scholarly journals A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 339
Author(s):  
Jonathan Li ◽  
Rohan Potru ◽  
Farhad Shahrokhi
Keyword(s):  
Approximation Algorithms ◽  
Real World ◽  
Hybrid Algorithm ◽  
Dominating Set ◽  
Performance Ratio ◽  
Performance Study ◽  
Similar Time ◽  
Sparse Graphs ◽  
Lp Rounding ◽  
Better Than

We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices.

TWO ALGORITHMS FOR CONNECTED r-HOP k-DOMINATING SET

2009 ◽  
Vol 01 (04) ◽  
pp. 485-498 ◽  
Author(s):  
ZHAO ZHANG ◽  
QINGHAI LIU ◽  
DEYING LI
Keyword(s):  
Wireless Sensor Network ◽  
Approximation Algorithms ◽  
Sensor Network ◽  
Connected Graph ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Performance Ratio ◽  
Wireless Sensor ◽  
Vertex Set

A vertex set D of a connected graph G is a (k, r)-connected dominating set ((k, r)-CDS) if every vertex in V(G)\D is at most r-hops away from at least k vertices in D. Finding a minimum (k, r)-CDS has wireless sensor network as its background. In this paper, we give two approximation algorithms to compute a minimum (k, r)-CDS, which improves previous works in regard of performance ratio.

scholarly journals The Construction of a Virtual Backbone with a Bounded Diameter in a Wireless Network

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jiarong Liang ◽  
Meng Yi ◽  
Yanyan Li ◽  
Xinyu Liang
Keyword(s):  
Wireless Network ◽  
Dominating Set ◽  
Optimal Solution ◽  
Performance Ratio ◽  
Absorbing Set ◽  
Virtual Backbone ◽  
Simulation Experiments ◽  
Strongly Connected ◽  
Better Than ◽  
A Performance

We usually use a digraph to represent a wireless network (WN). Correspondingly, a connected dominating set (CDS) of the digraph is usually used to denote a virtual backbone (VB) of the corresponding WN. In this article, focusing on the problem of a minimum strongly connected dominating and absorbing set (MSCDAS) with a bounded diameter (or guaranteed routing cost) for a digraph, which is strongly connected, we introduce two algorithms. One is called the guaranteed routing cost strongly connected dominating and absorbing set (GOC-SCDAS), which can generate a strongly connected dominating and absorbing set (SCDAS) with a performance ratio 14.4k+1/22 in respect of the optimal solution. Another is called the α guaranteed routing cost strongly connected bidirectional dominating and absorbing set (α-GOC-SCBDAS), which can generate a strongly connected bidirectional dominating and absorbing set (SCBDAS) with a performance ratio 8.8443k+1/22k+1/22 in respect of the optimal solution and a better routing cost, where k=rmax/rmin and rmin,rmax is the transmission range of nodes in the network. Through the simulation experiments, we obtain the conclusion that in terms of the diameter and average routing path length (ARPL) of CDS, the outputs of our algorithms are better than those of the algorithm in (Du et al. 2006).

On the Power of Lookahead in Greedy Scheme for Finding a Minimum CDS for Unit Disk Graphs

2016 ◽  
Vol 27 (07) ◽  
pp. 829-843
Author(s):  
Satoshi Fujita
Keyword(s):  
Unit Disk ◽  
Greedy Algorithm ◽  
Dominating Set ◽  
Performance Ratio ◽  
Connected Subgraph ◽  
Bounded Degree ◽  
Unit Disk Graphs ◽  
Optimum Solution ◽  
General Graphs ◽  
Better Than

A connected dominating set (CDS, for short) for graph G is a dominating set which induces a connected subgraph of G. In this paper, we consider the problem of finding a minimum CDS for unit disk graphs, which have recently attracted considerable attention as a model of virtual backbone in multi-hop wireless networks. This optimization problem is known to be NP-hard and many approximation algorithms have been proposed in the literature. This paper proves a lower bound on the performance ratio of a greedy algorithm of Guha and Khuller which was originally proposed for general graphs and is known to be a representative in which the lookahead plays a crucial role in selecting a vertex to be contained in the CDS. More specifically, we show that for any fixed ε>0 and integer n0≥1, there is a unit disk graph with bounded degree consisting of at least n0 vertices for which the output of the greedy algorithm is no better than 3−ε times of an optimum solution to the same graph.

scholarly journals A Novel Hybrid Algorithm for Minimum Total Dominating Set Problem

