On the number of maximal independent sets in a graph

Miller and Muller (1960) and independently Moon and Moser (1965) determined the maximum number of maximal independent sets in an $n$-vertex graph. We give a new and simple proof of this result

Enumerating maximal cliques in link streams with durations

Link streams model interactions over time, and a clique in a link stream is defined as a set of nodes and a time interval such that all pairs of nodes in this set interact permanently during this time interval. This notion was introduced recently in the case where interactions are instantaneous. We generalize it to the case of interactions with durations and show that the instantaneous case actually is a particular case of the case with durations. We propose an algorithm to detect maximal cliques that improves our previous one for instantaneous link streams, and performs better than the state of the art algorithms in several cases of interest

An Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths

A chordless cycle (induced cycle) $C$ of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the problems of enumerating chordless cycles/paths of a given graph $G=(V,E),$ and propose algorithms taking $O(|E|)$ time for each chordless cycle/path. In the existing studies, the problems had not been deeply studied in the theoretical computer science area, and no output polynomial time algorithm has been proposed. Our experiments showed that the computation time of our algorithms is constant per chordless cycle/path for non-dense random graphs and real-world graphs. They also show that the number of chordless cycles is much smaller than the number of cycles. We applied the algorithm to prediction of NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the prediction

Computing maximal cliques in link streams

A link stream is a collection of triplets $(t, u, v)$ indicating that an interaction occurred between u and v at time t. We generalize the classical notion of cliques in graphs to such link streams: for a given $\Delta$, a $\Delta$-clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least once during each sub-interval of duration $\Delta$. We propose an algorithm to enumerate all maximal (in terms of nodes or time interval) cliques of a link stream, and illustrate its practical relevance on a real-world contact trace

Co-location rules discovery process focused on reference spatial features using decision tree learning

The co-location discovery process serves to find subsets of spatial features frequently located together. Many algorithms and methods have been designed in recent years; however, finding this kind of patterns around specific spatial features is a task in which the existing solutions provide incorrect results. Throughout this paper we propose a knowledge discovery process to find co-location patterns focused on reference features using decision tree learning algorithms on transactional data generated using maximal cliques. A validation test of this process is provided.Fil: Merlino, Hernán Daniel. Universidad Nacional de Lanús; Argentina.Fil: Rottoli, Giovanni Daián. Universidad Tecnológica Nacional.Facultad Regional Concepción del Uruguay. Departamento Ingeniería en Sistemas de Información. Grupo de Investigación en Bases de Datos; Argentina.Fil: Rottoli, Giovanni Daián. Universidad Nacional de La Plata; Argentina.Fil: Rottoli, Giovanni Daián. Universidad Nacional de Lanús; Argentina.Fil: García Martínez, Ramón. Universidad Nacional de Lanús. Departamento Desarrollo Productivo y Tecnológico. Grupo de Investigación en Sistemas de Información; Argentina.Fil: García Martínez, Ramón. Comisión de Investigaciones Científicas; Argentina.Peer Reviewe