Recognizing Chordal-Bipartite Probe Graphs

A graph G is chordal-bipartite probe if its vertices can be partitioned into two sets P (probes) and N (non-probes) where N is a stable set and such that G can be extended to a chordal-bipartite graph by adding edges between non-probes. A bipartite graph is called chordal-bipartite if it contains no chordless cycle of length strictly greater than 5. Such probe/non-probe completion problems have been studied previously on other families of graphs, such as interval graphs and chordal graphs. In this paper, we give a characterization of chordal-bipartite probe graphs, in the case of a fixed given partition of the vertices into probes and nonprobes. Our results are obtained by solving first the more general case without assuming that N is a stable set, and then this can be applied to the more specific case. Our characterization uses an edge elimination ordering which also implies a polynomial time recognition algorithm for the class. This research was conducted in the context of a France-Israel Binational project, while the French team visited Haifa in March 2007

Parameterized Domination in Circle Graphs

A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs. To the best of our knowledge, nothing was known about the parameterized complexity of these problems in circle graphs. In this paper we prove the following results, which contribute in this direction: Dominating Set, Independent Dominating Set, Connected Dominating Set, Total Dominating Set, and Acyclic Dominating Set are W[1]-hard in circle graphs, parameterized by the size of the solution. Whereas both Connected Dominating Set and Acyclic Dominating Set are W[1]-hard in circle graphs, it turns out that Connected Acyclic Dominating Set is polynomial-time solvable in circle graphs. If T is a given tree, deciding whether a circle graph has a dominating set isomorphic to T is NP-complete when T is in the input, and FPT when parameterized by |V(T)|. We prove that the FPT algorithm is subexponential

High gamma oscillations in medial temporal lobe during overt production of speech and gestures

The study of the production of co-speech gestures (CSGs), i.e., meaningful hand movements that often accompany speech during everyday discourse, provides an important opportunity to investigate the integration of language, action, and memory because of the semantic overlap between gesture movements and speech content. Behavioral studies of CSGs and speech suggest that they have a common base in memory and predict that overt production of both speech and CSGs would be preceded by neural activity related to memory processes. However, to date the neural correlates and timing of CSG production are still largely unknown. In the current study, we addressed these questions with magnetoencephalography and a semantic association paradigm in which participants overtly produced speech or gesture responses that were either meaningfully related to a stimulus or not. Using spectral and beamforming analyses to investigate the neural activity preceding the responses, we found a desynchronization in the beta band (15-25 Hz), which originated 900 ms prior to the onset of speech and was localized to motor and somatosensory regions in the cortex and cerebellum, as well as right inferior frontal gyrus. Beta desynchronization is often seen as an indicator of motor processing and thus reflects motor activity related to the hand movements that gestures add to speech. Furthermore, our results show oscillations in the high gamma band (50-90 Hz), which originated 400 ms prior to speech onset and were localized to the left medial temporal lobe. High gamma oscillations have previously been found to be involved in memory processes and we thus interpret them to be related to contextual association of semantic information in memory. The results of our study show that high gamma oscillations in medial temporal cortex play an important role in the binding of information in human memory during speech and CSG production

Caracterisation des graphes chaines-completables

National audienc

A characterization of chain probe graphs

International audienceA chain probe graph is a graph that admits an independent set $S$ of vertices and a set $F$ of pairs of elements of $S$ such that $G+F$ is a chain graph (i.e., a $2K_2$-free bipartite graph). We show that chain probe graphs are exactly the bipartite graphs that do not contain as an induced subgraph a member of a family of six forbidden subgraphs, and deduce an $O(n^2)$ recognition algorithm

Factoring and Recognition of Read-Once Functions using Cographs and Normality

An approach for factoring general boolean functions was described in [5] which is based on graph partitioning algorithms. In this paper, we presentavery fast algorithm for recognizing and factoring read-once functions which is needed as a dedicated factoring subroutine to handle the lower levels of that factoring process. The algorithm is based on algorithms for cograph recognition and on checking normality. Our method has been implemented in the SIS environment, and an empirical evaluation is given