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Search results for: game chromatic number
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T-colorings, divisibility and circular chromatic number
PublicationLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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Infinite chromatic games
PublicationIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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2-Coloring number revisited
Publication2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Liczby Ramseya on-line dla różnych klas grafów
PublicationRozpatrujemy grę rozgrywaną na nieskończonej liczbie wierzchołków, w której każda runda polega na wskazaniu krawędzi przez jednego gracza - Budowniczego oraz pokolorowaniu jej przez drugiego gracza - Malarkę na jeden z dwóch kolorów, czerwony lub niebieski. Celem Budowniczego jest zmuszenie Malarki do stworzenia monochromatycznej kopii wcześniej ustalonego grafu H w jak najmniejszej możliwej liczbie ruchów. Zakładamy, że gracze...
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Total chromatic sum for trees
PublicationThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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Game about space or game in the space?
PublicationThe article analyzes various aspects of the actions taken by participants involved in the process of a spatial change. Such a process is described as a game about space or a game in the space. Different terminology is presented, in particular the meaning of: spatial order, regional studies, eco-development, sustainable development. Different forms of the game are analyzed: space as a theater, as a casino, as an area of conflict....
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublicationWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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Integration of brood units in game universe
PublicationAn access to a great number of various services allows for decomposition of complex problems Developing a game universe usually involves creation of various units which can be encountered by a player. Those can be lonely or organized in broods animals and monsters wandering around the game world. In order to provide natural gaming experience those units should behave variously depending on the world situation. Those behaviours...
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Relations between the domination parameters and the chromatic index of a graph
PublicationIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Model of emotions for game players
PublicationAffect-aware video games can respond to a game player's emotions. Such games seem to be more attractive for users. Therefore for that kind of games it is necessary to create a model of the player's emotions to know to which emotions the application should react. The paper describes different models of emotions. The questionnaire and experiment for video game players is presented. Some results of the tests are shown. Then the model...
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Game with a Purpose for Mappings Verification
PublicationMappings verification is a laborious task. The paper presents a Game with a Purpose based system for verification of automatically generated mappings. General description of idea standing behind the games with the purpose is given. Description of TGame system, a 2D platform mobile game with verification process included in the gameplay, is provided. Additional mechanisms for anti-cheating, increasing player’s motivation and gathering...
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Application of Game Theory to Conflict Management in a Construction Contract
PublicationInterest has recently grown in the application of game theory (GT) to solve a number of diverse problems in the field of construction. The use of GT by a general contractor (GC) of construction works to indicate the best strategy leading to winning court proceedings in a situation of conflict with investor (IN), has not been investigated until now. Thus the aim of this paper is to indicate the optimal strategy from the GC viewpoint...
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Bringing Common Sense to WordNet with a Word Game
PublicationWe present a tool for common sense knowledge acquisition in form of a twenty questions game. The described approach uses WordNet dictionary, which rich taxonomy allows to keep cognitive economy and accelerate knowledge propagation, although sometimes inferences made on hierarchical relations result in noise. We extend the dictionary with common sense assertions acquired during the games played with humans. The facts added to the...
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Game Theory Analysis of Bidding for a Construction Contract
PublicationThe authors are concerned with a bidding problem. There are two companies (P1 and P2) bidding for a highway construction project. In order to be more competitive, P1 considers buying a new gravel pit near the construction site. The basic cost of the pit is known to both companies. However, there is also an additional, hidden, cost (C) known only to P1. P2 is uncertain whether the hidden cost is C = 0 or C = x. P1 plans to bid for...
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Assessing Word Difficulty for Quiz-Like Game
PublicationMappings verification is a laborious task. Our research aims at providing a framework for manual verification of mappings using crowdsourcing approach. For this purpose we plan on implementing a quiz like game. For this purpose the mappings have to be evaluated in terms of difficulty to better present texts in respect of game levels. In this paper we present an algorithm for assessing word difficulty. Three approaches...
