Directed graphs are an intuitive and versatile representation of natural language meaning because they can capture relationships between instances of events and entities, including cases where entities play multiple roles. Yet, there are few approaches in natural language processing that use graph manipulation techniques for semantic parsing. This dissertation studies graph-based representations of natural language meaning, discusses a formal-grammar based approach to the semantic construction of graph representations, and develops methods for open-domain semantic parsing into such representations. To perform string-to-graph translation I use synchronous hyperedge replacement grammars (SHRG). The thesis studies this grammar formalism from a formal, linguistic, and algorithmic perspective. It proposes a new lexicalized variant of this formalism (LSHRG), which is inspired by tree insertion grammar and provides a clean syntax/semantics interface. The thesis develops a new method for automatically extracting SHRG and LSHRG grammars from annotated “graph banks”, which uses existing syntactic derivations to structure the extracted grammar. It also discusses a new method for semantic parsing with large, automatically extracted grammars, that translates syntactic derivations into derivations of the synchronous grammar, as well as initial work on parse reranking and selection using a graph model. I evaluate this work on the Abstract Meaning Representation (AMR) dataset. The results show that the grammar-based approach to semantic analysis shows promise as a technique for semantic parsing and that string-to-graph grammars can be induced efficiently. Taken together, the thesis lays the foundation for future work on graph methods in natural language semantics.

Worst-case analysis is often meaningless in practice. Some problems never reach the anticipated worst-case complexity. Other solutions get bogged down with impractical constants during implementation, despite having favorable asymptotic running times. In this thesis, we investigate these contrasts in the context of finding maximum flows in planar digraphs. We suggest analytic techniques that adapt to the problem instance, and present a structural property that concludes equivalence between shortest paths and maximum st-flow in planar graphs. The best known algorithm for maximum st-flow in directed planar graphs is an augmenting- paths algorithm with O(n) iterations. Using dynamic trees, each iteration can be implemented in O(log n) time. Long before, Itai and Shiloach showed that when s and t are on the boundary of a common face, the O(n)-iteration augmenting-paths algorithm is equivalent to Dijkstra's algorithm in the graph���s dual: the max st-planar st-flow problem can be solved with one single-source shortest-path computation. In this thesis we show that (a) when s and t are separated by p faces, the max st-flow can be found with at most 2p single-source shortest-path computations, which, using the linear-time shortest-paths algorithm for planar graphs, results in an O(np)-time algorithm, and (b) that the equivalence between augmenting-paths and Dijkstra's extends to the most general non-st-planar digraphs, using their half-infinite universal cover graph. / Graduation date: 2013

The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is outlined. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Finding a visually pleasing layout from a set of vertices and edges is the goal of automatic graph drawing. A requirement that has been barely explored however, is that users would like to specify portions of their layouts that are not altered by such algorithms. For example the user may have put a lot of manual effort into fixing a portion of a large layout and, while they would like an automatic layout applied to most of the layout, they do not want their work undone on the portion they manually fixed earlier. CluStic, the system developed and evaluated in this thesis, provides this capability. CluStic maintain the internal structure of a cluster by giving it priority over other elements in the graph. After high priority element has been positioned, non-priority vertices may be placed at the most appropriate remaining positions. Furthermore CluStic produces layouts which also maintain common aesthetic criteria: edge crossing minimization, layout height and edge straightening. Our method in this thesis is to first conduct an initial exploration study where we cross compare four industrial tools: Cytogate, GraphDraw, Diagram.Net and GraphNet. A set of layouts are generated with these tools and the user is timed on a task to identify the longest path. Through this exploration study we develop out intuition and determined that Cytogate is the best performing tool for longest path identification. Given this experience we fully develop CluStic and conduct our main study where we cross compare it with Cytogate and a baseline Breadth-first Search algorithm. Results show that CluStic produces drawings of good quality, Clustic achieves a visualization efficiency score of 1,4 which is an increase compared to the BFS layout (-3,8). CluStic is outperformed by Cytogate which achieves a visualization efficiency score of 1,9 and therefore produces less visually pleasing drawings. However Clustic, unlike Cytogate can preserve initial static structures, thus when a graph contains elements in which their position cannot be altered CluStic is a better choice. / Målet med automatiserad grafritning är att utifrån en uppsättning noder och kanter hitta en layout som är visuellt tillfredställande. Ett delområde som inte utforskats nog är möjligheten till att låsa vissa komponenter i grafen som sedan inte får alterneras av grafritningsalgoritmen. En användare som exempel, strukturerar vissa delar av grafen manuellt och applicerar sedan automatisk layout av resterande element utan att förstöra den struktur som manuellt skapats. CluStic, grafritningsverktyget som skapats och utvärderats i denna masters uppsats fyller denna funktion. CluStic bevarar den interna strukturen för ett kluster genom att tilldela en högre prioritet för noder i klustret med avseende på övriga element i grafen. Efter att högprioritets element placerats tilldelas resterande element sina bäst tillgängliga positioner. Utöver detta så uppfyller CluStic några av de vanligaste estetiska mål inom grafritning: minimera antalet kantkorsningar, minimera höjden, och räta ut kanter. Metoden som används i denna master uppsatts var att först gör en inledande studie där vi undersöker fyra populära grafritnings verktyg: Cytogate, GraphDraw, Diagram.Net och GraphNet. En uppsättning grafer genereras av dessa verktyg och vi mäter hur lång tid det tar för en användare att hitta den längsta vägen i grafen. Genom denna studie konstaterar vi att Cytogate presenterade grafer med best kvalitet. Från kunskap samlad i den inledande studien utvecklar vi CluStic och utför uppsatsens huvud studie där vi jämför CluStic med avseende på Cytogate och en bas layout Breddenförst algoritm. CluStic uppnår ett visualiserings effektivitetsvärde på 1,4 vilket är en ökning jämtemot Bredden-först algoritmen (-3,8). CluStic levererar inte layouter som är mer visuellt tillfredställande än de som skapats av Cytogate som får ett visualiserings effektivitetsvärde på 1,9. CluStic tillskillnad från Cytogate bevarar den internt fixa strukturen mellan element med hög prioritet vilket gör CluStic till det bättre verktyget för grafer med statiska element.

