Implementing path coloring algorithms on planar graphs

Master's Project (M.S.) University of Alaska Fairbanks, 2017A path coloring of a graph partitions its vertex set into color classes such that each class induces a disjoint union of paths. In this project we implement several algorithms to compute path colorings of graphs embedded in the plane. We present two algorithms to path color plane graphs with 3 colors based on a proof by Poh in 1990. First we describe a naive algorithm that directly follows Poh's procedure, then we give a modified algorithm that runs in linear time. Independent results of Hartman and Skrekovski describe a procedure that takes a plane graph G and a list of 3 colors for each vertex, and computes a path coloring of G such that each vertex receives a color from its list. We present a linear time implementation based on Hartman and Skrekovski's proofs. A C++ implementation is provided for all three algorithms, utilizing the Boost Graph Library. Instructions are given on how to use the implementation to construct colorings for plane graphs represented by Boost data structures

The Construction of Quantitative Indicators for Internal Comparisons

The paper illuminates the necessity for developing internationally consistent statistical and methodological practices required to perform meaningful national and international, particularly East-West, comparative analyses. It addresses the susceptibility of inaccurate and delayed quantification and identification of phenomena in the social sciences as a result of the strict use of conventional indicators and methods of analysis. Throughout the paper, the theme alludes to the urgency to unify the previously divergent "eastern" and "western" economic thinking to facilitate the development of usable international economic comparisons. The lack of common measures and adequate data results in a deficiency of East-West quantitative comparative studies. The content also encompasses a very concise review of the present methodologies available for using statistical data and developing traditional and, more or less, non-traditional indicators. In reference to this topic, special emphasis is given to the problems and dilemmas of interpreting change in transitional economies, which certainly cannot be solely described by conventional indicators used during an era of stability. Dissatisfaction among experts with the state of existing measurement and monitoring techniques of different aspects of socio-economic development has lead to an on-going construction of now, non-traditional indicators. These attempts are themselves evidence for the heterogeneous manner of approaching essentially the common goal of developing more trustworthy and meaningful indicators. The desire is to find a process of measurement that is applicable in transition phases as well as stabilized phases of socio-economic development. For precisely this reason, the author favors the linguistic methodology, which is presently the principal approach used in the IIASA Economic Reform and Integration Project for the construction of integral quantitative indicators oriented towards East-West comparative analysis. Finally, he addresses the substance and sequence of the research expected to be performed within the Project

A risk science perspective on the discussion concerning Safety I, Safety II and Safety III

Recently, there has been a discussion in the safety science community concerning the validity of basic approaches to safety, referred to as Safety I, Safety II and Safety III, with Erik Hollnagel and Nancy Leveson in leading roles. The present paper seeks to obtain new knowledge concerning the issues raised, by adding a contemporary risk science perspective to the discussion. Risk is, to a limited degree, addressed in the literature presenting and studying these three approaches; however, as argued in the paper, the concept of risk and risk analysis and management principles and methods are highly relevant and useful for understanding the three safety approaches, deciding on their suitability, and eventually applying them. The paper underlines the importance of an integration of the safety and risk sciences, to further enhance concepts, approaches, principles, methods and models for understanding, assessing, communicating and managing system performance.publishedVersio

A risk and safety science perspective on the precautionary principle

The precautionary principle is strongly debated as a policy for handling risk and safety concerns. It is commonly claimed that the principle is paralyzing, unscientific and promotes a culture of irrational fear. The risk and safety literature contains considerable work providing support for such claims but also argumentation backing the principle. The present paper aims at contributing to this discussion by investigating the principle in view of what is here referred to as contemporary risk and safety science. Common beliefs about the principle are revisited. New insights are obtained by clarifying the risk and safety fundamentals necessary to understand the principle’s motivation, applicability and limitations. The paper concludes that the precautionary principle is only relevant when the uncertainties and risks are considerable and scientific. Confusion arises, as the principle is mixed with the basic idea of risk management to give weight to uncertainties, in order to prudently handle risk. Properly understood and implemented, the precautionary principle can be aligned with decision analysis and other scientific methods.publishedVersio

Risk literacy : Foundational issues and its connection to risk science

A new research area is developing, risk literacy. The term “risk literacy” basically refers to one's ability to understand and evaluate risk, in order to support and make appropriate decisions. In this article, we discuss how risk literacy relates to risk analysis/science with its topics of risk fundamentals (concepts), risk understanding, risk assessments, risk characterizations, risk perception, risk communication, and risk handling (covering risk management, risk governance, and policies on risk). We question how issues and research topics addressed in risk literacy relate to risk analysis/science knowledge, particularly on risk understanding. The main conclusion of the article is that risk literacy addresses an important topic—from both a theoretical and a practical societal relevancy perspective—and brings the potential for many additional developments and further insights if the topic is better integrated with risk science knowledge more broadly.publishedVersio

On the gap between theory and practice in defining and understanding risk

The risk concept is used in all types of situations and applications, ranging from technology to medicine and security issues. Many definitions of the concept exist, and there is an ongoing discussion on what is the most suitable way of defining and understanding the concept. In recent years, several overriding frameworks have been developed, aiming at providing conceptual clarity and structure and including most of the existing definitions as special cases. A key feature of these frameworks is that uncertainty is a main component of risk. Risk science literature and recognized societies and organizations have actively promoted these frameworks and definitions. Nonetheless, applied risk analysis and management is characterized by all types of definitions and understandings of risk, many that go back to conventions made several decades ago. It can be argued that there is a considerable gap between contemporary risk science knowledge and the practice of risk analysis and risk management in these areas. This paper discusses why we have this gap, why it is important to close it and how this can be achieved. A main goal of the paper is to refute the claim that the gap is due to a disconnection between risk science and the application of risk science.publishedVersio

Cases of real-life policies related to risk: how can they enhance risk analysis and risk science

Policies on risk constitute a core topic of risk analysis and risk science, and it is common at risk conferences to present real-life cases of such policies, for example related to the handling of climate change and pandemics. Although these are of broad interest, showing how important issues in society are dealt with, it can be questioned to what extent and how these cases contribute to enhancing risk analysis and risk science. The present paper addresses this concern. It is argued that, in order to learn from the cases, they need in general to be more thoroughly followed up with discussions of concepts, principles, approaches, and methods for assessing, characterizing, communicating and handling risk. Describing a governmental policy on, for example, the handling of COVID-19 is a point of departure for interesting discussions concerning its justification and performance, in particular in relation to risk and the most updated knowledge from the risk analysis field. Such discussions are, however, often lacking. The paper points to some key obstacles and challenges for the learning process, including the difficulty of distinguishing between policies, policy analysis, and politics.publishedVersio