58,907 research outputs found
On the probabilistic min spanning tree Problem
No full textInternational audienceWe study a probabilistic optimization model for min spanning tree, where any vertex v i of the input-graph G(V, E) has some presence probability p i in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any GG is optimal for G′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively
No advantageous merging in minimum cost spanning tree problems
No full textIn the context of cost sharing in minimum cost spanning tree problems, we introduce a property called No Advantageous Merging. This property implies that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using No Advantageous Merging.Minimum cost spanning tree problems; cost sharing; Bird rule; No Advantageous Merging
A declarative characterization of different types of multicomponent tree adjoining grammars
No full textMulticomponent Tree Adjoining Grammars (MCTAGs) are a formalism that has been shown to be useful for many natural language applications. The definition of non-local MCTAG however is problematic since it refers to the process of the derivation itself: a simultaneity constraint must be respected concerning the way the members of the elementary tree sets are added. Looking only at the result of a derivation (i.e., the derived tree and the derivation tree), this simultaneity is no longer visible and therefore cannot be checked. I.e., this way of characterizing MCTAG does not allow to abstract away from the concrete order of derivation. In this paper, we propose an alternative definition of MCTAG that characterizes the trees in the tree language of an MCTAG via the properties of the derivation trees (in the underlying TAG) the MCTAG licences. We provide similar characterizations for various types of MCTAG. These characterizations give a better understanding of the formalisms, they allow a more systematic comparison of different types of MCTAG, and, furthermore, they can be exploited for parsing
A declarative characterization of different types of multicomponent tree adjoining grammars
No full textMulticomponent Tree Adjoining Grammars (MCTAG) is a formalism that has been shown to be useful for many natural language applications. The definition of MCTAG however is problematic since it refers to the process of the derivation itself: a simultaneity constraint must be respected concerning the way the members of the elementary tree sets are added. This way of characterizing MCTAG does not allow to abstract away from the concrete order of derivation. In this paper, we propose an alternative definition of MCTAG that characterizes the trees in the tree language of an MCTAG via the properties of the derivation trees (in the underlying TAG) the MCTAG licences. This definition gives a better understanding of the formalism, it allows a more systematic comparison of different types of MCTAG, and, furthermore, it can be exploited for parsing
Modeling Compatible Single-Tree Aboveground Biomass Equations of Masson Pine (Pinus massoniana) in South China
No full textIn the background of facing up to the global climate change, it is becoming the inevitable demand to add forest biomass estimation to national forest resource monitoring. The biomass equations to be developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine (Pinus Massoniana Lamb.) in south China, the one, two and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations were constructed using the error-in-variable simultaneous equations in this paper. The results showed: (i) the prediction precision of aboveground biomass estimates from one variable equation was more than 95%; (ii) the regressions of aboveground biomass equations improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically significant; (iii) for biomass conversion function on one variable, the conversion factor was decreased with growing diameter, but for conversion function on two variables, the factor was increased with growing diameter while decreased with growing tree height
Tree parsing with synchronous tree-adjoining grammars
No full textRestricting the input or the output of a grammar-induced translation to a given set of trees plays an important role in statistical machine translation. The problem for practical systems is to find a compact (and in particular, finite) representation of said restriction. For the class of synchronous tree adjoining grammars, partial solutions to this problem have been described, some being restricted to the unweighted case, some to the monolingual case. We introduce a formulation of this class of grammars which is effectively closed under input and output restrictions to regular tree languages, i.e., the restricted translations can again be represented by grammars. Moreover, we present an algorithm that constructs these grammars for input and output restriction, which is inspired by Earley’s algorithm
Suffix Tree Construction and Storage with Limited Main Memory
No full textSchürmann K-B, Stoye J. Suffix Tree Construction and Storage with Limited Main Memory. Forschungsberichte. Bielefeld: Technische Fakultät der Universität Bielefeld; 2003.Suffix trees have been established as one of the most versatile index structures for unstructured string data like genomic sequences and other strings. In this work, our goal is the development of algorithms for the efficient construction of suffix trees for very large strings and their convenient storage regarding fast access when main memory is limited. We present a construction algorithm which, to the best of our knowledge, is currently the fastest practical construction method for large suffix trees.
Further we propose a clustered storage scheme for the suffix tree that takes into account the locality behavior of typical query types, which leads to a significant speed-up particularly for the exact string matching problem. For very large strings the query time is faster than that of other recent index structures like the enhanced suffix array
Estimation of tree lists from airborne laser scanning by combining single-tree and area-based methods
No full textIndividual tree crown segmentation from airborne laser scanning (ALS) data often fails to detect all trees depending on the forest structure. This paper presents a new method to produce tree lists consistent with unbiased estimates at area level. First, a tree list with height and diameter at breast height (DBH) was estimated from individual tree crown segmentation. Second, estimates at plot level were used to create a target distribution by using a k-nearest neighbour (k-NN) approach. The number of trees per field plot was rescaled with the estimated stem volume for the field plot. Finally, the initial tree list was calibrated using the estimated target distribution. The calibration improved the estimates of the distributions of tree height (error index (EI) from 109 to 96) and DBH (EI from 99 to 93) in the tree list. Thus, the new method could be used to estimate tree lists that are consistent with unbiased estimates from regression models at field plot level
Phylogram derived from combined <i>T. cati</i> and <i>T. canis</i> data, which strongly support the placement of <i>T. cati</i> and <i>T. canis</i> in distinct species, although they are supposedly an anamorph/teleomorph pair; (A) Un-rooted tree, (B) Rooted tree.
No full text<p>Phylogram derived from combined <i>T. cati</i> and <i>T. canis</i> data, which strongly support the placement of <i>T. cati</i> and <i>T. canis</i> in distinct species, although they are supposedly an anamorph/teleomorph pair; (A) Un-rooted tree, (B) Rooted tree.</p
Finding the Two-Core of a Tree
No full textThe 1-core of a graph is a path minimizing the sum of the distances of all vertices of the graph from the path. A linear algorithm for finding a 1-core of a tree was presented by Morgan and Slater. The problem for general graphs is NP-Hard. A 2-core of a graph is a set of two paths minimizing the sum of the distances of all vertices of the graph from any of the two paths. We consider both cases of disjoint paths and intersecting paths for a tree. Interesting relations between 1-core and 2-core of a tree are found. These relations imply efficient algorithms for finding the 2-core. The complexity of the algorithms is O(IVI.d(T)) where d(T) is the number of edges in the diameter of the tree. These algorithms are applicable for routing highways in a system of roads. A w-point core is a path minimizing the sum of the distances of all vertices of the graph from either the vertex w or the path. A linear algorithm for finding a w-point core of a tree is presented. It is applied as a procedure for the previous algorithms.Technical report DCS-TR-12
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