6 research outputs found
Improved Average Complexity for Comparison-Based Sorting
This paper studies the average complexity on the number of comparisons for
sorting algorithms. Its information-theoretic lower bound is . For many efficient algorithms, the first term is easy to
achieve and our focus is on the (negative) constant factor of the linear term.
The current best value is for the MergeInsertion sort. Our new value
is , narrowing the gap by some . An important building block of
our algorithm is "two-element insertion," which inserts two numbers and
, , into a sorted sequence . This insertion algorithm is still
sufficiently simple for rigorous mathematical analysis and works well for a
certain range of the length of for which the simple binary insertion does
not, thus allowing us to take a complementary approach with the binary
insertion.Comment: 21 pages, 2 figure
Optimal Coding for Streaming Authentication and Interactive Communication
We consider the task of communicating a data stream-a long, possibly infinite message not known in advance to the sender-over a channel with adversarial noise. For any given noise rate c 1/2