Climate graph

Abstract: The location of a number of service centres on a network (graph) in such a way so that every node (demand point) lies within a critical distance of at least one of the centres appears often in problems involving emergency services. When the number p of centres is fixed and what is required is their location so that this critical distance is the smallest possible, the resulting location is called "the absolute p-centre of the graph". This paper presents an iterative algorithm for finding absolute p-centres in general (weighted or unweighted) graphs. The algorithm is shown to be computationally efficient for quite large graphs. Results (computing times and numbers of iterations) are given for 15 test graphs varying in size from 10 to 50 nodes and from 20 to 120 links.

Abstract: Communicating climate information is challenging due to the interdisciplinary nature of the topic along with compounding cognitive and affective learning challenges. Graphs are a common representation used by scientists to communicate evidence of climate change. However, it is important to identify how and why individuals on the continuum of expertise navigate graphical data differently as this has implications for effective communication of this information. We collected and analyzed eye-tracking metrics of geoscience graduate students and novice undergraduate students while viewing graphs displaying climate information. Our findings indicate that during fact-extraction tasks, novice undergraduates focus proportionally more attention on the question, title and axes graph elements, whereas geoscience graduate students spend proportionally more time viewing and interpreting data. This same finding was enhanced during extrapolation tasks. Undergraduate novices were also more likely to describe general trends, while graduate students identified more specific patterns. Undergraduates who performed high on the pre-test measuring graphing skill, viewed graphs more similar to graduate students than their peers who performed lower on the pre-test.

Abstract: The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a blockcycle graph the zero forcing number equals the path cover number. We also give a purely graph theoretical proof that the positive zero forcing number of any outerplanar graphs equals the tree cover number of the graph. These ideas are then extended to the setting of k-trees, where the relationship between the positive zero forcing number and the tree cover number becomes more complex.

Abstract: This paper introduces average case analysis of fully dynamic graph connectivity (when the operations are edge insertions and deletions) To this end we introduce the model of stochastic graph processes, ie dynamically changing random graphs with random equiprobable edge insertions and deletions, which generalizes Erdos and Renyi's 35 year-old random graph process As the stochastic graph process continues indefinitely, all potential edge locations (in V × V) may be repeatedly inspected (and learned) by the algorithm This learning of the structure seems to imply that traditional random graph analysis methods cannot be employed (since an observed edge is not a random event anymore) However, we show that a small (logarithmic) number of dynamic random updates are enough to allow our algorithm to re-examine edges as if they were random with respect to certain events (ie the graph “forgets” its structure) This short memory property of the stochastic graph process enables us to present an algorithm for graph connectivity which admits an amortized expected cost of O(log3n) time per update In contrast, the best known deterministic worst-case algorithms for fully dynamic connectivity require n1/2 time per update