Array DBMS in Environmental Science: Sea Surface Height Data in the Cloud
Heaps are well-studied fundamental data structures, having myriads of applications, both theoretical and practical. We consider the problem of designing a heap with an “optimal” extract-min operation. Assuming an arbitrary linear ordering of keys, a heap with n elements typically takes O(log n) time to extract the min-imum. Extracting all elements faster is impossible as this would violate the Ω(n log n) bound for comparison-based sorting. It is known, however, that is takes only O(n + k log k) time to sort just k smallest elements out of n given, which prompts that there might be a faster heap, whose extract-min performance depends on the number of elements extracted so far. In this paper we show that is indeed the case. We present a version of heap that performs insert in O(1) time and takes only O(log ∗ n + log k) time to carry out the k-th extraction (where log ∗ denotes the iterated logarithm). All the above bounds are worst-case.
We assess and compare computer science skills among final-year computer science undergraduates (seniors) in four major economic and political powers that produce approximately half of the science, technology, engineering, and mathematics graduates in the world. We find that seniors in the United States substantially outperform seniors in China, India, and Russia by 0.76–0.88 SDs and score comparably with seniors in elite institutions in these countries. Seniors in elite institutions in the United States further outperform seniors in elite institutions in China, India, and Russia by ∼0.85 SDs. The skills advantage of the United States is not because it has a large proportion of high-scoring international students. Finally, males score consistently but only moderately higher (0.16–0.41 SDs) than females within all four countries.