Counting Shortest Two Disjoint Paths in Cubic Planar Graphs with an NC Algorithm

Given an undirected graph and two disjoint vertex pairs $s_1,t_1$ and $s_2,t_2$, the Shortest two disjoint paths problem (S2DP) asks for the minimum total length of two vertex disjoint paths connecting $s_1$ with $t_1$, and $s_2$ with $t_2$, respectively. We show that for cubic planar graphs there are NC algorithms, uniform circuits of polynomial size and polylogarithmic depth, that compute the S2DP and moreover also output the number of such minimum length path pairs. Previously, to the best of our knowledge, no deterministic polynomial time algorithm was known for S2DP in cubic planar graphs with arbitrary placement of the terminals. In contrast, the randomized polynomial time algorithm by Bj\"orklund and Husfeldt, ICALP 2014, for general graphs is much slower, is serial in nature, and cannot count the solutions. Our results are built on an approach by Hirai and Namba, Algorithmica 2017, for a generalisation of S2DP, and fast algorithms for counting perfect matchings in planar graphs

Linking Reading Assessment Data to Intervention Using the 4-Box Instructional Decision Making Model

Reading is a vital skill and failing to learn how to read has consequences beyond the walls of the classroom. The importance of reading and its link to later success in life has gained the attention of many, including Congress, over the past couple of decades. Yet, despite an intense research focus and large amounts of time and resources being devoted to improving reading performance, too many American students continue to struggle to obtain reading proficiency. One possible explanation for this disconnect maybe the failure to match evidence-based instruction to struggling readers based on their specific reading needs. The 4-Box Instructional Decision Making Model developed by Harkin in 2008 is a promising tool that may improve the ability of educators to match struggling readers to effective interventions. The 4-Box Instructional Decision Making Model is discussed and its effectiveness in identifying students in need of reading interventions and linking them to evidence-based reading interventions are displayed

Narrow sieves for parameterized paths and packings

We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in time exponential only in the parameter (k, p, q) and using polynomial space; the constant bases of the exponentials are significantly smaller than in previous works. For example, for the k-path problem the improvement is from 2 to 1.66. We also show how to detect if a d-regular graph admits an edge coloring with $d$ colors in time within a polynomial factor of O(2^{(d-1)n/2}). Our techniques build upon and generalize some recently published ideas by I. Koutis (ICALP 2009), R. Williams (IPL 2009), and A. Bj\"orklund (STACS 2010, FOCS 2010)

Computing Graph Distances Parameterized by Treewidth and Diameter

We show that the eccentricity of every vertex in an undirected graph on n vertices can be computed in time n exp O(k*log(d)), where k is the treewidth of the graph and d is the diameter. This means that the diameter and the radius of the graph can be computed in the same time. In particular, if the diameter is constant, it can be determined in time n*exp(O(k)). This result matches a recent hardness result by Abboud, Vassilevska Williams, and Wang [SODA 2016] that shows that under the Strong Exponential Time Hypothesis of Impagliazzo, Paturi, and Zane [J. Comp. Syst. Sc., 2001], for any epsilon > 0, no algorithm with running time n^{2-epsilon}*exp(o(k)) can distinguish between graphs with diameter 2 and 3

Wirkungen und Wirksamkeit der externen Schulevaluation: Überblick zum Stand der Forschung

Zusammenfassung: Schulinspektionen erlangen in verschiedenen europäischen Ländern einen immer höheren Stellenwert. Gleichzeitig steigen damit auch die Erwartungen in ihre Wirksamkeit, wobei vor allem Wirksamkeit in Hinblick auf nachhaltige Schulentwicklung gemeint ist. Ausgehend von einer Darstellung der Funktionen von Schulinspektionen gibt der Artikel eine Übersicht über Wirksamkeitsmodelle und Forschungsarbeiten. Teilweise wird in den Forschungsarbeiten davon ausgegangen, dass die Wirksamkeit von Inspektionen hinsichtlich der Schulentwicklung direkt an den Schülerleistungen messbar ist. Allerdings bleibt unklar, wie die schulinternen Verarbeitungsprozesse als Bindeglied zwischen Schulinspektion und verbesserter Schülerleistung gestaltet sind. Andere Studien betrachten die Einstellungen oder Reaktionen der Akteure auf die Inspektion, wobei teils Wirksamkeitserwartungen und tatsächliche Schulentwicklung konfundiert sind. Ausgehend von der Rekonstruktion der unterschiedlichen Forschungsansätze zeigt der Artikel den Bedarf für Modelle auf, die die schulischen Verarbeitungsprozesse im Anschluss an Inspektionen stärker in den Blick nehme

Using Anti-Racist Education to Diminish Educational Debt

Bringing in student culture, ethnicity, and backgrounds into the classroom can be beneficial for all learners (Gay, 2013). Anthropologists have been urging schools to insert culture into education instead of education into culture for decades (Ladson-Billings, 2006). Yet, our country is more divided than ever. There continue to be dramatic gaps in performance between White students and Black Indigenous People of Color students. Therefore, schools must push past multicultural education and the notion of integrating culture into schools and instead commit to implementing anti-racist education. There are three common goals of anti-racist education: (a) identifying or making visible systematic oppression; (b) challenging denial of complicity in such oppression; and (c) transforming structural inequalities. The adoption of an anti-racist education through the implementation of these goals is the only way that schools will start closing the opportunity gaps that have been plaguing our schools for decades. The steps necessary for educators and schools to achieve these goals are described in this paper

Polynomial fixed-parameter algorithms : a case study for longest path on interval graphs.

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path; it is NP-hard in general but known to be solvable in O(n^4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis for polynomial-time solvable problems offers a very fertile ground for future studies for all sorts of algorithmic problems. It may enable a refined understanding of efficiency aspects for polynomial-time solvable problems, similarly to what classical parameterized complexity analysis does for NP-hard problems