Random Graphs and the Probabilistic Method
نویسنده
چکیده
These notes accompany a lecture given in the summer of 2006 at the Center for Combinatorics at Nankai University. They are provided as a reference (and especially bibliography) for students new to the probabilistic method. The goal in these notes is twofold. First we wish to demonstrate the basics of the probabilistic method, covering both the expectation and second moment applications. Second, I wish to introduce the study of random graphs and their connection to the probabilistic method. The next lecture on “Sharp Concentration Phenomena” will delve more deeply into the topic of random graphs. Finally, let me mention that none of this material is original, and much of it can be found in Alon and Spencer’s well written book [1].
منابع مشابه
Support vector regression with random output variable and probabilistic constraints
Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...
متن کاملCalibration of Load and Resistance Factors for Reinforced Concrete
Current approach for designing of reinforced concrete members is based on the load and resistance factor. However the load and resistance parameters are random variables, the constant values have been designated for them in the designing procedure. Assuming these factors as the constants, will be led to the unsafe and uneconomical designs. Safe designing of structures requires appropriate recog...
متن کاملA Design Methodology for Reliable MRF-Based Logic Gates
Probabilistic-based methods have been used for designing noise tolerant circuits recently. In these methods, however, there is not any reliability mechanism that is essential for nanometer digital VLSI circuits. In this paper, we propose a novel method for designing reliable probabilistic-based logic gates. The advantage of the proposed method in comparison with previous probabilistic-based met...
متن کاملBurning graphs - a probabilistic perspective
In this paper, we study a graph parameter that was recently introduced, the burning number, focusing on a few probabilistic aspects of the problem. The original burning number is revisited and analyzed for binomial random graphs G(n, p), random geometric graphs, and the Cartesian product of paths. Moreover, new variants of the burning number are introduced in which a burning sequence of vertice...
متن کاملProbing the Probabilistic Effects of Imperfections on the Load Carrying Capacity of Flat Double-Layer Space Structures
Load carrying capacity of flat double-layer space structures majorly depends on the structures' imperfections. Imperfections in initial curvature, length, and residual stress of members are all innately random and can affect the load-bearing capacity of the members and consequently that of the structure. The double-layer space trusses are susceptible to progressive collapse due to sudden buckli...
متن کامل