Search
Filters
total: 658
filtered: 529
-
Catalog
Chosen catalog filters
Search results for: GRAPH COLOURING
-
Rearrangeability in multicast Clos networks is NP-complete
PublicationPrzestrajalność w polach Closa z połączeniami jeden do jeden jest problemem wielomianowym. W pracy pokazano, że w polach z połączeniami jeden do wiele problem ten jest NP zupełny.Three-stage elos networks are commutation networks with circuit switching. So far, graph theory has been very useful tool for solving issues related to these networks with unicast connections. This is so because if elos network is represented as a bipartite...
-
Embedded Representations of Wikipedia Categories
PublicationIn this paper, we present an approach to building neural representations of the Wikipedia category graph. We test four different methods and examine the neural embeddings in terms of preservation of graphs edges, neighborhood coverage in representation space, and their influence on the results of a task predicting parent of two categories. The main contribution of this paper is application of neural representations for improving the...
-
Hat problem on odd cycles
PublicationThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can...
-
On minimum cost edge searching
PublicationWe consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph G. We call such a strategy ideal. We prove, by an example, that ideal search strategies do not...
-
Comparison of hydrogen bonds and diverse weak interactions of the nitro group in 2-methyl-4-nitroanilinium nitrate, bisulfate and two hexafluoridosilicates: elementary graph-set approach
PublicationCrystal structures of (H2m4na)NO3 (1), (H2m4na)HSO4 (2), (H2m4na)2SiF6 (3) and (H2m4na)2SiF6*2H2O (4), where 2m4na = 2-methyl-4-nitroaniline, are presented. Two layers of interactions occur in the structures, N—H...O/F hydrogen bonds and interactions with the nitro group. Although diverse, hydrogen-bonding patterns are compared with each other by means of interrelations among elementary graph-set descriptors and descriptors of hydrogen-bonding...
-
Bond graph modeling of the new generation engine cooling systems = Zastosowanie metody grafów wiązań do modelowania nowej generacji układów chłodzenia silników spalinowych
PublicationW referacie szczegółowo opisano modele wymiany ciepła i przepływów w układzie chłodzenia. Metoda grafów wiązań okazała się szczególnie użyteczną dla modelowania skomplikowanych systemów energetycznych o różnych postaciach energii. Jako przykładu użyto obiegu chłodzenia silnika badawczego na hamowni silnikowej.
-
The complexity of minimum-length path decompositions
PublicationWe consider a bi-criteria generalization of the pathwidth problem, where, for given integers k, l and a graph G, we ask whether there exists a path decomposition P of G such that the width of P is at most k and the number of bags in P, i.e., the length of P, is at most l. We provide a complete complexity classification of the problem in terms of k and l for general graphs. Contrary to the original pathwidth problem, which is fixed-parameter...
-
Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
PublicationSmart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....
-
On trees attaining an upper bound on the total domination number
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. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
-
Certified domination
PublicationImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...
-
Modelling of Objects Behaviour for Their Re-identification in Multi-camera Surveillance System Employing Particle Filters and Flow Graphs
PublicationAn extension of the re-identification method of modeling objects behavior in muti-camera surveillance systems, related to adding a particle filter to the decision-making algorithm is covered by the paper. A variety of tracking methods related to a single FOV (Field of Vision) are known, proven to be quite different for inter-camera tracking, especially in case of non-overlapping FOVs. The re-identification methods refer to the...
-
Drawing maps with advice
PublicationW pracy podejmujemy temat konstrukcji algorytmu dla agenta, który zostaje umieszczony w dowolnym wierzchołku grafu (wierzchołki są nierozróżnialne, krawędzie mają etykiety portów), po czym realizuje algorytm zmierzający do znalezienia drzewa spinającego grafu lub izomorficznej kopii grafu. Dla obu problemów podajemy asymptotycznie dokładne lub prawie dokładne oszacowania na ilość bitów dodatkowej informacji, którą agent musi otrzymać...
-
Scheduling of compatible jobs on parallel machines
PublicationThe dissertation discusses the problems of scheduling compatible jobs on parallel machines. Some jobs are incompatible, which is modeled as a binary relation on the set of jobs; the relation is often modeled by an incompatibility graph. We consider two models of machines. The first model, more emphasized in the thesis, is a classical model of scheduling, where each machine does one job at time. The second one is a model of p-batching...
