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With rapid development of artificial intelligence (AI) technology, social network (SN) can use AI to extract useful knowledge of users to improve the quality of peoples lives. Although AI has achieved a very big breakthrough, it also faces many challenges for collecting data, such as larger data redundancy and higher energy consumption. To conquer those problems, a matrix completion-based Sampling Points Selection joint Intelligent Unmanned Aerial Vehicle (UAVs) Trajectory Optimization (SPS-IUTO) scheme for data acquisition is proposed. In terms of space, for one column, the probability that a sample point is selected is inversely proportional to the number of sample points selected by all previous rows. In terms of time, the first step is that sampling points with higher degree are selected as dominator sampling points in each row and column. The second step is that sampling points with lower degree are selected as virtual dominator sampling points. The movement trajectory of the UAV is optimized using the proposed algorithm. As is shown in the experimental results, the proposed scheme can achieve significant improvement in terms of energy and redundant data.

In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences as well as bounds on other orientations of oft studied tree topologies including generalized stars and caterpillars.

A dominator coloring is a proper coloring of the vertices of a graph such that each vertex of the graph dominates all vertices of at least one color class (possibly its own class). The dominator chromatic number of a graph G is the minimum number of color classes in a dominator coloring of G. In this paper, we determine the exact value of the dominator chromatic number of a subclass of forests which we call, generalized caterpillars forest, where every vertex of degree at least three is a support vertex.

The Maker–Breaker total domination game in graphs is introduced as a natural counterpart to the Maker–Breaker domination game recently studied by Duchene, Gledel, Parreau, and Renault. Both games are instances of the combinatorial Maker–Breaker games. The Maker–Breaker total domination game is played on a graph G by two players who alternately take turns choosing vertices of G . The first player, Dominator, selects a vertex in order to totally dominate G while the other player, Staller, forbids a vertex to Dominator in order to prevent him from reaching his goal. It is shown that there are infinitely many connected cubic graphs in which Staller wins and that no minimum degree condition is sufficient to guarantee that Dominator wins when Staller starts the game. An amalgamation lemma is established and used to determine the outcome of the game played on grids. Cacti are also classified with respect to the outcome of the game. A connection between the game and hypergraphs is established. It is proved that the game is PSPACE-complete on split and bipartite graphs. Several problems and questions are also posed.

The article deals with the spelling of the word обладатель (‘dominator, possessor’) , an important component of the title of Russian Tsars (e. g. многихъ земель обладатель or отчичь и дѣдичь наслѣдникъ и обладатель , etc.). This word was written in the title in a special manner, namely with two letters a , as ОБЛААДАТЕЛЬ. It is demonstrated in the article that the form with double a reflects the sacralization of the Tsar and his title. DOI: 10.31168/2305-6754.2020.9.1.6

This paper investigates a stable connected dominating set (CDS) construction algorithm for mobile ad hoc networks(MANETs). The proposed algorithm is based on the node velocity using the notion of Strong Neighborhood determined by the Threshold Neighborhood Distance Ratio (TNDR) constraint, which contributes to a stable CDS without considering unstable edges in the network. If a node has the lowest speed in all competing nodes with at least one neighbor that has not been explored, it is selected as a dominator. When a node becomes a CDS node, we say that all its neighbors are explored and have the opportunities to participate in the next iteration. This process of selecting nodes continues until all nodes in the network are explored. The tradeoff is that the size of the nodes and edges in CDS are slightly larger.

Costanzo Festa (ca. 1490–1545) and Jean Conseil (ca. 1498–1534) spent most of their life in the papal chapel and composed motets based on the same texts: 'Deus venerunt gentes’, probably written in response tothe sack of Rome in 1527, as well as 'Lumen ad revelationum / Nunc Dimittis’. The five-voice motet 'Dominator caelorum’ is ascribed both to Festa and to Conseil. Thus if 'Ecce advenit dominator’ was really composed by Costanzo Festa, a papal composer, and performed at the meeting between Charles V and Clement VII in Bologna, as Klaus Pietschmann persuasively demonstrates, could not 'Dominator caelorum’ have been Conseil’s small musical contribution to this event? If so, it may have been Conseil who composed 'Dominator caelorum’ to embellish the Bologna meeting as Festa did by composing 'Ecce advenit dominator’.

