PDF-Lecture Comparisonbased Lower Bounds for Sorting

1 Overview In this lecture we discuss the notion of lower bounds in particular for the problem of sorting We show that any deterministic comparisonbased sorting algo rithm must take 8486 log time to sort an array of elements in the worst case We th. 1 Overview In this lecture we discuss the notion of lower bounds in particular for the problem of sorting We show that any deterministic comparisonbased sorting algo rithm must take 8486 log time to sort an array of elements in the worst case We th Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . . waste. Sorting. line. Plastics. Yellow. . dustbin. Pet. . bottles. , . hollow. . wraps. , . foils. Ferry. , . sorting. , . pressing. No: linoleum . and. . floor. . coverings. , . wraps. . with. Reticulate Network of Multiple . Phylogenetic. Trees. Yufeng. . Wu. Dept. of Computer Science & Engineering. University of Connecticut, USA. ISMB 2010. 1. 1. 2. 3. 4. Keep. two . red. edges. Keep. Keyang. He. Discrete Mathematics. Basic Concepts. Algorithm . – . a . specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. Insertion Sort: . Θ. (n. 2. ). Merge Sort:. Θ. (. nlog. (n)). Heap Sort:. Θ. (. nlog. (n)). We seem to be stuck at . Θ. (. nlog. (n)). Hypothesis: . Every sorting algorithm requires . Ω. (. nlog. Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . Insertion Sort. Insertion Sort. Start with empty left hand, cards in pile on table.. Take first card from pile, put in left hand.. Take next card from pile, insert in proper place among cards in left hand.. unseen problems. David . Corne. , Alan Reynolds. My wonderful new algorithm, . Bee-inspired Orthogonal Local Linear Optimal . Covariance . K. inetics . Solver. Beats CMA-ES on 7 out of 10 test problems !!. approximate membership. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. Onset of . precip. – development of particles large enough to sediment relative to cloud droplets & ice crystals.. Larger particles tend to fall faster.. Differential Sedimentation (D.S.). Atmospheric flows (e.g. updrafts) can prolong D.S. due to the removal of small drops upward & exhausted through the anvil region.. Chapter 14. Selection. . Sort. A . sorting algorithm rearranges the elements of a collection so that they are stored . in . sorted order. . Selection sort sorts an array by repeatedly. . finding. Lecture 18 SORTING in Hardware SSEG GPO2 Sorting Switches LED Buttons GPI2 Sorting - Required I nterface Sort Clock R eset n DataIn N DataOut N Done RAdd L WrInit S (0=initialization 1=computations) Given. a set (container) of n elements . E.g. array, set of words, etc. . Goal. Arrange the elements in ascending order. Start .  . 1 23 2 56 9 8 10 100. End .  1 2 8 9 10 23 56 100 (Ascending).