-
Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublicationDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
-
Decision Support in Selecting a Reliable Strategy for Sustainable Urban Transport Based on Laplacian Energy of T-Spherical Fuzzy Graphs
Publication -
Bounds on the Cover Time of Parallel Rotor Walks
PublicationThe rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in...
-
The complexity of bicriteria tree-depth
PublicationThe tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph G. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some input integer b. We are interested in the case when G is the line graph of a tree, proving that the problem is NP-hard and obtaining a polynomial-time additive 2b-approximation algorithm. This particular...
-
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)....
-
Bounds on the cover time of parallel rotor walks
PublicationThe rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node successively propagates walkers visiting it along its outgoing arcs in round-robin fashion, according to a fixed ordering. We consider...
-
Preliminary study on the influence of UV-C irradiation on microorganism viability and polyphenol compounds content during winemaking of ‘Regent’ red grape cultivar
Publication -
Polyhedral Ramsey Numbers
PublicationGiven two polygons or polyhedrons P1 and P2, we can transform these figures to graphs G1 and G2, respectively. The polyhedral Ramsey number Rp(G1,G2) is the smallest integer n such that every graph, which represents polyhedron on n vertices either contains a copy of G1 or its complement contains a copy of G2. Using a computer search together with some theoretical results we have established some polyhedral Ramsey numbers, for example...
-
Non-volatile molecular composition and discrimination of single grape white of chardonnay, riesling, sauvignon blanc and silvaner using untargeted GC–MS analysis
PublicationThis study developed and applied a GC–MS method aiming at molecular fingerprinting of 120 commercial single grape white wines (Chardonnay, Riesling, Sauvignon Blanc and Silvaner) for possible authentication according to grape variety. The method allowed detection of 372 peaks and tentative identification of 146 metabolites including alcohols, organic acids, esters, amino acids and sugars. The grape variety effect explained 8.3%...
-
Concept of Multifactor Method and Non-Functional Requirements Solution to Increase Resilience through Functional Safety with Cybersecurity Analysis
PublicationIn the process of designing safety systems, an integrated approach in safety and cybersecurity analysis is necessary. The paper describes a new technique of increasing resilience through integrated analysis of functional safety and cybersecurity. It is a modeling methodology based on the combination of the multifactor method utilizing modified risk graphs, used previously for Safety Integrity Level (SIL) assessment, and the Non-Functional...
-
Global defensive secure structures
PublicationLet S ⊂ V (G) for a given simple non-empty graph G. We define for any nonempty subset X of S the predicate SECG,S(X) = true iff |NG[X]∩S| ≥ |NG[X]\S|. Let H be a non-empty family of graphs such that for each vertex v ∈ V (G) there is a subgraph H of G containing v and isomorphic to a member of H. We introduce the concept of H-alliance extending the concept of global defensive secure structures. By an H-alliance in a graph G we...
-
Modele i algorytmy dla grafowych struktur defensywnych
PublicationW niniejszej pracy przeprowadzono analizę złożoności istnienia struktur defensywnych oraz równowag strategicznych w grafach. W przypadku struktur defensywnych badano modele koalicji defensywnych, zbiorów defensywnych i koalicji krawędziowych – każdy z nich w wersji globalnej, tj. z wymogiem dominacji całego grafu. W przypadku modeli równowagi strategicznej badano równowagę strategiczną koalicji defensywnych, równowagę strategiczną...
-
GreedyMAX-type Algorithms for the Maximum Independent Set Problem
PublicationA maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued functionp defined on the vertex set V(G) and called a potential function of agraph G, while P(G) = max{vinV(G)| p(v)} is called a potential of G. For any graph P(G) <= D(G),...
-
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,...
-
On a matching distance between rooted phylogenetic trees
PublicationThe Robinson–Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach...
-
Rendezvous of Heterogeneous Mobile Agents in Edge-Weighted Networks
PublicationWe introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal...
-
Rendezvous of heterogeneous mobile agents in edge-weighted networks
PublicationWe introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal...