Both complicated interference and frequent handoffs exist in 5G ultra-dense small cell networks (UDNs), which significantly degrade the system performance. Therefore, a novel power control and simple traffic offloading scheme is proposed to handle the interference and handoffs. Owing to the severe interference coupling, this problem is formulated as a dynamic stochastic game (DSG) between small cells, which can characterize the stochastic property of channel states. Nevertheless, it is hard to solve the DSG system when the number of players exceeds 2. Therefore, to solve the DSG system in UDNs, we use the mean field approximation theory and convert the DSG into a mean field game (MFG) in which the game equilibrium is analyzed by solving two tractable partial differential equations, from the global and individual perspectives. In contrast to the conventional MFG works, there usually exists a dominating player, which introduces higher interference due to the location or larger transmit power in UDNs, for assumed generic player. Consequently, we formulate the framework of MFG with a dominating player and lots of generic players. Within the formulated framework, first we design the combined cost function considering both the aggregate interference and signal-to-interference-plus-noise ratio performances for both the generic player and its dominator. Then, we derive the corresponding Fokker–Planck–Kolmogorov and Hamilton–Jacobi–Bellman equations. Next, we propose a novel interference-aware traffic offloading and power control policy. Finally, we present numerical results showing the energy and spectrum efficiency performances of the proposed policy compared with the policy without traffic offloading.

The Maker-Breaker domination game is played on a graph G by Dominator and Staller. The players alternatively select a vertex of G that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper we introduce the Maker-Breaker domination number γMB(G) of G as the minimum number of moves of Dominator to win the game provided that he has a winning strategy and is the first to play. If Staller plays first, then the corresponding invariant is denoted γ M B ′ ( G ) . Comparing the two invariants it turns out that they behave much differently than the related game domination numbers. The invariant γMB(G) is also compared with the domination number. Using the Erdős-Selfridge Criterion a large class of graphs G is found for which γMB(G) > γ(G) holds. Residual graphs are introduced and used to bound/determine γMB(G) and γ M B ′ ( G ) . Using residual graphs, γMB(T) and γ M B ′ ( T ) are determined for an arbitrary tree. The invariants are also obtained for cycles. A list of open problems and directions for further investigations is given.

Domination game (Bresar et al. in SIAM J Discrete Math 24:979–991, 2010) and total domination game (Henning et al. in Graphs Comb 31:1453–1462 (2015) are by now well established games played on graphs by two players, named Dominator and Staller. In this paper, Z-domination game, L-domination game, and LL-domination game are introduced as natural companions of the standard domination games. Versions of the Continuation Principle are proved for the new games. It is proved that in each of these games the outcome of the game, which is a corresponding graph invariant, differs by at most one depending whether Dominator or Staller starts the game. The hierarchy of the five domination games is established. The invariants are also bounded with respect to the (total) domination number and to the order of a graph. Values of the three new invariants are determined for paths up to a small constant independent from the length of a path. Several open problems and a conjecture are listed. The latter asserts that the L-domination game number is not greater than 6 / 7 of the order of a graph.

A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other color class. In this paper, we obtain the dominator chromatic number for the Line graph of some graphs, Central graph of Line graph of Star graph and Central graph of Line graph of Double Star graph. And also we obtain the dominator chromatic number for J(S_{n}),J(C_{n}) and J(K_{1,n,n,n}) respectively.

Let G = ( V , E ) be a graph. A vertex u in G totally dominates a vertex v if u is adjacent to v in G . The total domination game played on G consists of two players, named Dominator and Staller, who alternately take turns choosing vertices of G such that each chosen vertex totally dominates at least one vertex not totally dominated by the vertices previously chosen. Dominator wishes to totally dominate the graph as fast as possible, while Staller wishes to delay the process as much as possible. The game total domination number γ t g ( G ) (resp. the Staller-start game total domination number γ t g ′ ( G ) ) of G is the number of vertices chosen when Dominator starts the game (resp. when Staller starts the game) and both players play optimally. In this paper, we determine the exact value of γ t g ( G ) and γ t g ′ ( G ) when G is a cyclic bipartite graph.

Given a set of objects $O$O (such as hotels), each can be represented as a point in a multi-dimensional feature space where each dimension corresponds to one attribute of the objects (such as price). Given the preference of a customer, the objects in $O$O not dominated by any other object (i.e., beat in all dimensions) are those worthy to be further considered. Such objects are known as skyline objects in database community. Suppose we have an object $o\in O$o∈O. If $o$o is a skyline point, other skyline objects are called peers of $o$o. If $o$o is not a skyline object, it must be dominated by some skyline objects which are called dominators of $o$o. Given a large number of user preferences, an interesting problem is to identify the most frequent peer/dominator (MFP/MFD) of $o$o. The MFP/MFD search has unique values in competitor analysis of various information systems. However, it is a challenging task because of the complexity to process a large number of user preferences. In this work, we provide robust solutions including exact and approximate methods. While the exact solutions explore the dominance relationship in the feature space, the approximate solutions are based on sampling techniques with theoretical bounds. We did extensive tests on large data sets which are up to 100 million user preferences generated from commercial surveys. The test resutls demonstrate the exact algorithms outperform various baseline algorithms significantly, and the approximate algorithms make further improvement by one order of magnitude with 90-98 percent accuracy.

