NP-Complete Problems: Advanced Algorithmic Techniques

Daniel Mertz Kane serves as a full professor with a joint appointment in Mathematics and Computer Science at the University of California, San Diego, where he has established himself as a leading researcher in theoretical computer science, combinatorics, and number theory. Born in 1986 to academic parents in Madison, Wisconsin, his extraordinary mathematical talent emerged early, mastering K-9 mathematics by third grade and conducting university-level research under Ken Ono while still in high school. His academic achievements include two gold medals in the International Mathematical Olympiad (2002, 2003), being one of only eight people in history to become a four-time Putnam Fellow, and winning the 2007 Morgan Prize. After earning dual bachelor's degrees from MIT in mathematics with computer science and physics (2007), he completed his Ph.D. at Harvard under Barry Mazur in 2011. His research contributions span multiple areas, including groundbreaking work in computational statistics, Boolean functions, and machine learning, earning him numerous awards including the IBM Pat Goldberg Memorial and PODS best paper awards. He recently co-authored a book on robust statistics with Ilias Diakonikolas, to be published by Cambridge University Press

Alexander S. Kulikov serves as a visiting professor at the University of California, San Diego, and a leading research fellow at the Steklov Institute of Mathematics in St. Petersburg. His academic journey includes earning his Ph.D. in 2009 and Dr.Sci. in 2017 from the St. Petersburg Department of Steklov Institute of Mathematics. His research focuses on algorithms for NP-hard problems and circuit complexity, with significant contributions to computational complexity theory and algorithm design. He has authored several influential educational resources, including "Learning Algorithms Through Programming and Puzzle Solving" and co-created major online courses on platforms like Coursera and edX. His teaching experience spans more than eight years, during which he has developed innovative approaches to algorithms education. Currently at JetBrains as a researcher, he continues to advance the field through his work on algorithmic problem-solving and computational complexity, while maintaining his academic connections through his visiting professorship at UCSD and research position at Steklov Institute.