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Game with a Purpose for Verification of Mappings Between Wikipedia and WordNet
PublicationThe paper presents a Game with a Purpose for verification of automatically generated mappings focusing on mappings between WordNet synsets and Wikipedia articles. General description of idea standing behind the games with the purpose is given. Description of TGame system, a 2D platform mobile game with verification process included in the game-play, is provided. Additional mechanisms for anti-cheating, increasing player’s motivation...
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Smooth start for strategry game development supported by XNA framework
PublicationTo attract young and casual game developers, Microsoft created a set of libraries oriented towards easier game development and end-product management. The aim of XNA Framework is to provide a unified software development environment for creating games for both PC's and dedicated platforms like XBOX consoles or mobile phones capable of 3D acceleration. The use of modern, object oriented languages available for the .NET platform...
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Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
PublicationWe study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the...
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Analysis and improvement attempt of prof. Alan Fowler’s negotiation game
PublicationThe main goal of the following article is to design an improved version of the negotiation game created by prof. Alan Fowler (Fowler, 1997). I have tried to achieve this by constructing four separate versions of the game which represent different approaches while preserving rules, chosen basic technical assumptions and the simplicity of the base game. Each version of the game is supposed to i.a. make it less obvious, create new...
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Zero-Visibility Cops and Robber Game on a Graph
PublicationWe examine the zero-visibility cops and robber graph searching model, which differs from the classical cops & robber game in one way: the robber is invisible. We show that this model is not monotonic. We also provide bounds on both the zero-visibility copnumber and monotonic zero-visibility copnumber in terms of the pathwidth.
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A proposition for integrating elements of game universe by means of behavioral trees
PublicationModern computer games often involve autonomous beings collaborating and competing with each other to reach their objectives in the game universe. It seems only natural to use agent-oriented approach in such cases. This article identifies the rules of building a game universe as an environment for executing agents. The paper also covers a method for decomposing compound behaviors into behavioral trees. Dividing complex behaviors...
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Concept description vectors and the 20 question game
PublicationKnowledge of properties that are applicable to a given object is a necessary prerequisite to formulate intelligent question. Concept description vectors provide simplest representation of this knowledge, storing for each object information about the values of its properties. Experiments with automatic creation of concept description vectors from various sources, including ontologies, dictionaries, encyclopedias and unstructured...
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Isolation Number versus Domination Number of Trees
PublicationIf G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....
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Designing effective educational games - a case study of a project management game
PublicationThis paper addresses the issues of designing effective educational games. We aim at investigating how the cognitive, behavioral and emotional aspects of the games influence their educational effectiveness. The results were obtained with an observational user experience study extended with affect analysis carried out for a project management game GraPM. We analyzed the...
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A Biofeedback System that Uses the Game to Study Electrical Muscle Activity
PublicationThe aim of this project was to design a system that will allow performing repetitive muscle exercises using a biofeedback device. It is supposed to enhance the motivation and attractiveness of the performed tasks thanks to an interactive game developed for mobile devices with the Android operating system. The built-in calibration mechanisms enable the users to play a game that is independent of their abilities which evens out the...
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The Waiter Game: Structure and Development of an Hospitality Training Game
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Chromatic scheduling in a cyclic open shop
PublicationPraca jest poświęcona złożoności obliczeniowej problemu cyklicznego szeregowania w systemie otwartym. Autorzy analizując wykazują, że problem jest NP-trudny dla 3 procesorów i konstruują algorytm dokładny dla przypadku dwóch procesorów.Ponadto analizowany jest zwarty wariant cyklicznego systemu otwartego. W tym przypadku autorzy pokazują, że już szeregowanie na dwóch procesorach prowadzi do problemu NP-trudnego.
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Adjusting Game Difficulty by Recreating Behavioral Trees of Human Player Actions
PublicationThis paper presents a proposition of a method for adjusting game difficulty to the current level of player's skills in one-on-one games. The method is based on recognition of human player's actions and recording of those actions in the form of behavioral trees. Such trees are later used to drive behaviors of computer-controlled opponents so that human player has beat hit own strategy and improve on it, to win subsequent games....
