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Updated in [June 30th, 2023]

Approximation Algorithms Part I is a course that provides an introduction to the design and analysis of algorithms for solving NP-hard combinatorial optimization problems. It assumes knowledge of a standard undergraduate Algorithms course, and particularly emphasizes algorithms that can be designed using linear programming. Upon completion, students will be able to recognize when faced with a new combinatorial optimization problem, whether it is close to one of a few known basic problems, and will be able to design linear programming relaxations and use randomized rounding to attempt to solve their own problem. The course content and in particular the homework is of a theoretical nature without any programming assignments. This is the first of a two-part course on Approximation Algorithms.

[Applications]
Upon completion of this course, students will be able to apply the knowledge they have gained to recognize and design linear programming relaxations for combinatorial optimization problems. They will also be able to use randomized rounding to attempt to solve their own problems. Additionally, they will be able to identify when a new combinatorial optimization problem is close to one of a few known basic problems.

[Career Path]
One job position path that is recommended to learners of this course is that of a Combinatorial Optimization Analyst. This position involves designing and analyzing algorithms to solve complex combinatorial optimization problems. The analyst must be able to recognize when a problem is close to one of a few known basic problems, and be able to design linear programming relaxations and use randomized rounding to attempt to solve the problem. The analyst must also be able to analyze the performance of the algorithms and provide feedback on their effectiveness.

The development trend for this position is that it is becoming increasingly important as more and more businesses are relying on algorithms to solve complex problems. Companies are looking for analysts who can design and analyze algorithms that are both efficient and effective. As such, the demand for this position is expected to continue to grow in the future.

[Education Path]
The development trend of this course is to continue to add more modules and content to the course. This includes more advanced topics such as Trees, Graphs, and Heaps. Additionally, the course will continue to add more coding assignments and exams to ensure that students are able to apply the concepts they have learned. The course will also continue to add more visualizations and exploratory labs to help students better understand the data structures and algorithms. Finally, the course will continue to add more resources and materials to help students better understand the concepts and apply them in their own projects.