Topics in Graph Algorithms: Structural Results and Algorithmic Techniques, with Applications

Coping with computational intractability has inspired the development of a variety of algorithmic techniques. The main challenge has usually been the design of polynomial time algorithms for NP-complete problems in a way that guarantees some, often worst-case, satisfactory performance when compared to exact (optimal) solutions. We mainly study some emergent techniques that help to bridge the gap between computational intractability and practicality. We present results that lead to better exact and approximation algorithms and better implementations. The problems considered in this dissertation share much in common structurally, and have applications in several scientific domains, including circuit design, network reliability, and bioinformatics. We begin by considering the relationship between graph coloring and the immersion order, a well-quasi-order defined on the set of finite graphs. We establish several (structural) results and discuss their potential algorithmic consequences. We discuss graph metrics such as treewidth and pathwidth. Treewidth is well studied, mainly because many problems that are NP-hard in general have polynomial time algorithms when restricted to graphs of bounded treewidth. Pathwidth has many applications ranging from circuit layout to natural language processing. We present a linear time algorithm to approximate the pathwidth of planar graphs that have a fixed disk dimension. We consider the face cover problem, which has potential applications in facilities location and logistics. Being fixed-parameter tractable, we develop an algorithm that solves it in time O(5k + n2) where k is the input parameter. This is a notable improvement over the previous best known algorithm, which runs in O(8kn). In addition to the structural and algorithmic results, this text tries to illustrate the practicality of fixed-parameter algorithms. This is achieved by implementing some algorithms for the vertex cover problem, and conducting experiments on real data sets. Our experiments advocate the viewpoint that, for many practical purposes, exact solutions of some NP-complete problems are affordable

Studies in Strindberg

In this volume Strindberg's accomplishments as a dramatist are set against his achievements in other fields, as an autobiographer, painter, letter writer and theatre director. There are studies of individual plays, in which Strindberg's theatre is related both to naturalism and the theatre of the absurd, and of the role played by his life-long interest in historical drama. Other essays range from studies of the problems posed by Strindberg's preoccupation with converting his own life into literature to a consideration of the importance he placed on letterwriting as a model for writing of all kinds. His letters are also used to explore his ideas about the theatre. A recurring concern is with the period of turmoil known as the Inferno Crisis, in which Strindberg refashioned himself as a writer. Robinson examines the importance of Strindberg's painting for his renewal as a writer and situates the achievement of his later works in relation to Symbolism and to Musical Expressionism. (DOI: 10.5334/bac

Alʔilbīrī’s Book of the rational conclusions. Introduction, Critical Edition of the Arabic Text and Materials for the History of the Ḫawāṣṣic Genre in Early Andalus

[eng] The Book of the rational conclusions, written perhaps somewhen in the 10th c. by a physician from Ilbīrah (Andalus), is a multi-section medical pandect. The author brings together, from a diversity of sources, materials dealing with matters related to drug-handling, natural philosophy, therapeutics, medical applications of the specific properties of things, a regimen, and a dispensatory. This dissertation includes three different parts. First the transmission of the text, its contents, and its possible context are discussed. Then a critical edition of the Arabic text is offered. Last, but certainly not least, the subject of the specific properties is approached from several points of view. The analysis of Section III of the original book leads to an exploration of the early Andalusī assimilation of this epistemic tradition and to the establishment of a well-defined textual family in which our text must be inscribed. On the other hand, the concept itself of ‘specific property’ is often misconstrued and it is usually made synonymous to magic and superstition. Upon closer inspection, however, the alleged irrationality of the knowledge of these properties appears to be largely the result of anachronistic interpretation. As a complement of this particular research and as an illustration of the genre, a sample from an ongoing integral commentary on this section of the book is presented.[cat] El Llibre de les conclusions racionals d’un desconegut metge d’Ilbīrah (l’Àndalus) va ser compilat probablement durant la segona meitat del s. X. Es tracta d’un rudimentari però notablement complet kunnaix (un gènere epistèmic que és definit sovint com a ‘enciclopèdia mèdica’) en què l’autor aplega materials manllevats (sovint de manera literal i no-explícita) de diversos gèneres. El llibre obre amb una secció sobre apoteconomia (una mena de manual d’apotecaris) però se centra després en les diferents branques de la medicina. A continuació d’uns prolegòmens filosòfics l’autor copia, amb mínima adaptació lingüística, un tractat sencer de terapèutica, després un altre sobre les aplicacions mèdiques de les propietats específiques de les coses, una sèrie de fragments relacionats amb la dietètica (un règim en termes tradicionals) i, finalment, una col·lecció de receptes mèdiques. Cadascuna d’aquestes seccions mostren evidents lligams d’intertextualitat que apunten cap a una intensa activitat sintetitzadora de diverses tradicions aliades a la medicina a l’Àndalus califal. El text és, de fet, un magnífic objecte sobre el qual aplicar la metodologia de la crítica textual i de fonts. L’edició crítica del text incorpora la dimensió cronològica dins l’aparat, que esdevé així un element contextualitzador. Quant l’estudi de les fonts, si tot al llarg de la primera part d’aquesta tesi és només secundari, aquesta disciplina pren un protagonisme gairebé absolut en la tercera part, especialment en el capítol dedicat a l’anàlisi individual de cada passatge recollit en la secció sobre les propietats específiques de les coses

Bowdoin Orient v.76, no.1-19 (1946-1947)

https://digitalcommons.bowdoin.edu/bowdoinorient-1940s/1007/thumbnail.jp