-
Brushing with additional cleaning restrictions
PublicationIn graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. We consider the process where at each time step, a vertex that has at least as many brushes as incident, contaminated edges, sends brushes down these edges to clean them. Various problems arise, such as determining the minimum number of brushes (called the brush number) that are required to clean the entire graph. Here, we study a new variant...
-
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...
-
Leader election for anonymous asynchronous agents in arbitrary networks
PublicationWe consider the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their positions in it, hence they must gain this knowledge by navigating in the graph...
-
On the ratio between 2-domination and total outer-independent domination numbers of trees
PublicationA 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D. A total outer-independent 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, and the set V(G)D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
-
Computational algorithm for the analysis of mechatronic systems with distributed parameter elements
PublicationThe paper presents a systematic computational package for analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The algorithm is based on the transfer function method (DTFM). With this algorithm, a bond graph technique for the modelling is developed to simplify computations. Analysis of different systems requires only changing the inputs data in the form of the bond graph diagram
-
Modelling of Mechatronic Systems with Distributed Parameter Components
PublicationThe paper presents an uniform, port-based approach to modelling of both lumped and distributed parameter systems. Port-based model of distributed system has been defined by application of the bond graph methodology and the distributed transfer function method (DTFM). The proposed method of modelling enables to formulate input data for computer analysis by application of the DTFM. The computational package for the analysis of complex...
-
An upper bound for the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent 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, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove...
-
Scanning networks with cactus topology
PublicationThe family of Pursuit and Evasion problems is widelystudied because of its numerous practical applications,ranging from communication protocols to cybernetic andphysical security. Calculating the search number of a graphis one of most commonly analyzed members of this problemfamily. The search number is the smallest number of mobileagents required to capture an invisible and arbitrarily fastfugitive, for instance piece of malicious...
-
Clonal selection in discrete optimization
PublicationW rozprawie zajmujemy się efektywnymi metodami przybliżonego rozwiązywania problemów optymalizacji dyskretnej, a w szczególności algorytmami opartymi na metodzie selekcji klonalnej (SK), należącymi do kategorii sztucznych systemów immunologicznych. Techniki optymalizacji to znaczące pole badań w informatyce, a niektóre ze starszych technik, takie jak algorytmy genetyczne, symulowane wyżarzanie czy przeszukiwanie tabu, stały się...
-
A lower bound on the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent 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, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
-
Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots
PublicationWe study two variants of delivery problems for mobile robots sharing energy. Each mobile robot can store at any given moment at most two units of energy, and whenever two robots are at the same location, they can transfer energy between each other, respecting the maximum capacity. The robots operate in a simple graph and initially each robot has two units of energy. A single edge traversal by an robot reduces its energy by one...
-
On the Hat Problem on the Cycle C7
PublicationThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can...
-
A lower bound on the total outer-independent domination number of a tree
PublicationA total outer-independent 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, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...
-
A survey on known values and bounds on the Shannon capacity
PublicationIn this survey we present exact values and bounds on the Shannon capacity for different classes of graphs, for example for regular graphs and Kneser graphs. Additionally, we show a relation between Ramsey numbers and Shannon capacity.
-
Software tool for modelling of mechatronic systems with elastic continua
PublicationThe paper presents a systematic computational package for modelling and analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The constructed computer program enables the frequency domain analysis of a class of linear systems and to obtain reduced order model in the form of bond graph. Obtained modal bond graph can be directly exported into 20-Sim package to further processing including nonlinear...
-
An upper bound on the 2-outer-independent domination number of a tree
PublicationA 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
-
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,...
-
Bounds on the vertex-edge domination number of a tree
PublicationA vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...
-
Finding small-width connected path decompositions in polynomial time
PublicationA connected path decomposition of a simple graph $G$ is a path decomposition $(X_1,\ldots,X_l)$ such that the subgraph of $G$ induced by $X_1\cup\cdots\cup X_i$ is connected for each $i\in\{1,\ldots,l\}$. The connected pathwidth of $G$ is then the minimum width over all connected path decompositions of $G$. We prove that for each fixed $k$, the connected pathwidth of any input graph can be computed in polynomial-time. This answers...
-
Weighted 2-sections and hypergraph reconstruction
PublicationIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...