scholarly journals On Hyper-Chordal graphs

2021 ◽  
Vol 37 (1) ◽  
pp. 119-126
Author(s):  
MIHAI TALMACIU
Keyword(s):  
Combinatorial Optimization ◽  
Linear Complexity ◽  
Optimization Algorithms ◽  
Recognition Algorithm ◽  
Chordal Graphs ◽  
Induced Subgraph ◽  
Recognition Algorithms ◽  
Triangulated Graphs ◽  
Triangulated Graph

Triangulated graphs have many interesting properties (perfection, recognition algorithms, combinatorial optimization algorithms with linear complexity). Hyper-triangulated graphs are those where each induced subgraph has a hyper-simplicial vertex. In this paper we give the characterizations of hyper-triangulated graphs using an ordering of vertices and the weak decomposition. We also offer a recognition algorithm for the hyper-triangulated graphs, the inclusions between the triangulated graphs generalizations and we show that any hyper-triangulated graph is perfect.

Linear layouts of weakly triangulated graphs

2016 ◽  
Vol 08 (03) ◽  
pp. 1650038 ◽  
Author(s):  
Asish Mukhopadhyay ◽  
S. V. Rao ◽  
Sidharth Pardeshi ◽  
Srinivas Gundlapalli
Keyword(s):  
Time Algorithm ◽  
Chordal Graphs ◽  
Sparse Graphs ◽  
Interesting Connection ◽  
Triangulated Graphs ◽  
Distance Data ◽  
Point Placement ◽  
Appl Math ◽  
Block Tree ◽  
Triangulated Graph

A graph [Formula: see text] is said to be triangulated if it has no chordless cycles of length 4 or more. Such a graph is said to be rigid if, for a valid assignment of edge lengths, it has a unique linear layout and non-rigid otherwise. Damaschke [Point placement on the line by distance data, Discrete Appl. Math. 127(1) (2003) 53–62] showed how to compute all linear layouts of a triangulated graph, for a valid assignment of lengths to the edges of [Formula: see text]. In this paper, we extend this result to weakly triangulated graphs, resolving an open problem. A weakly triangulated graph can be constructively characterized by a peripheral ordering of its edges. The main contribution of this paper is to exploit such an edge order to identify the rigid and non-rigid components of [Formula: see text]. We first show that a weakly triangulated graph without articulation points has at most [Formula: see text] different linear layouts, where [Formula: see text] is the number of quadrilaterals (4-cycles) in [Formula: see text]. When [Formula: see text] has articulation points, the number of linear layouts is at most [Formula: see text], where [Formula: see text] is the number of nodes in the block tree of [Formula: see text] and [Formula: see text] is the total number of quadrilaterals over all the blocks. Finally, we propose an algorithm for computing a peripheral edge order of [Formula: see text] by exploiting an interesting connection between this problem and the problem of identifying a two-pair in [Formula: see text]. Using an [Formula: see text] time solution for the latter problem, we propose an [Formula: see text] time algorithm for computing its peripheral edge order, where [Formula: see text] and [Formula: see text] are respectively the number of edges and vertices of [Formula: see text]. For sparse graphs, the time complexity can be improved to [Formula: see text], using the concept of handles [R. B. Hayward, J. P. Spinrad and R. Sritharan, Improved algorithms for weakly chordal graphs, ACM Trans. Algorithms 3(2) (2007) 19pp].

scholarly journals A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 105
Author(s):  
Serafino Cicerone
Keyword(s):  
Polynomial Time ◽  
Detection Algorithm ◽  
Recognition Algorithm ◽  
Forbidden Subgraphs ◽  
Induced Subgraph ◽  
Hole Detection

Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of the well known distance-hereditary graphs, which actually correspond to 1-distance-hereditary graphs. In this paper we make a step forward in the study of these new graphs by providing characterizations for the class of all the k-distance-hereditary graphs such that k<2. The new characterizations are given in terms of both forbidden subgraphs and cycle-chord properties. Such results also lead to devise a polynomial-time recognition algorithm for this kind of graph that, according to the provided characterizations, simply detects the presence of quasi-holes in any given graph.

THE EFFECT OF DIFFERENT OCCUPATIONAL BACKGROUND NOISES ON VOICE RECOGNITION ACCURACY

2022 ◽  
pp. 1-30
Author(s):  
Song Li ◽  
Mustafa Ozkan Yerebakan ◽  
Yue Luo ◽  
Ben Amaba ◽  
William Swope ◽  
...  
Keyword(s):  
Background Noise ◽  
Recognition Accuracy ◽  
Voice Recognition ◽  
Recognition Algorithm ◽  
Control Mechanisms ◽  
Recognition Algorithms ◽  
Significant Performance ◽  
Industrial Productivity ◽  
Overall Performance ◽  
Occupational Background

Abstract Voice recognition has become an integral part of our lives, commonly used in call centers and as part of virtual assistants. However, voice recognition is increasingly applied to more industrial uses. Each of these use cases has unique characteristics that may impact the effectiveness of voice recognition, which could impact industrial productivity, performance, or even safety. One of the most prominent among them is the unique background noises that are dominant in each industry. The existence of different machinery and different work layouts are primary contributors to this. Another important characteristic is the type of communication that is present in these settings. Daily communication often involves longer sentences uttered under relatively silent conditions, whereas communication in industrial settings is often short and conducted in loud conditions. In this study, we demonstrated the importance of taking these two elements into account by comparing the performances of two voice recognition algorithms under several background noise conditions: a regular Convolutional Neural Network (CNN) based voice recognition algorithm to an Auto Speech Recognition (ASR) based model with a denoising module. Our results indicate that there is a significant performance drop between the typical background noise use (white noise) and the rest of the background noises. Also, our custom ASR model with the denoising module outperformed the CNN based model with an overall performance increase between 14-35% across all background noises. . Both results give proof that specialized voice recognition algorithms need to be developed for these environments to reliably deploy them as control mechanisms.

