Exhaustive Search, Combinatorial Optimization and Enumeration: Exploring the Potential of Raw Computing Power

For half a century since computers came into existence, the goal of finding elegant and efficient algorithms to solve "simple" (welldefined and well-structured) problems has dominated algorithm design. Over the same time period, both processing and storage capacity of computers have increased by roughly a factor of a million. The next few decades may well give us a similar rate of growth in raw computing power, due to various factors such as continuing miniaturization, parallel and distributed computing. If a quantitative change of orders of magnitude leads to qualitative advances, where will the latter take place? Only empirical research can answer this question. Asymptotic complexity theory has emerged as a surprisingly effective tool for predicting run times of polynomial-time algorithms. For NPhard problems, on the other hand, it yields overly pessimistic bounds. It asserts the non-existence of algorithms that are efficient across an entire problem class, but ignores the ...

• Type: Conference
• Year: 2000
• Where: SOFSEM
• Authors: Jürg Nievergelt
• Keywords: Algorithms, Asymptotic Complexity Theory, Efficient Algorithms, SOFSEM 2000, Theoretical Computer Science