Olivier Raynaud

Counting of moore families for n=7

Given a set Un={0,1,...,n−1}, a collection

Interactive association rules discovery

\mathcal{M}

Building FCA-Based Decision Trees for the Selection of Heterogeneous Services

of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a given n, denoted by Mn, increases very quickly with n, thus |M3| is 61 and |M4| is 2480. In [1] the authors determined the number for n=6 and stated a 24h- computation-time. Thus, the number for n=7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for n=7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.

A Quasi Optimal Bit-Vector Encoding of Tree Hierarchies. Application to Efficient Type Inclusion Tests

An interactive discovery method for finding association rules is presented. It consists in a user-guided search using reduction operators on a rule. Rules are generated on-demand according to the navigation made by the user. Main interest of this approach is that, at each step, the user has only a linear number of new rules to analyze and that all computations are done in polynomial time. Several reduction operators are presented. We also show that the search space can be reduced when clone items are present.

Recursive decomposition and bounds of the lattice of Moore co-families

Late-binding and substitutability offered by the service-oriented approach improve adaptability but increase the need for fast and efficient algorithms to select services. In this paper, we proposed to use the Formal Concept Analysis (FCA) approach as a classification tool to select services at runtime, according to user specifications. We propose to classify existing services and generate a decision tree to help user select the most appropriate service(s). One of advantages of using FCA is the ability to select without additional cost an equivalent service in the case of a service must be replaced at runtime. Our approach have been implemented and validated on pervasive use cases within a European collaborative project.

Generalized Polychotomic Encoding: A Very Short Bit-Vector Encoding of Tree Hierarchies

Type inclusion tests consist in determining whether a type is a subtype of another. An efficient implementation of type inclusion is an important feature of object oriented programming languages.A well-known method to achieve these tests is to associate to each type a subset of a set S = {1, . . . , k} such that type inclusion coincides with subset inclusion. Such an embedding of types into 2S (the lattice of all subsets of S) is called a bit-vector encoding of the type hierarchy. These encodings are known for several interesting features. Bit-vector encodings are perfectly appropriate for hierarchies with single subtyping as well as hierarchies with multiple subtyping. Subset inclusion tests can be performed very efficiently.Several works have studied bit-vector encodings froma theoretical point of view ([6, 7, 10, 14, 16, 18, 19]) and froma practical point of view ([3, 8, 9, 17]), in particular in order to minimize the size of the encoding, i.e. the size of S.In this article, we present a new algorithmw hich computes bit-vector encodings for single subtyping hierarchies, also called tree hierarchies.Our algorithm is simple, it computes the bit-vector encoding very quickly and gives good results for the size of the encoding. In particular, we have significantly improved the best bounds known for the encoding sizes of some benchmarks presented in [9].

Twin Vertices in Hypergraphs

A collection of sets on a ground set Un (Un = {1,2,...,n}) closed under intersection and containing Un is known as a Moore family. The set of Moore families for a fixed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted

Algorithms for a Bit-Vector Encoding of Trees

\mathbb{M}_n

Encoding partial orders through modular decomposition

. In this paper, we propose a recursive definition of the set of Moore co-families on Un. Then we apply this decomposition result to compute a lower bound on

Am I Really Who I Claim to Be

|\mathbb M_n|