The concept of vague graph was introduced early by Ramakrishna and substantial graph parameters on vague graphs were proposed such graph coloring, connectivity, dominating set, independent set, total dominating number and independent dominating number. In this paper, we introduce the concept of the dominator coloring and total dominator coloring of a vague graph and establish mathematical modelling for these problems.

Purpose The purpose of this paper is to design a contract to coordinate the biomass molding fuel supply chain consisting of a supplier with uncertain supply and a producer with cyclical demand as well as improve the profit of this supply chain. Design/methodology/approach In this paper, the supply chain model was build and all the variables and assumptions are set. Stackelberg game model was used to analyze and solve the problem. Furthermore, the authors give numerical examples and result analysis on the basis of data coming from field study and online information about a real biomass fuel supply chain. Findings The wholesale price with shortage penalty contract the authors proposed can coordinate the supply chain. And as the dominator of the supply chain, the producer can realize the redistribution of profits within the supply chain by determine the contract parameters. Research limitations/implications This one-to-one supply chain is a basic of complex supply chain system. Multi-to-one, one-to-multi and multi-to-multi supply chain can be studied in the future. Originality/value The results obtained in this paper can be used as a reference for enterprises in biomass energy supply chain to make contracts and realize the long-term co-operations among supply chain members.

In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph H by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the set of vertices dominated so far. The game is over if all vertices of H are dominated. Dominator aims to finish the game as soon as possible, while Staller aims to delay the end of the game. If each player plays optimally and Dominator starts, the length of the game is the invariant ‘game domination number’ denoted by γ g ( H ) . This definition is the generalization of the domination game played on graphs and it is a special case of the transversal game on hypergraphs. After some basic general results, we establish an asymptotically tight upper bound on the game domination number of k -uniform hypergraphs. In the remaining part of the paper we prove that γ g ( H ) ≤ 5 n ∕ 9 if H is a 3-uniform hypergraph of order n and does not contain isolated vertices. This also implies the following new result for graphs: If G is an isolate-free graph on n vertices and each of its edges is contained in a triangle, then γ g ( G ) ≤ 5 n ∕ 9 .

Optimizing the energy consumption of sensor nodes have been a big design issue in wireless sensor networks (WSNs). Energy efficient WSN usually compromise with network stability which is a crucial factor in ensuring full, lasting and reliable coverage of the network. Connected dominating set (CDS) based virtual backbone and traditional cluster based approach are two most commonly used data delivery protocols in a WSN. The paper proposes a distance based stable connected dominating set methodology using a meta-heuristic algorithm grey wolf optimization (DBSCDS-GWO) for achieving a stable, balanced and energy efficient CDS based WSN. We also propose a distance based stable clustering algorithm using GWO (DBSC-GWO) for improving the performance of cluster based WSN. DBSCDS-GWO performs better than RMCDS-GA and SAECDS-GA by 70.5% and 67.7% respectively and DBSC-GWO performs better than LEACH and DRESEP by 74.7% and 50.6% respectively in terms of both network stability and energy efficiency. Performance of the proposed algorithm is validated using Matlab simulation and Netsim Emulator.

In this paper we determine total dominator chromatic number in paths. Let be a graph without isolated vertices. A total dominator coloring of a graph G is a valid colouring of the graph G with the additional feature that each vertex in the graph G dominates a color class properly. The total dominator chromatic number of G is the fewest number of colors for which there is a total dominator coloring of G, and it is indicated by . The total dominator chromatic number in paths is determined in this research. n denotes an integer greater than or equal to 2 unless otherwise specified.

Global dominator coloring of the graph [Formula: see text] is the proper coloring of [Formula: see text] such that every vertex of [Formula: see text] dominates atleast one color class as well as anti-dominates atleast one color class. The minimum number of colors required for global dominator coloring of [Formula: see text] is called global dominator chromatic number of [Formula: see text] denoted by [Formula: see text]. In this paper, we characterize trees [Formula: see text] of order [Formula: see text] [Formula: see text] such that [Formula: see text] and also establish a strict upper bound for [Formula: see text] for a tree of even order [Formula: see text] [Formula: see text]. We construct some family of graphs [Formula: see text] with [Formula: see text] and prove some results on [Formula: see text]-partitions of [Formula: see text] when [Formula: see text].

