PPT-5.9 Heaps of optimal complexity

510 Doubleended heap structures and multidimensional heaps 511 Heaprelated structures with constant time updates AlShahrani Hasan Heaps of optimal complexity Optimal deletemin in Olog n . Data . Structures. Self-Adjusting. Data . Structures. 2. Lists. [D.D. . Sleator. , R.E. . Tarjan. , . Amortized Efficiency of List Update Rules. , Proc. 16. th. Annual ACM Symposium on Theory of Computing, 488-492, 1984]. COL 106. Shweta Agrawal and . Amit. Kumar. 2. Revisiting FindMin. Application: Find the smallest ( or highest priority) item quickly. Operating system. needs to schedule jobs according to priority instead of FIFO. Data . Structures. Self-Adjusting. Data . Structures. 2. Lists. [D.D. . Sleator. , R.E. . Tarjan. , . Amortized Efficiency of List Update Rules. , Proc. 16. th. Annual ACM Symposium on Theory of Computing, 488-492, 1984]. Uninformed search . algorithms. Discussion Class CS 171. Friday, October, 2nd. (Please read lecture topic material before and after each lecture on that topic). Thanks to professor . Kask. Some of the slides (page 2-7) were copied from his lectures.. Data . Structures. Self-Adjusting. Data . Structures. 2. Lists. [D.D. . Sleator. , R.E. . Tarjan. , . Amortized Efficiency of List Update Rules. , Proc. 16. th. Annual ACM Symposium on Theory of Computing, 488-492, 1984]. A heap is a binary tree.. A heap is best implemented in sequential representation (using an array).. Two important uses of heaps are: . (. i. ) efficient implementation of priority queues. (ii) sorting -- . Data . Structures. Self-Adjusting. Data . Structures. 2. Lists. [D.D. . Sleator. , R.E. . Tarjan. , . Amortized Efficiency of List Update Rules. , Proc. 16. th. Annual ACM Symposium on Theory of Computing, 488-492, 1984]. A heap is a binary tree.. A heap is best implemented in sequential representation (using an array).. Two important uses of heaps are: . (i) efficient implementation of priority queues. (ii) sorting -- Heapsort.. Mechanical Engineering Department. IIT Patna. ME512: Mobile Robotics. Path Planning Algorithms. Path Planning Problem. Given. Robot state. Obstacle positions. Robot capabilities. Compute collision free optimal path to a goal. Andris Ambainis (Latvia), . Martins Kokainis (Latvia), . Robin Kothari (MIT). communication complexity. Alice holds . x. X. , Bob holds . y. Y. .. D. cc. (f). - minimum amount of communication to compute . Advisor : Prof. Surender Baswana. - Shivam Taji. UGP Workflow. Attempted solving complex range query problems using Augmented Binary Trees. A Data Structure for Dynamic Trees. Analysis of Splay Trees. A binary min-heap allows the operations of push and pop to occur . in an average case of . Q. (1). and . Q. (. ln. (. n. )). time, respectively. Merging two binary min-heaps, however, is an . Q. (. Prof. . Neary. Based on slides from previous iterations of this course. Today’s Topics. Review of Min Heaps. Introduction of Left-. ist. Heaps. Merge Operation. Heap Operations. Review of Heaps. Min Binary Heap. Definition of a . d. -ary min heap . Implementation as a complete tree. Examples of binary, ternary, quaternary, and quinary min heaps. Properties. Relative speeds. Optimal choice is a quaternary heap.