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 222 ◽  
Author(s):  
Fuyu Yuan ◽  
Chenxi Li ◽  
Xin Gao ◽  
Minghao Yin ◽  
Yiyuan Wang
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Evolutionary Algorithm ◽  
Hybrid Algorithm ◽  
Dominating Set ◽  
Experimental Results ◽  
Total Dominating Set ◽  
Dominating Set Problem ◽  
Algorithm Search ◽  
Better Than

The minimum total dominating set (MTDS) problem is a variant of the classical dominating set problem. In this paper, we propose a hybrid evolutionary algorithm, which combines local search and genetic algorithm to solve MTDS. Firstly, a novel scoring heuristic is implemented to increase the searching effectiveness and thus get better solutions. Specially, a population including several initial solutions is created first to make the algorithm search more regions and then the local search phase further improves the initial solutions by swapping vertices effectively. Secondly, the repair-based crossover operation creates new solutions to make the algorithm search more feasible regions. Experiments on the classical benchmark DIMACS are carried out to test the performance of the proposed algorithm, and the experimental results show that our algorithm performs much better than its competitor on all instances.

scholarly journals Network robustness improvement via long-range links

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Vincenza Carchiolo ◽  
Marco Grassia ◽  
Alessandro Longheu ◽  
Michele Malgeri ◽  
Giuseppe Mangioni
Keyword(s):  
Complex Networks ◽  
Long Range ◽  
Real World ◽  
Network Robustness ◽  
Scale Free ◽  
Area Of Interest ◽  
Before And After ◽  
Significant Area ◽  
Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

Nature-inspired hybrid deep learning for race detection by face shape features

2020 ◽  
Vol 13 (3) ◽  
pp. 365-388
Author(s):  
Asha Sukumaran ◽  
Thomas Brindha
Keyword(s):  
Feature Extraction ◽  
Hybrid Algorithm ◽  
Shape Features ◽  
Error Performance ◽  
Color Feature ◽  
Content Type ◽  
Dragonfly Algorithm ◽  
Face Shape ◽  
Race Detection ◽  
Better Than

PurposeThe humans are gifted with the potential of recognizing others by their uniqueness, in addition with more other demographic characteristics such as ethnicity (or race), gender and age, respectively. Over the decades, a vast count of researchers had undergone in the field of psychological, biological and cognitive sciences to explore how the human brain characterizes, perceives and memorizes faces. Moreover, certain computational advancements have been developed to accomplish several insights into this issue.Design/methodology/approachThis paper intends to propose a new race detection model using face shape features. The proposed model includes two key phases, namely. (a) feature extraction (b) detection. The feature extraction is the initial stage, where the face color and shape based features get mined. Specifically, maximally stable extremal regions (MSER) and speeded-up robust transform (SURF) are extracted under shape features and dense color feature are extracted as color feature. Since, the extracted features are huge in dimensions; they are alleviated under principle component analysis (PCA) approach, which is the strongest model for solving “curse of dimensionality”. Then, the dimensional reduced features are subjected to deep belief neural network (DBN), where the race gets detected. Further, to make the proposed framework more effective with respect to prediction, the weight of DBN is fine tuned with a new hybrid algorithm referred as lion mutated and updated dragon algorithm (LMUDA), which is the conceptual hybridization of lion algorithm (LA) and dragonfly algorithm (DA).FindingsThe performance of proposed work is compared over other state-of-the-art models in terms of accuracy and error performance. Moreover, LMUDA attains high accuracy at 100th iteration with 90% of training, which is 11.1, 8.8, 5.5 and 3.3% better than the performance when learning percentage (LP) = 50%, 60%, 70%, and 80%, respectively. More particularly, the performance of proposed DBN + LMUDA is 22.2, 12.5 and 33.3% better than the traditional classifiers DCNN, DBN and LDA, respectively.Originality/valueThis paper achieves the objective detecting the human races from the faces. Particularly, MSER feature and SURF features are extracted under shape features and dense color feature are extracted as color feature. As a novelty, to make the race detection more accurate, the weight of DBN is fine tuned with a new hybrid algorithm referred as LMUDA, which is the conceptual hybridization of LA and DA, respectively.

k-Efficient domination: Algorithmic perspective

2022 ◽  
Author(s):  
Mohsen Alambardar Meybodi
Keyword(s):  
Decision Problem ◽  
Dominating Set ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Chordal Graphs ◽  
Sparse Graphs ◽  
Fpt Algorithm ◽  
Domination Problem ◽  
Efficient Dominating Set ◽  
Np Complete

