External Memory Algorithms and Data Structures. Winter 2004/2005
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1 External Memory Algorithms and Data Structures Winter 2004/2005 Riko Jacob Peter Widmayer Assignments: Yoshio Okamoto EMADS 04/ 05: Course Description Page 1
2 External Memory Algorithms and Data Structures Winter 2004/2005 Riko Jacob Peter Widmayer Assignments: Yoshio Okamoto based on a lecture in Aarhus, DK, by Gerth Stølting Brodal and Rolf Fagerberg EMADS 04/ 05: Course Description Page 1
3 Course Lectures: Based on articles. Theoretical. New stuff: Aim: General principles and methods. EMADS 04/ 05: Course Description Page 2
4 Course Lectures: Based on articles. Theoretical. New stuff: Aim: General principles and methods. Homepage: EMADS 04/ 05: Course Description Page 2
5 Analysis of algorithms The standard model: Memory CPU EMADS 04/ 05: Course Description Page 3
6 Analysis of algorithms The standard model: Memory CPU Add: 1 unit of time Mult: 1 unit of time Branch: 1 unit of time MemAccess: 1 unit of time EMADS 04/ 05: Course Description Page 3
7 Reality Memory hierarchy: RAM CPU Cache2 Reg. Cache1 Disk Tertiary Storage EMADS 04/ 05: Course Description Page 4
8 Reality Memory hierarchy: RAM CPU Cache2 Reg. Cache1 Disk Tertiary Storage Access time Volume Registers 1 cycle 1 Kb Cache 5 cycles 512 Kb RAM 50 cycles 512 Mb Disk 20,000,000 cycles 80 Gb EMADS 04/ 05: Course Description Page 4
9 Reality Memory hierarchy: RAM CPU Cache2 Reg. Cache1 Disk Tertiary Storage Access time Volume Registers 1 cycle 1 Kb Cache 5 cycles 512 Kb RAM 50 cycles 512 Mb Disk 20,000,000 cycles 80 Gb CPU speed improves faster than RAM access time and much faster than disk access time EMADS 04/ 05: Course Description Page 4
10 Reality Many real-life problems of Gigabyte, Terabyte, and even Petabyte size: Databases weather geology/geograpy astrology financial WWW phone companies Geographic Information Systems (maps). Computer graphics, animation. VLSI design. EMADS 04/ 05: Course Description Page 5
11 I/O bottleneck I/O is the bottleneck I/O should be optimized (not instruction count) EMADS 04/ 05: Course Description Page 6
12 Analysis of algorithms New I/O-model: CPU Memory 1 Block Memory 2 EMADS 04/ 05: Course Description Page 7
13 Analysis of algorithms New I/O-model: CPU Memory 1 Block Memory 2 Parameters: N = no. of elements in problem. M = no. of elements that fit in RAM. B = no. of elements in a block on disk. D = no. of disks (copies of Memory 2) EMADS 04/ 05: Course Description Page 7
14 Analysis of algorithms New I/O-model: CPU Memory 1 Block Memory 2 Parameters: N = no. of elements in problem. M = no. of elements that fit in RAM. B = no. of elements in a block on disk. D = no. of disks (copies of Memory 2) Cost: Number of I/O s (block transfers) between Memory 1 and Memory 2. EMADS 04/ 05: Course Description Page 7
15 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
16 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
17 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
18 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
19 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
20 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
21 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
22 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
23 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. EMADS 04/ 05: Course Description Page 8
24 Generic Example Consider two O(n) algorithms: 1. Memory accessed randomly page fault at each memory access. 2. Memory accessed sequentially page fault every B memory accesses. O(N) I/Os vs. O(N/B) I/Os Typically, B EMADS 04/ 05: Course Description Page 8
25 Specific Examples QuickSort sequential access vs. HeapSort random access QuickSort: HeapSort: O(N log 2 (N/M)/B) O(N log 2 (N/M)) EMADS 04/ 05: Course Description Page 9
26 Course Contents (approximate): The I/O model(s). Algorithms, data structures, and lower bounds for basic problems: Permuting Sorting Searching I/O efficient algorithms and data structures for problems from computational geometry, strings, graphs. EMADS 04/ 05: Course Description Page 10
27 Course Contents (approximate): The I/O model(s). Algorithms, data structures, and lower bounds for basic problems: Permuting Sorting Searching I/O efficient algorithms and data structures for problems from computational geometry, strings, graphs. Along the way I: Generic principles for designing I/O-efficient algorithms. Along the way II: Hands-on experience via projects. EMADS 04/ 05: Course Description Page 10
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