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The complexity of minimum-length path decompositions
PublikacjaWe 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...
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No-Wait & No-Idle Open Shop Minimum Makespan Scheduling with Bioperational Jobs
PublikacjaIn the open shop scheduling with bioperational jobs each job consists of two unit operations with a delay between the end of the first operation and the beginning of the second one. No-wait requirement enforces that the delay between operations is equal to 0. No-idle means that there is no idle time on any machine. We model this problem by the interval incidentor (1, 1)-coloring (IIR(1, 1)-coloring) of a graph with the minimum...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublikacjaConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Cooperative Word Net Editor for Lexical Semantic Acquisition
PublikacjaThe article describes an approach for building Word Net semantic dictionary in a collaborative approach paradigm. The presented system system enables functionality for gathering lexical data in a Wikipedia-like style. The core of the system is a user-friendly interface based on component for interactive graph navigation. The component has been used for Word Net semantic network presentation on web page, and it brings functionalities...
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Zastosowanie odcinków nieliniowej krzywizny w torze zwrotnym rozjazdu kolejowego
PublikacjaW pracy została przedstawiona analityczna metoda kształtowania toru zwrotnego rozjazdu kolejowego posiadającego na swojej długości odcinki nieliniowej krzywizny. Odcinki te służą łagodzeniu wykresu krzywizny w skrajnych strefach rozjazdu W omawianej metodzie dokonano identyfikacji problemu rozkładu krzywizny za pomocą równań różniczkowych. Uzyskane rozwiązania mają charakter uniwersalny; m. in. pozwalają na przyjmowanie dowolnych...
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Reliability of production machines in the bakery industry – theoretical and practical issues
PublikacjaThe aim of the article is to present probabilistic models, which were then used to analyze the reliability of production machines in the baking industry. The author conducted research in the period from January 2, 2016 to December 31, 2018 regarding the measurement of reliability of a traditional production system based on a probabilistic concept. Due to the limited scope of the article, reliability calculations for a set of thermo-oil...
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Proposal of a method for effective tasks distribution in the execution of compolex problems
PublikacjaAn access to a great number of various services allows for decomposition of complex problems into smaller and less complex tasks. Those tasks can be presented in a form of a dependency graph. This paper shows an idea of executing such a problem using cooperating autonomous agents. Main focus of this work is cooperation covering effective tasks distribution among executors. This paper presents an algorithm for dynamic executor selection...
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Study of the Flow Dynamics of Surface Water Masses in the Area of the Coastal Gulf of Gdansk
PublikacjaThe paper describes two methods of predicting the movement of small objects with surface water masses. One of the methods uses graph theory to describe the motion of water masses in port docks. The results of this study were compared to a simulation using the hydrodynamic numerical model M3D. The results obtained in a virtual environment were related to the experiments in the real world. In the coastal area of the Gulf of Gdansk,...
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ProSIL Software for functional saferty management in life cycle = Aplikacja ProSIL do zarządzania bezpieczeństwem funkcjonalnym w cyklu życia
PublikacjaIn the paper the ProSIL software to aid the functional safety management is presented. The software consists of three modules to aid: determination of the required SIL level (ProSILen), veryfication of the SIL level (ProSILver). In the aplication the method of the calibrated risk graph to determine the required safety integrity level SIL for defined safety instrumented functions is applied. The methods concerning functional safety...
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Port-Based Modelling of Distributed-Lumped Parameter Systems
PublikacjaThere in the paper is presented an uniform, port-based approach to modelling of both lumped and distributed parameter systems. Port-based model of the distributed system has been defined by application of bond graph methodology and distributed transfer function method (DTFM). The approach proposed combines versatility of port-based modelling and accuracy of distributed transfer function method. The concise representation of lumped-distributed...
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Polyhedral Ramsey Numbers
PublikacjaGiven 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...
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Chromatic cost coloring of weighted bipartite graphs
PublikacjaGiven 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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Rearrangeability in multicast Clos networks is NP-complete
PublikacjaPrzestrajalność 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...
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Certified domination
PublikacjaImagine 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...
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On-line Search in Two-Dimensional Environment
PublikacjaWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph...
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A city is not a tree: a multi-city study on street network and urban life
PublikacjaChristopher Alexander, a British-American scholar, differentiated an old (natural) city from a new (planned) one by structure. The former resembles a “semilattice”, or a complex system encompassing many interconnected sub-systems. The latter is shaped in a graph-theoretical “tree”, which lacks the structural complexity as its sub-systems are compartmentalized into a single hierarchy. This structural distinction explains why, or...
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublikacjaFor 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 in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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On trees with equal domination and total outer-independent domination numbers
PublikacjaFor a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
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Characterizing the Performance of <span class="sc">xor</span> Games and the Shannon Capacity of Graphs
PublikacjaIn this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party xor game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games...
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Asynchronous Networked Estimation System for Continuous Time Stochastic Processes
PublikacjaIn this paper we examine an asynchronous networked estimation system for state estimation of continuous time stochastic processes. Such a system is comprised of several estimation nodes connected using a possibly incomplete communication graph. Each of the nodes uses a Kalman filter algorithm and data from a local sensor to compute local state estimates of the process under observation. It also performs data fusion of local estimates...
