Polynomial-time algorithm for Maximum Weight Independent Set on P6P_6-free graphs

In the classic Maximum Weight Independent Set problem we are given a graph $G$ with a nonnegative weight function on vertices, and the goal is to find an independent set in $G$ of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any $P_6$-free graph, that is, a graph that has no path on $6$ vertices as an induced subgraph. This improves the polynomial-time algorithm on $P_5$-free graphs of Lokshtanov et al. (SODA 2014), and the quasipolynomial-time algorithm on $P_6$-free graphs of Lokshtanov et al (SODA 2016). The main technical contribution leading to our main result is enumeration of a polynomial-size family $\mathcal{F}$ of vertex subsets with the following property: for every maximal independent set $I$ in the graph, $\mathcal{F}$ contains all maximal cliques of some minimal chordal completion of $G$ that does not add any edge incident to a vertex of $I$

A Flexible Approach to the Multidimensional Model: The Fuzzy Datacube

As a result of the use of OLAP technology in new fields of knowledge and the merge of data from different sources, it has become necessary for models to support this technology. In this paper, we propose a new multidimensional model that can manage imprecision both in dimensions and facts. Consequently, the multidimensional structure is able to model data imprecision resulting from the integration of data from different sources or even information from experts, which it does by means of fuzzy logic

Multi-fuzzy sets and their correspondence to other sets

This paper discusses the properties of multi-fuzzy sets with product order and dictionary order on their membership functions. In particular the relationship between multi-fuzzy sets and other sets such as intuitionistic fuzzy sets, type-2 fuzzy sets, multisets and fuzzy multisets are studied

Magnetic Domains

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.Comment: 42 pages, minor improvements, published versio

Multi-fuzzy sets and their correspondence to other sets

This paper discusses the properties of multi-fuzzy sets with product order and dictionary order on their membership functions. In particular the relationship between multi-fuzzy sets and other sets such as intuitionistic fuzzy sets, type-2 fuzzy sets, multisets and fuzzy multisets are studied