Algorithmic Aspects of Outer-Independent Total Roman Domination in Graphs

2021 ◽  
pp. 1-9
Author(s):  
Amit Sharma ◽  
P. Venkata Subba Reddy
Keyword(s):  
Linear Time ◽  
Domination Number ◽  
Chordal Graphs ◽  
Roman Domination ◽  
Induced Subgraph ◽  
Bounded Treewidth ◽  
Roman Domination Number ◽  
Vertex Set ◽  
Roman Dominating Function ◽  
Domination In Graphs

For a simple, undirected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called an outer-independent total Roman dominating function (OITRDF) of [Formula: see text] with weight [Formula: see text]. (C1) For all [Formula: see text] with [Formula: see text] there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text], (C2) The induced subgraph with vertex set [Formula: see text] has no isolated vertices and (C3) The induced subgraph with vertex set [Formula: see text] is independent. For a graph [Formula: see text], the smallest possible weight of an OITRDF of [Formula: see text] which is denoted by [Formula: see text], is known as the outer-independent total Roman domination number of [Formula: see text]. The problem of determining [Formula: see text] of a graph [Formula: see text] is called minimum outer-independent total Roman domination problem (MOITRDP). In this article, we show that the problem of deciding if [Formula: see text] has an OITRDF of weight at most [Formula: see text] for bipartite graphs and split graphs, a subclass of chordal graphs is NP-complete. We also show that MOITRDP is linear time solvable for connected threshold graphs and bounded treewidth graphs. Finally, we show that the domination and outer-independent total Roman domination problems are not equivalent in computational complexity aspects.

Inductive graph invariants and approximation algorithms

2021 ◽  
Author(s):  
C. R. Subramanian
Keyword(s):  
Optimization Problems ◽  
Independence Number ◽  
Optimal Solution ◽  
Maximum Size ◽  
Chordal Graphs ◽  
Minimum Size ◽  
Optimal Size ◽  
Induced Subgraph ◽  
Special Cases ◽  
Optimal Formula

We introduce and study an inductively defined analogue [Formula: see text] of any increasing graph invariant [Formula: see text]. An invariant [Formula: see text] is increasing if [Formula: see text] whenever [Formula: see text] is an induced subgraph of [Formula: see text]. This inductive analogue simultaneously generalizes and unifies known notions like degeneracy, inductive independence number, etc., into a single generic notion. For any given increasing [Formula: see text], this gets us several new invariants and many of which are also increasing. It is also shown that [Formula: see text] is the minimum (over all orderings) of a value associated with each ordering. We also explore the possibility of computing [Formula: see text] (and a corresponding optimal vertex ordering) and identify some pairs [Formula: see text] for which [Formula: see text] can be computed efficiently for members of [Formula: see text]. In particular, it includes graphs of bounded [Formula: see text] values. Some specific examples (like the class of chordal graphs) have already been studied extensively. We further extend this new notion by (i) allowing vertex weighted graphs, (ii) allowing [Formula: see text] to take values from a totally ordered universe with a minimum and (iii) allowing the consideration of [Formula: see text]-neighborhoods for arbitrary but fixed [Formula: see text]. Such a generalization is employed in designing efficient approximations of some graph optimization problems. Precisely, we obtain efficient algorithms (by generalizing the known algorithm of Ye and Borodin [Y. Ye and A. Borodin, Elimination graphs, ACM Trans. Algorithms 8(2) (2012) 1–23] for special cases) for approximating optimal weighted induced [Formula: see text]-subgraphs and optimal [Formula: see text]-colorings (for hereditary [Formula: see text]’s) within multiplicative factors of (essentially) [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the inductive analogue (as defined in this work) of optimal size of an unweighted induced [Formula: see text]-subgraph of the input and [Formula: see text] is the minimum size of a forbidden induced subgraph of [Formula: see text]. Our results generalize the previous result on efficiently approximating maximum independent sets and minimum colorings on graphs of bounded inductive independence number to optimal [Formula: see text]-subgraphs and [Formula: see text]-colorings for arbitrary hereditary classes [Formula: see text]. As a corollary, it is also shown that any maximal [Formula: see text]-subgraph approximates an optimal solution within a factor of [Formula: see text] for unweighted graphs, where [Formula: see text] is maximum size of any induced [Formula: see text]-subgraph in any local neighborhood [Formula: see text].

scholarly journals On the Robustness of Face Recognition Algorithms Against Attacks and Bias

2020 ◽  
Vol 34 (09) ◽  
pp. 13583-13589
Author(s):  
Richa Singh ◽  
Akshay Agarwal ◽  
Maneet Singh ◽  
Shruti Nagpal ◽  
Mayank Vatsa
Keyword(s):  
Face Recognition ◽  
Recognition Performance ◽  
Recognition Algorithm ◽  
Future Research ◽  
Research Directions ◽  
Recognition Algorithms ◽  
Future Research Directions ◽  
And Gender ◽  
Gender Variations ◽  
Very High

Face recognition algorithms have demonstrated very high recognition performance, suggesting suitability for real world applications. Despite the enhanced accuracies, robustness of these algorithms against attacks and bias has been challenged. This paper summarizes different ways in which the robustness of a face recognition algorithm is challenged, which can severely affect its intended working. Different types of attacks such as physical presentation attacks, disguise/makeup, digital adversarial attacks, and morphing/tampering using GANs have been discussed. We also present a discussion on the effect of bias on face recognition models and showcase that factors such as age and gender variations affect the performance of modern algorithms. The paper also presents the potential reasons for these challenges and some of the future research directions for increasing the robustness of face recognition models.

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