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A directed graph (digraph) G can primitively positively construct another digraph H if H is homomorphically equivalent to a first order interpretation of G that only uses primitive positive formulas. In this way, we define the poset of all finite digraphs ordered by primitive positive constructability. This poset, which is the object studied in this dissertation, is important for studying the complexity of constraint satisfaction problems and for studying clones ordered by minion homomorphisms. In this thesis I will introduce the poset and amoung other results I will present the three topmost levels of the poset and I will describe the subposet consisting of digraphs without sources or sinks.

The closed neighbourhood of a vertex in a graph is the vertex together with the set of adjacent vertices. A di®erentiating-dominating set, or identifying code, is a collection of vertices whose intersection with the closed neighbour- hoods of each vertex is distinct and nonempty. A di®erentiating-dominating set in a graph serves to uniquely identify all the vertices in the graph. Chapter 1 begins with the necessary de¯nitions and background results and provides motivation for the following chapters. Chapter 1 includes a summary of the lower identi¯cation parameters, °L and °d. Chapter 2 de- ¯nes co-distinguishable graphs and determines bounds on the number of edges in graphs which are distinguishable and co-distinguishable while Chap- ter 3 describes the maximum number of vertices needed in order to identify vertices in a graph, and includes some Nordhaus-Gaddum type results for the sum and product of the di®erentiating-domination number of a graph and its complement. Chapter 4 explores criticality, in which any minor modi¯cation in the edge or vertex set of a graph causes the di®erentiating-domination number to change. Chapter 5 extends the identi¯cation parameters to allow for orientations of the graphs in question and considers the question of when adding orientation helps reduce the value of the identi¯cation parameter. We conclude with a survey of complexity results in Chapter 6 and a collection of interesting new research directions in Chapter 7. / Mathematical Sciences / PhD (Mathematics)

The closed neighbourhood of a vertex in a graph is the vertex together with the set of adjacent vertices. A di®erentiating-dominating set, or identifying code, is a collection of vertices whose intersection with the closed neighbour- hoods of each vertex is distinct and nonempty. A di®erentiating-dominating set in a graph serves to uniquely identify all the vertices in the graph. Chapter 1 begins with the necessary de¯nitions and background results and provides motivation for the following chapters. Chapter 1 includes a summary of the lower identi¯cation parameters, °L and °d. Chapter 2 de- ¯nes co-distinguishable graphs and determines bounds on the number of edges in graphs which are distinguishable and co-distinguishable while Chap- ter 3 describes the maximum number of vertices needed in order to identify vertices in a graph, and includes some Nordhaus-Gaddum type results for the sum and product of the di®erentiating-domination number of a graph and its complement. Chapter 4 explores criticality, in which any minor modi¯cation in the edge or vertex set of a graph causes the di®erentiating-domination number to change. Chapter 5 extends the identi¯cation parameters to allow for orientations of the graphs in question and considers the question of when adding orientation helps reduce the value of the identi¯cation parameter. We conclude with a survey of complexity results in Chapter 6 and a collection of interesting new research directions in Chapter 7. / Mathematical Sciences / PhD (Mathematics)

The thesis deals with the stability studies, economic models and with their qualitative solutions. Economic problems usually face information shortage and mathematical models are too sensitive to initial values, therefore solutions provided by conventional approaches can be applied only under specific and unrealistic conditions. Qualitative reasoning and qualitative approach bring however new methods but they are following only the trends. The work presents algorithms in order to find a stabilization cycles, thus providing an insight into the most probable behavior of economic systems. By using different case studies the thesis presented broad usability of qualitative approaches and suggests a way of quantifying the stability of different models. The programmed algorithms were created in MATLAB.