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Construction of a picewise-linear classifier by applaing discriminant analysis to decision tree induction
PublikacjaArtykuł prezentuje metodę konstrukcji drzew decyzyjnych. W odróżnieniu od większości popularnych algorytmów, które wybierają pojedyncze cechy do budowy reguł decyzyjnych w węzłach drzewa, ta metoda łączy wszystkie cechy. Używa ona wieloklasowego kryterium Fishera do wydzielenia nowych cech, które są liniowa kombinacją cech pierwotnych. Takie drzewa mogą aproksymować złożone regiony decyzyjne używając mniejszej liczby węzłów w porównaniu...
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Improving all-reduce collective operations for imbalanced process arrival patterns
PublikacjaTwo new algorithms for the all-reduce operation optimized for imbalanced process arrival patterns (PAPs) are presented: (1) sorted linear tree, (2) pre-reduced ring as well as a new way of online PAP detection, including process arrival time estimations, and their distribution between cooperating processes was introduced. The idea, pseudo-code, implementation details, benchmark for performance evaluation and a real case example...
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All-gather Algorithms Resilient to Imbalanced Process Arrival Patterns
PublikacjaTwo novel algorithms for the all-gather operation resilient to imbalanced process arrival patterns (PATs) are presented. The first one, Background Disseminated Ring (BDR), is based on the regular parallel ring algorithm often supplied in MPI implementations and exploits an auxiliary background thread for early data exchange from faster processes to accelerate the performed all-gather operation. The other algorithm, Background Sorted...
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The complexity of bicriteria tree-depth
PublikacjaThe 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...
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On extremal sizes of locally k-tree graphs
PublikacjaA graph G is a locally k-tree graph if for any vertex v the subgraph induced by the neighbours of v is a k-tree, k>=0, where 0-tree is an edgeless graph, 1-tree is a tree. We characterize the minimum-size locally k-trees with n vertices. The minimum-size connected locally k-trees are simply (k + 1)-trees. For k >= 1, we construct locally k-trees which are maximal with respect to the spanning subgraph relation. Consequently, the...
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Evaluation of the content of inorganic anions in tree saps
PublikacjaTree saps were once commonly used in the countries of Northern, Central and Eastern Europe. Although once almost forgotten, their popularity has been growing recently as part of an interest in organic food and traditional medicine. Tree saps, tapped mainly from birch and maple trees, are drunk both fresh and fermented or are used as raw material for the production of food products, e.g. syrups. The aim of this study was to determine...
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The reliability of tree and star networks
PublikacjaThis paper investigated the reliability of tree and star networks. Following measures of network reliability are assumed: the expected number of nodes, that can communicate with the central node; the expected number of node pairs, that are connected by a path through the central node; the expected number of node pairs communicating.
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Empirical analysis of tree-based classification models for customer churn prediction
PublikacjaCustomer churn is a vital and reoccurring problem facing most business industries, particularly the telecommunications industry. Considering the fierce competition among telecommunications firms and the high expenses of attracting and gaining new subscribers, keeping existing loyal subscribers becomes crucial. Early prediction of disgruntled subscribers can assist telecommunications firms in identifying the reasons for churn and...
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Incremental construction of Minimal Tree Automata [online]
PublikacjaWe describe an algorithm that allows the incremental addition or removal of unranked ordered trees to minimal frontier-to-root deterministic tree automaton (DTA). The algorithm takes a tree t and a minimal DTA A as input; it outputs a minimal DTA A' which accepts the language L(A) accepted by A incremented (or decremented) with the tree t. The algorithm can be used to efficiently maintain dictionaries which store large collections...
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The reliability of tree and star networks.
PublikacjaOne of the important parameters characterizing the quality of computer networks is the network's reliability with respect to failures of the communication links and nodes. This chapter investigated the reliability of tree and star networks. The tree and star topology is used in centralized computer networks. In centralized computer networks all communication must take place through some central computer. Following measures of network...
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Average Size of a Suffix Tree for Markov Sources
PublikacjaWe study a suffix tree built from a sequence generated by a Markovian source. Such sources are more realistic probabilistic models for text generation, data compression, molecular applications, and so forth. We prove that the average size of such a suffix tree is asymptotically equivalent to the average size of a trie built over n independentsequences from the same Markovian source. This equivalenceis only known for memoryless...
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Perfect hashing tree automata
PublikacjaWe present an algorithm that computes a function that assigns consecutive integers to trees recognized by a deterministic, acyclic, finite-state, bottom-up tree automaton. Such function is called minimal perfect hashing. It can be used to identify trees recognized by the automaton. Its value may be seen as an index in some other data structures. We also present an algorithm for inverted hashing.Przedstawiamy algorytm, który oblicza...
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An Algorithm for Listing All Minimal 2-Dominating Sets of a Tree
PublikacjaWe provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time O(1.3248n) . This implies that every tree has at most 1.3248 n minimal 2-dominating sets. We also show that this bound is tigh.
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An algorithm for listing all minimal double dominating sets of a tree
PublikacjaWe provide an algorithm for listing all minimal double dominating sets of a tree of order $n$ in time $\mathcal{O}(1.3248^n)$. This implies that every tree has at most $1.3248^n$ minimal double dominating sets. We also show that this bound is tight.
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MINERAL CONTENT OF TREE SAP FROM THE SUBCARPATHIAN REGION
Publikacjabut also as medicinal substance in folk medicine. Traditionally, it was used to treat various conditions, mostly anaemia and chronic fatigue. This study has been designed to establish the content of metallic elements (sodium, potassium, calcium, magnesium, zinc and copper) in sap collected from eight different species (silver birch, downy birch, hornbeam, Norway maple, boxelder maple, black walnut, black alder and white willow)...
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Bounds on the vertex-edge domination number of a tree
PublikacjaA 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...
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Atmospheric deposition in coniferous and deciduous tree stands in Poland
PublikacjaThe objective of this study was to assess the transformation of precipitation in terms of quantity and chemical composition following contact with the crown layer in tree stands with varied species composition, to investigate the effect of four predominant forest-forming species (pine, spruce, beech, and oak) on the amount and composition of precipitation reaching forest soils, and to determine the sources of pollution in atmospheric...
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Gossiping by energy-constrained mobile agents in tree networks
PublikacjaEvery node of an edge-weighted tree network contains a data packet. At some nodes are placed mobile agents, each one possessing an amount of energy (not necessarily the same for all agents). While walking along the network, the agents spend the energy proportionally to the distance traveled and collect copies of the data packets present at the visited network nodes. An agent visiting a node deposits there copies of all currently...
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Perfect hashing with pseudo-minimal bottom-up deterministic tree automata
PublikacjaWe describe a technique that maps unranked trees to their hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to techniques implemented with minimal tree automata, our procedure builds a pseudo-minimal DTA. Pseudo-minimal automata are larger than the minimal ones but in turn the mapping can be arbitrary, so it can be determined prior to the automaton construction. We also provide procedures to build incrementally...
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A lower bound on the total outer-independent domination number of a tree
PublikacjaA 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,...