The Lexicon Graph Model : a generic model for multimodal lexicon development

Trippel T. The Lexicon Graph Model : a generic model for multimodal lexicon development. Bielefeld (Germany): Bielefeld University; 2006.Das Lexicon Graph Model stellt ein Modell für Lexika dar, die korpusbasiert sein können und multimodale Informationen enthalten. Hierbei wird die Perspektive der Lexikontheorie eingenommen, wobei die zugrundeliegenden Datenstrukturen sowohl vom Lexikon als auch von Annotationen betrachtet werden. Letztere fallen dadurch in das Blickfeld, weil sie als Grundlage für die Erstellung von Lexika gesehen werden. Der Begriff des Lexikons bezieht sich hier sowohl auf den Bereich des Wörterbuchs als auch der in elektronischen Applikationen integrierten Lexikondatenbanken. Die existierenden Formalismen und Ansätze der Lexikonentwicklung zeigen verschiedene Probleme im Zusammenhang mit Lexika auf, etwa die Zusammenfassung von existierenden Lexika zu einem, die Disambiguierung von Mehrdeutigkeiten im Lexikon auf verschiedenen lexikalischen Ebenen, die Repräsentation von anderen Modalitäten im Lexikon, die Selektion des lexikalischen Schlüsselbegriffs für Lexikonartikel, etc. Der vorliegende Ansatz geht davon aus, dass sich Lexika zwar in ihrem Inhalt, nicht aber in einer grundlegenden Struktur unterscheiden, so dass verschiedenartige Lexika im Rahmen eines Unifikationsprozesses dublettenfrei miteinander verbunden werden können. Hieraus resultieren deklarative Lexika. Für Lexika können diese Graphen mit dem Lexikongraph-Modell wie hier dargestellt modelliert werden. Dabei sind Lexikongraphen analog den von Bird und Libermann beschriebenen Annotationsgraphen gesehen und können daher auch ähnlich verarbeitet werden. Die Untersuchung des Lexikonformalismus beruht auf vier Schritten. Zunächst werden existierende Lexika analysiert und beschrieben. Danach wird mit dem Lexikongraph-Modell eine generische Darstellung von Lexika vorgestellt, die auch implementiert und getestet wird. Basierend auf diesem Formalismus wird die Beziehung zu Annotationsgraphen hergestellt, wobei auch beschrieben wird, welche Maßstäbe an angemessene Annotationen für die Verwendung zur Lexikonentwicklung angelegt werden müssen.The Lexicon Graph Model provides a model and framework for lexicons that can be corpus based and contain multimodal information. The focus is more from the lexicon theory perspective, looking at the underlying data structures that are part of existing lexicons and corpora. The term lexicon in linguistics and artificial intelligence is used in different ways, including traditional print dictionaries in book form, CD-ROM editions, Web based versions of the same, but also computerized resources of similar structures to be used by applications. These applications cover systems for human-machine communication as well as spell checkers. The term lexicon in this work is used as the most generic term covering all lexical applications. Existing formalisms in lexicon development show different problems with lexicons, for example combining different kinds of lexical resources, disambiguation on different lexical levels, the representation of different modalities in a lexicon. The Lexicon Graph Model presupposes that lexicons can have different structures but have fundamentally a similar structure, making it possible to combine lexicons in a unification process, resulting in a declarative lexicon. The underlying model is a graph, the Lexicon Graph, which is modeled similar to Annotation Graphs as described by Bird and Libermann. The investigation of the lexicon formalism contains four steps, that is the analysis of existing lexicons, the introduction of the Lexicon Graph Model as a generic representation for lexicons, the implementation of the formalism in different contexts and an evaluation of the formalism. It is shown that Annotation Graphs and Lexicon Graphs are indeed related not only in their formalism and it is shown, what standards have to be applied to annotations to be usable for lexicon development

An efficient parallel algorithm for planarity

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 56-57.by Philip Nathan Klein.M.S

An efficient parallel algorithm for planarity

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 56-57.by Philip Nathan Klein.M.S

Parameterized Algorithms for String Matching to DAGs: Funnels and Beyond

The problem of String Matching to Labeled Graphs (SMLG) asks to find all the paths in a labeled graph G = (V, E) whose spellings match that of an input string S ? ?^m. SMLG can be solved in quadratic O(m|E|) time [Amir et al., JALG 2000], which was proven to be optimal by a recent lower bound conditioned on SETH [Equi et al., ICALP 2019]. The lower bound states that no strongly subquadratic time algorithm exists, even if restricted to directed acyclic graphs (DAGs). In this work we present the first parameterized algorithms for SMLG on DAGs. Our parameters capture the topological structure of G. All our results are derived from a generalization of the Knuth-Morris-Pratt algorithm [Park and Kim, CPM 1995] optimized to work in time proportional to the number of prefix-incomparable matches. To obtain the parameterization in the topological structure of G, we first study a special class of DAGs called funnels [Millani et al., JCO 2020] and generalize them to k-funnels and the class ST_k. We present several novel characterizations and algorithmic contributions on both funnels and their generalizations

Steinitz Theorems for Orthogonal Polyhedra

We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By analogy to Steinitz's theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric projection in the plane with only one hidden vertex, xyz polyhedra, in which each axis-parallel line through a vertex contains exactly one other vertex, and arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz polyhedra are exactly the bipartite cubic polyhedral graphs, and every bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of a corner polyhedron. Based on our characterizations we find efficient algorithms for constructing orthogonal polyhedra from their graphs.Comment: 48 pages, 31 figure