Bounded Search Tree Algorithms for Parameterized Cograph Deletion: Efficient Branching Rules by Exploiting Structures of Special Graph Classes

Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general search strategy that branches on the forbidden subgraphs of a graph class relaxation. By using the class of $P_4$-sparse graphs as the relaxed graph class, we obtain efficient bounded search tree algorithms for several parameterized deletion problems. We give the first non-trivial bounded search tree algorithms for the cograph edge-deletion problem and the trivially perfect edge-deletion problems. For the cograph vertex deletion problem, a refined analysis of the runtime of our simple bounded search algorithm gives a faster exponential factor than those algorithms designed with the help of complicated case distinctions and non-trivial running time analysis [21] and computer-aided branching rules [11].Comment: 23 pages. Accepted in Discrete Mathematics, Algorithms and Applications (DMAA

A Replica Inference Approach to Unsupervised Multi-Scale Image Segmentation

We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters ("communities" or "solutes") against a background or "solvent". Within our multiresolution approach, we compute information theory based correlations among multiple solutions ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations as manifest in information theory overlaps. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed both at zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentation correspond to the "easy phase" of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images.Comment: 26 pages, 22 figure

Linear-Time Recognition of Double-Threshold Graphs

A graph G=(V, E) is a double-threshold graph if there exist a vertex-weight function w:V→ℝ and two real numbers lb, ub ∈ ℝ such that uv ∈ E if and only if lb ≤ w(u)+w(v) ≤ ub. In the literature, those graphs are studied also as the pairwise compatibility graphs that have stars as their underlying trees. We give a new characterization of double-threshold graphs that relates them to bipartite permutation graphs. Using the new characterization, we present a linear-time algorithm for recognizing double-threshold graphs. Prior to our work, the fastest known algorithm by Xiao and Nagamochi [Algorithmica 2020] ran in O(n³ m) time, where n and m are the numbers of vertices and edges, respectively

Monotonic Stable Solutions for Minimum Coloring Games

For the class of minimum coloring games (introduced by Deng et al. (1999)) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont (1990)). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4, 2K2)-free (or, equivalently, if its complement graph G is quasi-threshold). Moreover, we provide a procedure that for these graphs always selects an integer population monotonic allocation scheme.Minimum coloring game;population monotonic allocation scheme;(P4;2K2)-free graph;quasi-threshold graph

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

Near infrared flares of Sagittarius A*: Importance of near infrared polarimetry

We report on the results of new simulations of near-infrared (NIR) observations of the Sagittarius A* (Sgr A*) counterpart associated with the super-massive black hole at the Galactic Center. The observations have been carried out using the NACO adaptive optics (AO) instrument at the European Southern Observatory's Very Large Telescope and CIAO NIR camera on the Subaru telescope (13 June 2004, 30 July 2005, 1 June 2006, 15 May 2007, 17 May 2007 and 28 May 2008). We used a model of synchrotron emission from relativistic electrons in the inner parts of an accretion disk. The relativistic simulations have been carried out using the Karas-Yaqoob (KY) ray-tracing code. We probe the existence of a correlation between the modulations of the observed flux density light curves and changes in polarimetric data. Furthermore, we confirm that the same correlation is also predicted by the hot spot model. Correlations between intensity and polarimetric parameters of the observed light curves as well as a comparison of predicted and observed light curve features through a pattern recognition algorithm result in the detection of a signature of orbiting matter under the influence of strong gravity. This pattern is detected statistically significant against randomly polarized red noise. Expected results from future observations of VLT interferometry like GRAVITY experiment are also discussed.Comment: 26 pages, 38 figures, accepted for publication by A&