In this paper, we introduce and study a new coloring problem of graphs called the double total dominator coloring. A double total dominator coloring of a graph [Formula: see text] with minimum degree at least 2 is a proper vertex coloring of [Formula: see text] such that each vertex has to dominate at least two color classes. The minimum number of colors among all double total dominator coloring of [Formula: see text] is called the double total dominator chromatic number, denoted by [Formula: see text]. Therefore, we establish the close relationship between the double total dominator chromatic number [Formula: see text] and the double total domination number [Formula: see text]. We prove the NP-completeness of the problem. We also examine the effects on [Formula: see text] when [Formula: see text] is modified by some operations. Finally, we discuss the [Formula: see text] number of square of trees by giving some bounds.

This paper combines the inquiry teaching mode of cultivating top-notch innovative talents with the "online" + "offline" blended teaching mode to reform the manufacturing technology foundation course. Through the inquiry questions, students can effectively use online resources to understand and answer the inquiry questions. This way can change the dominator of classroom time from teachers to students. It seamlessly realizes the combination of online and offline. And the corresponding diversified evaluation methods are established. The effect of the reform is significant in terms of attendance and students' feedback. Besides mastering professional knowledge, students' abilities in other aspects have also been greatly improved.

Mutation Testing offers a powerful approach to assessing unit test set quality; however, software developers may be reluctant to embrace the technique due to the tremendous number of mutants it generates, including redundant and equivalent mutants. Recent research indicates that redundant mutants affect a test engineer’s work effort only slightly, whereas equivalent mutants have a direct linear impact. Moreover, the time invested analyzing equivalent mutants produces no unit tests. Dominator mutants seek to address the redundancy problem, but they require the identification of all subsumption relationships, which implicitly identifies all equivalent mutants. This research study shows that, when equally informed, random selection can perform as well as dominator mutants.

In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph $G$ can be preprocessed in $O(n\log^2{n}/\log\log{n})$ time, producing an $O(n\log{n})$-space data structure that can answer in $O(\log{n})$ time whether $u$ can reach $v$ in $G$ if the vertex $x$ (the edge~$f$) is removed from $G$, for any query vertices $u,v$ and failed vertex $x$ (failed edge $f$). To the best of our knowledge, this is the first data structure for planar directed graphs with nearly optimal preprocessing time that answers all-pairs queries under any kind of failures in polylogarithmic time. We also consider 2-reachability problems, where we are given a planar digraph $G$ and we wish to determine if there are two vertex-disjoint (edge-disjoint) paths from $u$ to $v$, for query vertices $u,v$. In this setting we provide a nearly optimal 2-reachability oracle, which is the existential variant of the reachability oracle under single failures, with the following bounds. We can construct in $O(n\log^{O(1)}{n})$ time an $O(n\log^{3+o(1)}{n})$-space data structure that can check in $O(\log^{2+o(1)}{n})$ time for any query vertices $u,v$ whether $v$ is 2-reachable from $u$, or otherwise find some separating vertex (edge) $x$ lying on all paths from $u$ to $v$ in $G$. To obtain our results, we follow the general recursive approach of Thorup for reachability in planar graphs [J.~ACM~'04] and we present new data structures which generalize dominator trees and previous data structures for strong-connectivity under failures [Georgiadis et al., SODA~'17]. Our new data structures work also for general digraphs and may be of independent interest., Full version of a SODA'21 paper

A dominator coloring of a graph G is a proper coloring of the vertices of G in which each vertex of the graph dominates every vertex of some color class, where a vertex dominates itself and all vertices adjacent to it. The dominator chromatic number of G is the minimum number of colors among all dominator coloring of G. A total dominator coloring of a graph G is a proper coloring of the vertices of G in which each vertex of the graph dominates every vertex of some color class other than its own. The total dominator chromatic number of G is the minimum number of colors among all total dominator coloring of G. In this chapter, we present selected results on the dominator chromatic number and total dominator chromatic number of a graph.

Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .

The following question was posed by Bresar, Gologranc, Milanic,, M. Rall, and Rizzi. What if the domination game is played by only one of the players using his or her goal? Naturally, if Dominator is the only one to play a domination game in a graph G, the resulting number of moves will be the domination number γ(G). A more interesting version of this question is: What happens when only Staller is playing the game? The corresponding graph invariant, called the Grundy domination number, thus presents the worst outcome of a greedy algorithm for constructing a dominating set if one is processing the addition of vertices one at a time.

