The quest for efficiency in computational methods yields not only fast algorithms, but also insights that lead to elegant, simple, and general problem-solving methods. Robert E. Tarjan was surprised and delighted to be selected as a co-recipient of the 1986 Turing Award. He decided to share his thoughts on his work and its relevance to computing. His research focuses on the design and analysis of efficient algorithms, aiming to create problem-solving methods that are fast and use minimal storage. Theoretical analysis of algorithms is valuable because it is independent of programming details and provides broad applicability. However, there is a deeper dimension to efficient algorithm design, which involves focusing on important aspects of a problem to avoid redundant computations and design data structures that exactly represent needed information. This approach leads to insights and methods that can be transferred to other problems. Tarjan illustrates algorithm design by discussing two algorithms: a graph algorithm for testing planarity and a self-adjusting search tree. He discusses the development of a planarity test, which involves biconnected components and depth-first search. He also describes the development of a self-adjusting search tree, the splay tree, which adapts to usage and has amortized efficiency close to optimal. The splay tree is a self-adjusting form of binary search tree that restructures itself after each retrieval to improve future access times. The splay tree has theoretical and practical value, performing as well as balanced trees in an amortized sense. Tarjan emphasizes the importance of choosing the right data structures for efficient algorithms. He discusses the use of amortized analysis, which considers the total time of a sequence of operations rather than individual operations. He also highlights the importance of connecting theory and practice, and the need for experimental analysis and efficient programming languages. He concludes by expressing his appreciation for the computing community and the individuals who have contributed to his work.The quest for efficiency in computational methods yields not only fast algorithms, but also insights that lead to elegant, simple, and general problem-solving methods. Robert E. Tarjan was surprised and delighted to be selected as a co-recipient of the 1986 Turing Award. He decided to share his thoughts on his work and its relevance to computing. His research focuses on the design and analysis of efficient algorithms, aiming to create problem-solving methods that are fast and use minimal storage. Theoretical analysis of algorithms is valuable because it is independent of programming details and provides broad applicability. However, there is a deeper dimension to efficient algorithm design, which involves focusing on important aspects of a problem to avoid redundant computations and design data structures that exactly represent needed information. This approach leads to insights and methods that can be transferred to other problems. Tarjan illustrates algorithm design by discussing two algorithms: a graph algorithm for testing planarity and a self-adjusting search tree. He discusses the development of a planarity test, which involves biconnected components and depth-first search. He also describes the development of a self-adjusting search tree, the splay tree, which adapts to usage and has amortized efficiency close to optimal. The splay tree is a self-adjusting form of binary search tree that restructures itself after each retrieval to improve future access times. The splay tree has theoretical and practical value, performing as well as balanced trees in an amortized sense. Tarjan emphasizes the importance of choosing the right data structures for efficient algorithms. He discusses the use of amortized analysis, which considers the total time of a sequence of operations rather than individual operations. He also highlights the importance of connecting theory and practice, and the need for experimental analysis and efficient programming languages. He concludes by expressing his appreciation for the computing community and the individuals who have contributed to his work.