* Senior Lecturer, Department of Orthodontics, Sri Sankara Dental College, Varkala, Trivandrum, Kerala, India ** Senior Lecturer, Department of Periodontics, Sri Sankara Dental College, Varkala, Trivandrum, Kerala, India *** Senior Lecturer, Department of Periodontics, Kannur Dental College, Anjarakandy, Kannur, Kerala, India † Senior Lecturer, Department of Orthodontics, Kannur Dental College,...

In this section, we start the study of LOCAL vertex-coloring algorithms for general graphs. The eventual goal would be to obtain (∆ + 1)-coloring of the graphs — that is, an assignment of colors {1, 2, . . . ,∆ + 1} to vertices such that no two adjacent vertices receive the same color — where ∆ denotes the maximum degree. Notice that by a simple greedy argument, each graph with maximum degree a...

In this section we discuss the theory of Fourier Series for functions of a real variable. In the next sections we will study an analogue which is the “discrete” Fourier Transform. Early in the Nineteenth century, Fourier studied sound and oscillatory motion and conceived of the idea of representing periodic functions by their coefficients in an expansion as a sum of sines and cosines rather tha...

Recall that many combinatorial problems of interest can be encoded as integer linear programs. Solving integer linear programs is in general NP-hard, so we nearly always relax the integrality requirement into a linear constraint like nonnegativity during our analysis. Our previous algorithms for solving these problems never solved the relaxed program explicitly (e.g. using simplex). In LP round...

In these notes, we study the intersection of communication complexity and distributed computing. To understand why distributed computing researchers care about communication complexity tools and results, we briefly turn our attention to distributed computing. In traditional distributed computing models, local computation is free, and communication between parties is expensive. Typical complexit...

In this paper we report our findings from an experiment with the teleoperated android Geminoid-DK. The geminoid took up the role of a university lecturer and delivered a 45 minute lecture in front of 150 freshmen students at Aalborg University. While considering the role of the geminoid in this educational context, we report results relating to large-room teaching, as well as gender differences...

It known that teachers as educators should have competence that shows its quality so that the lecture material provided can be absorbed by the student. The competencies in this term include the pedagogic, professional, personality, and social. The competence that owned by lecturer can be obtained from the results of the assessment conducted by the student through the filling of the questionnair...

In this lecture, we will study a different type of graph cuts than the max-cut problem previously discussed. Let us recall that the maximum-cut problem is to find a 2-coloring of the vertices to maximize the total weight of the edges whose endpoints have different colors. We have seen a simple factor-1/2 approximation in Homework #1, and an SDP-based factor-0.878 approximation in Lecture 14. We...

For ≤ 1, the first expression is always the binding constraint, so for -differential privacy, we can simply set: ′ = √ 8k ln 1/δ′ Compare this to if we wanted pure -differential privacy, in which case we would have had to set ′ = /k. Lets consider what this means for answering k sensitivity 1 queries with the Laplace mechanism. For -differential privacy, we can answer each query by adding noise...