The present study considers the literary production from the American author Alice Walker; whose representations bring questions that submerge from human social practices. The aim in this paper is to express the possible reflections that literature promotes from the text The right to life: What the white man said to the black woman?, which is written and pronounced by Walker. Methodologically, the analysis is organized based on this narrative and it is built from the scope of theoretical studies, especially from those that consider the literature written by black women in the twentieth century and that are linked to sociocultural criticism. The results show that the literature, in addition to being the space and time for reflection, allows that the tensions between the oppressor's discourses and those who suffer domination can be identified. Walker confronts history, denounces and questions the dominator's responsibility while she shares her literary art in the collectively way. El presente estudio considera la producción literaria de la estadounidense Alice Walker, cuyas representaciones traen interrogantes que se sumergen desde las prácticas sociales humanas. El objetivo de este trabajo es mostrar las posibles reflexiones que la literatura promueve a partir del texto The right to life: What the white man said to the black woman?, escrito y pronunciado por Walker. Metodológicamente, el análisis se organiza en base a esta narrativa y el alcance de los estudios teóricos, especialmente aquellos que consideran la literatura escrita por mujeres negras en el siglo XX y que están vinculadas a la crítica sociocultural. Los resultados muestran que la literatura, además de ser un espacio y tiempo de reflexión, permite identificar las tensiones entre los discursos del opresor y los que sufren la dominación. Walker se enfrenta a la historia, denuncia y cuestiona la responsabilidad del dominador mientras comparte su arte literaria colectivamente. O presente estudo considera a produção literária da norte-americana Alice Walker, cujas representações trazem questões que submergem das práticas sociais humanas. O objetivo deste trabalho é mostrar as possíveis reflexões que a literatura promove a partir do texto The right to life: What the white man said to the black woman?, escrito e pronunciado por Walker. Metodologicamente, a análise organiza-se a partir dessa narrativa e do escopo de estudos teóricos, especialmente os que consideram a literatura escrita por mulheres negras no século XX e que estão ligadas à crítica sociocultural. Os resultados apontam que a literatura, além de ser o espaço e tempo de reflexão, possibilita que as tensões entre os discursos do opressor e de quem sofre dominação sejam identificadas. Walker confronta a história, denuncia e questiona a responsabilidade do dominador enquanto, de modo coletivo, compartilhada a sua arte literária.

Embedded systems are often used in safety-critical applications like cars or airplanes. This makes it crucial to verify their hardware and software under all circumstances. In previous work, we have presented an approach for the formal verification of integrated hardware/software systems using the satisfiability modulo theory solving based verification system UCLID. However, the transformation of integrated hardware/software systems into the input language of the UCLID verification system causes a considerable overhead in the number of symbolic simulation steps necessary for k-inductive verification. In this paper, we overcome this problem by presenting two optimizations for the symbolic simulation of cooperatively scheduled concurrent processes: First, we realize a reduction of redundant states in individual functions that respects all data, control and inter-process dependencies. To capture these dependencies precisely, we present the novel concept of a cooperative dominator tree, which extends the classical concept of a dominator tree to cooperatively scheduled concurrent processes. Second, we present a process parallelization for cooperatively scheduled concurrent processes based on a SystemC dependence graph. In our evaluation based on a set of 21 synthetic case studies, we reach an average reduction of the inductive verification times by 40 %.

With the enhancement of people's health awareness, more and more users are willing to wear portable micro-health monitoring equipment and communicate with remote medicine center for real-time diagnosis. Although, under normal circumstances, users' health status can be detected at any time, in extreme circumstances, such as earthquakes, how to make the medical center monitor user data for a long time for rescue will be of great significance. In this paper, we will study the networking of portable wearable devices based on wireless sensor networks. We mainly use minimal connected dominating sets (MCDSs) to organize nodes in extreme environments effectively, form virtual backbone networks, send data to the rescue or medical personnel, and maximize network lifetime. Specifically, we propose an adverse dominator selection procedure (ADSP), where the dominators are selected by their children-independent nodes. The ADSP has two versions, which are Independent node degree-based Adverse Dominator Selection Procedure (IADSP) and residual Energy-based Adverse Dominator Selection Procedure (EADSP). Based on IADSP and EADSP, two approximation MCDS construction algorithms named Independent node degree based MCDS (IMCDS) and Energy-efficient Independent neighbor-based MCDS (EIMCDS) are proposed, respectively. Both of them have the message complexity as O($N\Delta $ ). The performance ratio of IMCDS has an upper bound as O($\sqrt {N}$ ). The simulation results show that IMCDS and EIMCDS perform well in terms of CDS size, and the routing algorithm based on EIMCDS has better energy efficiency performance than that of IMCDS and classical routing protocol.