roots Decompositions

International audienceThis paper introduces a systematic approach for estimating the number of solutions of cardinality constraints. A main difficulty of solutions counting on a specific constraint lies in the fact that it is, in general, at least as hard as developing the constraint and its propaga-tors, as it has been shown on alldifferent and gcc constraints. This paper introduces a probabilistic model to systematically estimate the number of solutions on a large family of cardinality constraints including alldifferent, nvalue, atmost, etc. Our approach is based on their decomposition into range and roots, and exhibits a general pattern to derive such estimates based on the edge density of the associated variable-value graph. Our theoretical result is finally implemented within the maxSD search heuristic, that aims at exploring first the area where there are likely more solutions

Marine microbial biodiversity, bioinformatics and biotechnology (M2B3) data reporting and service standards

Contextual data collected concurrently with molecular samples are critical to the use of metagenomics in the fields of marine biodiversity, bioinformatics and biotechnology. We present here Marine Microbial Biodiversity, Bioinformatics and Biotechnology (M2B3) standards for “Reporting” and “Serving” data. The M2B3 Reporting Standard (1) describes minimal mandatory and recommended contextual information for a marine microbial sample obtained in the epipelagic zone, (2) includes meaningful information for researchers in the oceanographic, biodiversity and molecular disciplines, and (3) can easily be adopted by any marine laboratory with minimum sampling resources. The M2B3 Service Standard defines a software interface through which these data can be discovered and explored in data repositories. The M2B3 Standards were developed by the European project Micro B3, funded under 7th Framework Programme “Ocean of Tomorrow”, and were first used with the Ocean Sampling Day initiative. We believe that these standards have value in broader marine science

Combining Symmetry Breaking and Global Constraints

Abstract. We propose a new family of constraints which combine together lexicographical ordering constraints for symmetry breaking with other common global constraints. We give a general purpose propagator for this family of constraints, and show how to improve its complexity by exploiting properties of the included global constraints.