A Survey of Constant Time Parallel Sorting

This has been quite an exciting summer for computational complexity. The 15th Conference on Computational Complexity held July 4-7 in Florence was a great success. We had many interesting talks and a wonderful invited talks and tutorials by Paul Beame, Luca Trevisan and Russell Impagliazzo. Preparations are underway for the 16th Conference next summer in Chicago. The Institute of Advanced Studies in Princeton had a three-week summer session on computational complexity theory. This included a graduate school giving introductions to many of the current exciting research areas in complexity theory. Lecturers included Sanjeev Arora, Paul Beame, Michael Ben-Or, Oded Goldreich, Ran Raz, Steven Rudich, Luca Trevisan and Salil Vadhan. The summer session is part of a 2000-2001 special year on computational complexity at the institute. Our column has a new web site: http://www.neci.nj.nec.com/homepages/fortnow/beatcs. Most of the previous columns are available there as well as pointers to interesting complexity sites such as described above. This month we feature a survey on parallel sorting where we have a xed number of rounds. If you only have one round than all comparisons are needed. Surprisingly even for two rounds computing the optimal number of rounds is a surprisingly diÆcult problem.