Safety in s-t Paths, Trails and Walks

Given a directed graph G and a pair of nodes s and t, an s-t bridge of G is an edge whose removal breaks all s-t paths of G (and thus appears in all s-t paths). Computing all s-t bridges of G is a basic graph problem, solvable in linear time. In this paper, we consider a natural generalisation of this problem, with the notion of “safety” from bioinformatics. We say that a walk W is safe with respect to a set W' of s-t walks, if W is a subwalk of all walks in W'. We start by considering the maximal safe walks when consists of: all s-t paths, all s-t trails, or all s-t walks of G. We show that the solutions for the first two problems immediately follow from finding all s-t bridges after incorporating simple characterisations. However, solving the third problem requires non-trivial techniques for incorporating its characterisation. In particular, we show that there exists a compact representation computable in linear time, that allows outputting all maximal safe walks in time linear in their length. Our solutions also directly extend to multigraphs, except for the second problem, which requires a more involved approach. We further generalise these problems, by assuming that safety is defined only with respect to a subset of visible edges. Here we prove a dichotomy between the s-t paths and s-t trails cases, and the s-t walks case: the former two are NP-hard, while the latter is solvable with the same complexity as when all edges are visible. We also show that the same complexity results hold for the analogous generalisations of s-t articulation points (nodes appearing in all s-t paths). We thus obtain the best possible results for natural “safety”-generalisations of these two fundamental graph problems. Moreover, our algorithms are simple and do not employ any complex data structures, making them ideal for use in practice.Peer reviewe

Tigard Walks (A Plan for Walkable Neighborhoods in Tigard)

The Walkable Neighborhoods Plan for Tigard outlines a set of strategies to help Tigard’s residents, businesses, and leaders build their city into a more walkable place. These five strategies are based on three core values gleaned from StepUP Studio’s outreach efforts to the people living and working in and for the city of Tigard. This project was conducted under the supervision of Sy Adler, Marisa A. Zapata and Gil Kelle

From single steps to mass migration: the problem of scale in the movement ecology of the Serengeti wildebeest

A central question in ecology is how to link processes that occur over different scales. The daily interactions of individual organisms ultimately determine community dynamics, population fluctuations and the functioning of entire ecosystems. Observations of these multiscale ecological processes are constrained by various technological, biological or logistical issues, and there are often vast discrepancies between the scale at which observation is possible and the scale of the question of interest. Animal movement is characterized by processes that act over multiple spatial and temporal scales. Second-by-second decisions accumulate to produce annual movement patterns. Individuals influence, and are influenced by, collective movement decisions, which then govern the spatial distribution of populations and the connectivity of meta-populations. While the field of movement ecology is experiencing unprecedented growth in the availability of movement data, there remain challenges in integrating observations with questions of ecological interest. In this article, we present the major challenges of addressing these issues within the context of the Serengeti wildebeest migration, a keystone ecological phenomena that crosses multiple scales of space, time and biological complexity. This article is part of the theme issue ’Collective movement ecology’

MIXED-USE SAFETY ON RURAL FACILITIES IN THE PACIFIC NORTHWEST: Consideration of Vehicular, Non-Traditional, and Non-Motorized Users

In the United States, one in 12 households do not own a personal automobile and approximately 13% of those who are old enough to drive do not. Trips by these individuals are being made in one of many other possible modes, creating the need to “share space” between many forms of travel. The goal of this project is to: improve safety and minimize the dangers for all transportation mode types while traveling in mixed-use environments on rural facilities through the development and use of engineering and education safety measures. To that end, this report documents three specific efforts by the project team. First, a comprehensive literature review of mixed-use safety issues with consideration of non-motorized and non-traditional forms of transportation. Second, a novel analysis of trauma registry data. Third, development, execution and analysis of the Pacific Northwest Transportation Survey geared toward understanding safety perceptions of mixed-use users. Most notably, findings indicate that ATVs (and similar non-traditional-type vehicles) are used on or near roads 24% of the time and snowmachines are used on or near roads 23% of the time. There are significantly more (twice as many) ATV-related on-road traumas in connected places than isolated places in Alaska and three times more traumas in highway connected places than in secondary road connected places. Comparably, bicycles had 449 on-road traumas between 2004 and 2011 whereas ATVs had 352 on-road traumas. Users of all modes who received formalized training felt safer in mixed-use environments than those who reported having no training at all

MT SCORP: Facility and Natural Resource Recreation Area Needs: Facility Manager Responses 2012

A survey of local, state, federal, school and tribal mangers were surveyed to understand the quantity and quality of outdoor recreation facilities and area needs. This study was conducted for use in the State Comprehensive Outdoor Recreation Plan process