Graphical models, such as Bayesian Networks and Markov networks play an important role in artificial intelligence and machine learning. Inference is a central problem to be solved on these networks. This, and other problems on these graph models are often known to be hard to solve in general, but tractable on graphs with bounded Treewidth. Therefore, finding or approximating the Treewidth of a graph is a fundamental problem related to inference in graphical models. In this paper, we study the approximability of a number of graph problems: Treewidth and Pathwidth of graphs, Minimum Fill-In, OneShot Black (and Black-White) pebbling costs of directed acyclic graphs, and a variety of different graph layout problems such as Minimum Cut Linear Arrangement and Interval Graph Completion. We show that, assuming the recently introduced Small Set Expansion Conjecture, all of these problems are NP-hard to approximate to within any constant factor in polynomial time.

Numerous scholars have applied conceptual graphs for explanatory purposes. This study devised the 'Remedial-Instruction Decisive path (RID path)' algorithm for diagnosing individual student learning situation. This study focuses on conceptual graphs. According to the concepts learned by students and the weight values of relations among these concepts, this study established the remedial-instruction paths to identify their real missing concepts. This study applies diagnostic and remedial learning strategies to two courses -'Introduction and Implementation of RS-232' and 'Electronic Circuits Laboratory'. By analysing the scores of the midterm and final exams, evaluations of remedial learning yield positive experimental results. Participants who adopt the diagnostic and remedial learning strategy have better academic performance.

We study the approximability of a number of graph problems: treewidth and pathwidth of graphs, one-shot black (and black-white) pebbling costs of directed acyclic graphs, and a variety of different graph layout problems such as minimum cut linear arrangement and interval graph completion. We show that, assuming the recently introduced Small Set Expansion Conjecture, all of these problems are hard to approximate within any constant factor.

No abstract