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Chromatic cost coloring of weighted bipartite graphs
PublicationGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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On trees with double domination number equal to 2-domination number plus one
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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On trees with double domination number equal to total domination number plus one
PublicationA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...
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Bondage number of grid graphs
PublicationThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Navier number and transition to turbulence
PublicationThe motivation behind this article is to explain a role of the Navier number (Na -dimensionless slip-length) in prediction of closures for laminar to turbulent transition undergoing via eddies detachment from the slip layer in nano-cannals. Additionally the role of the Navier number Na in universal modeling of phenomenon of enhanced mass flow rate reported in micro- and nano-channels has been explained. The Na number should be...
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Evolving neural network as a decision support system — Controller for a game of “2048” case study
PublicationThe paper proposes an approach to designing the neuro-genetic self-learning decision support system. The system is based on neural networks being adaptively learned by evolutionary mechanism, forming an evolved neural network. Presented learning algorithm enables for a selection of the neural network structure by establishing or removing of connections between the neurons, and then for a finding the beast suited values of the network...
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Modeling a Traffic Remapping Attack Game in a Multi-hop Ad Hoc Network
PublicationIn multi-hop ad hoc networks, selfish nodes may unduly acquire high quality of service (QoS) by assigning higher priority to source packets and lower priority to transit packets. Such traffic remapping attacks (TRAs) are cheap to launch, impossible to prevent, hard to detect, and harmful to non-selfish nodes. While studied mostly in single-hop wireless network settings, TRAs have resisted analysis in multi-hop settings. In this paper...
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Game theory-based virtual machine migration for energy sustainability in cloud data centers
PublicationAs the demand for cloud computing services increases, optimizing resource allocation and energy consumption has become a key factor in achieving sustainability in cloud environments. This paper presents a novel approach to address these challenges through an optimized virtual machine (VM) migration strategy that employs a game-theoretic approach based on particle swarm optimization (PSO) (PSO-GTA). The proposed approach leverages...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...
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The circular chromatic index of some class 2 graphs
PublicationW artykule został wyznaczony cyrkularny indeks chromatyczny dla dwóch rodzin grafów klasy 2. Co więcej, podano nie trywialne oszacowania tego parametru dla snarków Isaacsa i Goldberga. Na koniec artykułu rozważana jest złożoność obliczeniowa problemów związanych z cyrkularnym kolorowaniem krawędzi.
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Edge-chromatic sum of trees and bounded cyclicity graphs
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On domination multisubdivision number of unicyclic graphs
PublicationThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublicationThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Game-based Sprint retrospectives: multiple action research
PublicationIn today’s fast-paced world of rapid technological change, software development teams need to constantly revise their work practices. Not surprisingly, regular reflection on how to become more effective is perceived as one of the most important principles of Agile Software Development. Nevertheless, running an effective and enjoyable retrospective meeting is still a challenge in real environments. As reported by several studies,...
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Equilibria of wireless multihoming game
PublicationTerminale podłączone do wielu sieci bezprzewodowych modelowane są jako uczestnicy gry niekooperacyjnej, której symetryczny punkt równowagi Nasha w strategiach mieszanych wyznaczono dla przypadku sieci WLAN standardu IEEE 802.11. Udziały pasma w punkcie równowagi okazują się niższe w porównaniu ze środowiskiem terminali stosujących ustawienia standardowe.
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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The convex domination subdivision number of a graph
PublicationLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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Developing Game-Structure Sensitive Matchmaking System for Massive-Multiplayer Online Games
PublicationProviding a fair matchmaking system is an essential issue, while developing every online video game. In the article, we show that the currently existing matchmaking system in League of Legends, one of the most popular online video games currently existing, is built on a base of conditions which do not hold true in the presence of empirical data. This, in short, decreases the effectiveness of the ranking system, and negatively affects...
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublicationA vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...
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Weakly convex domination subdivision number of a graph
PublicationA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...