A set [Formula: see text] of a graph [Formula: see text] is called an efficient dominating set of [Formula: see text] if every vertex [Formula: see text] has exactly one neighbor in [Formula: see text], in other words, the vertex set [Formula: see text] is partitioned to some circles with radius one such that the vertices in [Formula: see text] are the centers of partitions. A generalization of this concept, introduced by Chellali et al. [k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122], is called [Formula: see text]-efficient dominating set that briefly partitions the vertices of graph with different radiuses. It leads to a partition set [Formula: see text] such that each [Formula: see text] consists a center vertex [Formula: see text] and all the vertices in distance [Formula: see text], where [Formula: see text]. In other words, there exist the dominators with various dominating powers. The problem of finding minimum set [Formula: see text] is called the minimum [Formula: see text]-efficient domination problem. Given a positive integer [Formula: see text] and a graph [Formula: see text], the [Formula: see text]-efficient Domination Decision problem is to decide whether [Formula: see text] has a [Formula: see text]-efficient dominating set of cardinality at most [Formula: see text]. The [Formula: see text]-efficient Domination Decision problem is known to be NP-complete even for bipartite graphs [M. Chellali, T. W. Haynes and S. Hedetniemi, k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122]. Clearly, every graph has a [Formula: see text]-efficient dominating set but it is not correct for efficient dominating set. In this paper, we study the following: [Formula: see text]-efficient domination problem set is NP-complete even in chordal graphs. A polynomial-time algorithm for [Formula: see text]-efficient domination in trees. [Formula: see text]-efficient domination on sparse graphs from the parametrized complexity perspective. In particular, we show that it is [Formula: see text]-hard on d-degenerate graphs while the original dominating set has Fixed Parameter Tractable (FPT) algorithm on d-degenerate graphs. [Formula: see text]-efficient domination on nowhere-dense graphs is FPT.

scholarly journals Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

2017 ◽  
Vol 59 ◽  
pp. 463-494 ◽  
Author(s):  
Shaowei Cai ◽  
Jinkun Lin ◽  
Chuan Luo
Keyword(s):  
Local Search ◽  
Real World ◽  
Large Scale ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Search Algorithms ◽  
Theory And Practice ◽  
Sparse Graphs ◽  
Massive Graphs

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

scholarly journals Where the action could be: Speakers look at graspable objects and meaningful scene regions when describing potential actions

2019 ◽  
Author(s):  
Gwendolyn L Rehrig ◽  
Candace Elise Peacock ◽  
Taylor Hayes ◽  
Fernanda Ferreira ◽  
John M. Henderson
Keyword(s):  
Visual Attention ◽  
Real World ◽  
Language Production ◽  
Native English Speakers ◽  
English Speakers ◽  
Linguistic Processing ◽  
General Meaning ◽  
New Evidence ◽  
Shed Light ◽  
Better Than

The world is visually complex, yet we can efficiently describe it by extracting the information that is most relevant to convey. How do the properties of real-world scenes help us decide where to look and what to say? Image salience has been the dominant explanation for what drives visual attention and production as we describe displays, but new evidence shows scene meaning predicts attention better than image salience. Here we investigated the relevance of one aspect of meaning, graspability (the grasping interactions objects in the scene afford), given that affordances have been implicated in both visual and linguistic processing. We quantified image salience, meaning, and graspability for real-world scenes. In three eyetracking experiments, native English speakers described possible actions that could be carried out in a scene. We hypothesized that graspability would preferentially guide attention due to its task-relevance. In two experiments using stimuli from a previous study, meaning explained visual attention better than graspability or salience did, and graspability explained attention better than salience. In a third experiment we quantified image salience, meaning, graspability, and reach-weighted graspability for scenes that depicted reachable spaces containing graspable objects. Graspability and meaning explained attention equally well in the third experiment, and both explained attention better than salience. We conclude that speakers use object graspability to allocate attention to plan descriptions when scenes depict graspable objects within reach, and otherwise rely more on general meaning. The results shed light on what aspects of meaning guide attention during scene viewing in language production tasks.

The Role of the Computer in Team Problem-Solving: Critiquing or Partial Automation?

1993 ◽  
Vol 37 (15) ◽  
pp. 1029-1029
Author(s):  
Stephanie A. E. Guerlain ◽  
Philip J. Smith
Keyword(s):  
Problem Solving ◽  
Computer System ◽  
Real World ◽  
Automated System ◽  
Computer Interface ◽  
Rule Base ◽  
Heuristic Strategy ◽  
System Designs ◽  
Better Than

A testbed was developed for studying the effects of different computer system designs on human-computer team problem-solving, using the real-world task of antibody identification. The computer interface was designed so that practitioners could solve antibody identification cases using the computer as they normally would using paper and pencil. A rule-base was then encoded into the computer such that it had knowledge for applying a heuristic strategy that is often helpful for solving cases. With this testbed, studies have been run comparing different computer system designs. A critiquing system was found to be better than a partially automated system on cases where the computer's knowledge is incompetent.

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