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Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
PublikacjaThe problem of scheduling n identical jobs on 4 uniform machines with speeds s1>=s2>=s3>=s4 is considered.The aim is to find a schedule with minimum possible length. We assume that jobs are subject to mutual exclusion constraints modeled by a bipartite incompatibility graph of degree delta. We show that the general problem is NP-hard even if s1=s2=s3. If, however, delta<5 and s1>12s2 s2=s3=s4, then the problem can be solved to...
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Błędy w przedstawianiu wyników pomiarów i wartości wielkości fizycznych popełniane w pracach studenckich
PublikacjaArtykuł powstał na bazie doświadczeń zdobytych podczas pracy dydaktycznej autora jako wykładowcy i nauczyciela akademickiego prowadzącego zajęcia w Laboratorium Podstaw Metrologii. Przytoczono przykłady nieprawidłowości w przedsta-wianiu wyników pomiarów i wartości wielkości fizycznych pochodzące z prac pisemnych studentów i skonfrontowano je z zaleceniami Międzynarodowego Układu Jednostek Miar (SI), oraz polskimi aktami prawnymi.
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Ontology-Driven Rule-Based Model for an Extension of Information Technology Infrastructure Library Processes
PublikacjaThe aim of this study is to present the stages for building a development model to create information technology (IT) systems for IT service providers. In order to ensure the consistency of the model, a novel solution is proposed where the stages of the model's construction are controlled using ontologies dedicated to the ITIL standard. In this article, a description of models used to assess the provider organization, with particular...
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The application of nonlinear curvature sections in the turnout diverging track
PublikacjaThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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Bipartite theory of graphs: outer-independent domination
PublikacjaLet $G = (V,E)$ be a bipartite graph with partite sets $X$ and $Y$. Two vertices of $X$ are $X$-adjacent if they have a common neighbor in $Y$, and they are $X$-independent otherwise. A subset $D \subseteq X$ is an $X$-outer-independent dominating set of $G$ if every vertex of $X \setminus D$ has an $X$-neighbor in $D$, and all vertices of $X \setminus D$ are pairwise $X$-independent. The $X$-outer-independent domination number...
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Distributed state estimation using a network of asynchronous processing nodes
PublikacjaWe consider the problem of distributed state estimation of continuous-time stochastic processes using a~network of processing nodes. Each node performs measurement and estimation using the Kalman filtering technique, communicates its results to other nodes in the network, and utilizes similar results from the other nodes in its own computations. We assume that the connection graph of the network is not complete, i.e. not all nodes...
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Parallel Computations of Text Similarities for Categorization Task
PublikacjaIn this chapter we describe the approach to parallel implementation of similarities in high dimensional spaces. The similarities computation have been used for textual data categorization. A test datasets we create from Wikipedia articles that with their hyper references formed a graph used in our experiments. The similarities based on Euclidean distance and Cosine measure have been used to process the data using k-means algorithm....
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Distributed state estimation using a network of asynchronous processing nodes
PublikacjaWe consider the problem of distributed state estimation of continuous-time stochastic processes using a~network of processing nodes. Each node performs measurement and estimation using the Kalman filtering technique, communicates its results to other nodes in the network, and utilizes similar results from the other nodes in its own computations. We assume that the connection graph of the network is not complete, i.e. not all nodes...
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Global edge alliances in graphs
PublikacjaIn the paper we introduce and study a new problem of finding a minimum global edge alliance in a graph which is related to the global defensive alliance (Haynes et al., 2013; Hedetniemi, 2004) and the global defensive set (Lewoń et al., 2016). We proved the NP-completeness of the global edge alliance problem for subcubic graphs and we constructed polynomial time algorithms for trees. We found the exact values of the size of the...
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Big Data i 5V – nowe wyzwania w świecie danych (Big Data and 5V – New Challenges in the World of Data)
PublikacjaRodzaje danych, składające się na zbiory typu Big Data, to m.in. dane generowane przez użytkowników portali internetowych, dane opisujące transakcje dokonywane poprzez Internet, dane naukowe (biologiczne, astronomiczne, pomiary fizyczne itp.), dane generowane przez roboty w wyniku automatycznego przeszukiwania przez nie Internetu (Web mining, Web crawling), dane grafowe obrazujące powiązania pomiędzy stronami WWW itd. Zazwyczaj,...
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Knowledge-based functional safety management using ProSIL software
PublikacjaIn the article the ProSIL software for computer aided functional safety management is presented. The software consists of three modules for the determination of the required SIL level (ProSILen) and verification of the SIL level (ProSILver). In the ProSIL the calibrated knowledge-based risk graph method for determining the required safety integrity level (SIL) of the safety functions identified in hazard analysis is implemented....
