Order statistics Select the ith smallest of n elements(the element with rank i i=l: minimum, .i=n: marimum, i=L(n+1)/2]or[(n+1)/2 median Naive algorithm: Sort and index ith element Worst-case running time =o(n Ig n)+o(1 o(nIg n using merge sort or heapsort(not quicksort) c 2001 by Charles E Leiserson
ynamic order statistics OS-SELECT(i, S): returns the i th smallest element in the dynamic set S. OS-RANK(, S): returns the rank ofx E S in the sorted order of s s elements IDEA: Use a red-black tree for the set S, but keep subtree sizes in the nodes
I. Writing and Presentation 1. Typo and grammar mistake 2. Sentence and convention 3. Exercise and discussion II. Research Formulation 1. Definition before use 2. Research problem 3. Inadequacy of related work 4. Insight of your proposal 5. Exercise and discussion III. Experimentation 1. Questions and subjects 2. Experimental design 3. Threats to validity 4. Exercise and discussion