Approximation Algorithms equips learners with essential techniques to efficiently solve real-world algorithmic problems that are NP-hard. The course delves into the art of finding close approximations to optimal solutions, providing a crucial skill set for algorithmic problem-solving. Prior knowledge of algorithms, mathematics, and fundamental data structures is recommended for successful comprehension.
Throughout the course, students explore crucial topics including O-notation, basic calculus, probability theory, and data structures. They will also delve into graph terminology, representations of graphs, and fundamental graph algorithms, such as BFS, DFS, and topological sort. The course content is based on comprehensive course notes available under the resources tab.
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The course introduces approximation algorithms, load balancing problems, LP relaxation, and polynomial-time approximation schemes, offering in-depth insights into crucial algorithmic techniques and concepts.
The Introduction to Approximation Algorithms module provides a comprehensive overview of essential concepts and techniques. Students will delve into the significance of approximation algorithms and explore foundational skills necessary for solving NP-hard problems.
The Load Balancing problem module delves into the intricacies of a greedy algorithm for load balancing, the analysis of the greedy algorithm, and the ordered scheduling algorithm. Students will gain a deep understanding of load balancing and its implications in algorithmic problem-solving.
The LP Relaxation module offers an in-depth exploration of the vertex-cover problem, approximation algorithms for vertex-cover, and a brief introduction to linear programming. Students will also analyze weighted vertex-cover and LP relaxation techniques, essential for tackling algorithmic challenges.
The Polynomial-time approximation schemes module provides a comprehensive understanding of polynomial-time approximation schemes, the knapsack problem, dynamic-programming algorithms for knapsack, and PTAS for knapsack. Students will also analyze the approximation ratio and running time of PTAS for knapsack.
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