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Mitigation of Fake Data Content Poisoning Attacks in NDN via Blockchain
PublikacjaAbstract—Information-centric networks struggle with content poisoning attacks (CPAs), especially their stronger form called Fake Data CPA, in which an intruder publisher uploads content signed with stolen credentials. Following an existing graphinfection based approach leveraging the constrained time when stolen credentials are useful, we design a blockchain-based mitigation scheme for Named Data Networking architectures. We postulate...
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An O ( n log n ) algorithm for finding edge span of cacti
PublikacjaLet G=(V,E) be a nonempty graph and xi be a function. In the paper we study the computational complexity of the problem of finding vertex colorings c of G such that: (1) |c(u)-c(v)|>=xi(uv) for each edge uv of E; (2) the edge span of c, i.e. max{|c(u)-c(v)|: uv belongs to E}, is minimal. We show that the problem is NP-hard for subcubic outerplanar graphs of a very simple structure (similar to cycles) and polynomially solvable for...
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Hat problem on the cycle C4
PublikacjaThe topic of our paper is the hat problem. In that problem, each of n people is randomly tted with a blue or red hat. Then everybody can try to guess simultanously his own hat color looking at the hat colors of the other people. The team wins if at least one person 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 win. In this version every...
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The hat problem on a union of disjoint graphs
PublikacjaThe 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 winning. In this version every player...
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Global defensive secure structures
PublikacjaLet 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...
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Modal energy identification of large stucture idealised by the finite element method
PublikacjaPrzedstawiono metodę określania energii drgań układów dyskretnych otrzyma-nych w wyniku modelowania metodą elementów skończonych wybranych fragmentów konstrukcji samochodów. W odróżnieniu od poprzednio stosowanych podejść, ro-zważa się całkowite energie mechaniczne odpowiadające poszczególnym posta-ciom drgań własnych. Całkowitą energię mechaniczną oblicza się na podstawie parametrów modelu modalnego. Energię mechaniczną można...
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On the super domination number of lexicographic product graphs
PublikacjaThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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Graphs with equal domination and certified domination numbers
PublikacjaA setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...
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On the partition dimension of trees
PublikacjaGiven an ordered partition Π={P1,P2,…,Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),…,d(v,Pt)), where d(v,Pi) represents the distance between the vertex vv and the set Pi. A partition Π of V is a resolving partition of G if different vertices of G have different partition representations, i.e., for every...
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Applying case studies to teaching architectural investment
PublikacjaCase studies enable students to encounter practical issues during their education. Experiments conducted in class employing this method often feature simplified models of real-world situations. However, they still enable students to encounter actual problems, to which theoretical knowledge is applied. In architectural education, students carrying out semester projects usually rely on data provided by the teacher, without wondering...
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Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks
PublikacjaUncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof....
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Dobór optymalnej liczby jednostek funcjonalnych dla realizacji syntezy wysokiego poziomu układów cyfrowych
PublikacjaW pracy przedstawiono algorytm MNP (ang. minimization the number of procesing elements) wyznaczający liczbę jednostek funkcjonalnych niezbędnych do syntezy wysokiego poziomu zadania opisanego grafem przepływu danych (DFG - ang. data flow graph). Liczba jednostek funkcjonalnych wyznaczana przez prezentowany algorytm jest optymalna zarówno z punktu widzenia kosztów wykonania układu, jak i szybkości jego działania. Rozwiązanie tego...
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On a matching distance between rooted phylogenetic trees
PublikacjaThe 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...
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Extending Service Selection Algorithms with Interoperability Analysis
PublikacjaApplication development by integration of existing, atomic services reduces development cost and time by extensive reuse of service components. In Service Oriented Architecture, there exist alternative versions of services supplying the same functionality but differing in Quality of Service (QoS) attributes, which enables developers to select services with optimal QoS. Existing algorithms of service selection focus on the formal...
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Comparing Phylogenetic Trees by Matching Nodes Using the Transfer Distance Between Partitions
PublikacjaAbility to quantify dissimilarity of different phylogenetic trees describing the relationship between the same group of taxa is required in various types of phylogenetic studies. For example, such metrics are used to assess the quality of phylogeny construction methods, to define optimization criteria in supertree building algorithms, or to find horizontal gene transfer (HGT) events. Among the set of metrics described so far in...
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Research into the Movements of Surface Water Masses in the Basins Adjacent to the Port
PublikacjaThis paper presents the results of the practical and simulation research into determining the routes of movement of small objects moving together with surface water masses in basins adjacent to the port. The results of this research were referenced against the modelling of routes of small objects in port channel basins. The results of practical research concerning the movement of small objects in basins adjacent to the port were...
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Synchronous black hole search in directed graphs
PublikacjaThe paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one...
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublikacjaIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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A model, design, and implementation of an efficient multithreaded workflow execution engine with data streaming, caching, and storage constraints
PublikacjaThe paper proposes a model, design, and implementation of an efficient multithreaded engine for execution of distributed service-based workflows with data streaming defined on a per task basis. The implementation takes into account capacity constraints of the servers on which services are installed and the workflow data footprint if needed. Furthermore, it also considers storage space of the workflow execution engine and its cost....