62 research outputs found
Verification of partitions of 2d and 3d objects
We consider the problems of deciding whether a given collection of polygons (polyhedra resp.) forms (i) a partition or (ii) a cell complex decomposition of a given polygon (polyhedron resp.). We describe simple O(n log n)-time
and O(n)-space algorithms for these problems, where n is the total description size of the input. If, in the input, vertices are referenced by means of indices to an array of distinct vertices, then our cell complex decomposition verification algorithms run in O(n) time
A CASE STUDY OF TRAUMA-INFORMED PRACTICE AND IMPLEMENTATION TO SUPPORT MENTAL HEALTH AND LEARNING IN PUBLIC SCHOOL IN SUFFOLK COUNTY, NEW YORK
The purpose of this study is to examine the readiness of school districts in Suffolk County, New York, to implement a trauma-informed system to address the growing needs of mental health interventions in student populations. A review of the literature will show a historical prevalence of mental health providers and individual student interventions within the school building, or in partnership with community agencies. Recent literature shows an increase in school-related issues have origins in student trauma or adverse childhood experiences. The study will examine the issue by conducting a mixed method analysis, using a survey instrument and focus group interviews, of members of the Suffolk Directors of Guidance. Significance of the study will help districts who want to implement a systematic and districtwide approach to mitigating trauma-related student issues by identifying current readiness and examining gaps in preparation to implement the National Dropout Prevention Center’s Trauma-Skilled Schools Model
Join-Reachability Problems in Directed Graphs
For a given collection G of directed graphs we define the join-reachability
graph of G, denoted by J(G), as the directed graph that, for any pair of
vertices a and b, contains a path from a to b if and only if such a path exists
in all graphs of G. Our goal is to compute an efficient representation of J(G).
In particular, we consider two versions of this problem. In the explicit
version we wish to construct the smallest join-reachability graph for G. In the
implicit version we wish to build an efficient data structure (in terms of
space and query time) such that we can report fast the set of vertices that
reach a query vertex in all graphs of G. This problem is related to the
well-studied reachability problem and is motivated by emerging applications of
graph-structured databases and graph algorithms. We consider the construction
of join-reachability structures for two graphs and develop techniques that can
be applied to both the explicit and the implicit problem. First we present
optimal and near-optimal structures for paths and trees. Then, based on these
results, we provide efficient structures for planar graphs and general directed
graphs
On the Recognition of Bipolarizable and P_4-simplicial Graphs
The classes of Raspail (also known as Bipolarizable) and P_4-simplicial graphs were introduced by Hoà ng and Reed who showed that both classes are perfectly orderable and admit polynomial-time recognition algorithms HR1. In this paper, we consider the recognition problem on these classes of graphs and present algorithms that solve it in O(n m) time. In particular, we prove properties and show that we can produce bipolarizable and P_4-simplicial orderings on the vertices of the input graph G, if such orderings exist, working only on P_3s that participate in a P_4 of G. The proposed recognition algorithms are simple, use simple data structures and both require O(n + m) space. Additionally, we show how our recognition algorithms can be augmented to provide certificates, whenever they decide that G is not bipolarizable or P_4-simplicial; the augmentation takes O(n + m) time and space. Finally, we include a diagram on class inclusions and the currently best recognition time complexities for a number of perfectly orderable classes of graphs
- …