I/O-algorithms, Spring 2011

Description:

In many modern applications that deal with massive data sets, communication between internal and external memory, and not actual computation time, is the bottleneck in the computation. This is due to the huge difference in access time of fast internal memory and slower external memory such as disks. In order to amortize this time over a large amount of data, disks typically read or write large blocks of contiguous data at once. This means that it is important to design algorithms with a high degree of locality in their disk access pattern, that is, algorithms where data accessed close in time is also stored close on disk. Such algorithms take advantage of block transfers by amortizing the large access time over a large number of accesses. In the area of I/O-efficient algorithms the main goal is to develop algorithms that minimize the number of block transfers (I/Os) used to solve a given problem.

This class will cover I/O-efficient algorithms and data structures for fundamental problems in e.g. graph theory and computational geometry, with focus on the techniques used to design such algorithms. After the class the participants should be well-equipped to conduct master or phd level research in the area.

Instructor:

Lars Arge

Office: Turing 224
Phone: 8942-9336
E-mail: large@madalgo.au.dk

Lectures:

Third quarter: and fourth quarter: Tuesday 9:15-12:00 in 5523.131 (Incuba science park)

Course Synopsis:

The class will cover a subset of the following:

  • Hierarchical memory models and fundamental bounds
  • External sorting and searching, e.g. merge and distribution sort, B-trees, and Buffer-trees
  • Geometric searching problems, e.g. interval trees, point location, priority search trees, range trees, kdB-trees, O-trees, and R-trees
  • Batched geometric problems, e.g. distribution sweeping, batched filtering, line segment intersection
  • Graph problems, e.g. list ranking, MST, SSSP, planer graph algorithms, and graph blocking
  • Cache-oblivious algorithms
  • Implementation I/O algorithms and data structures

Summary of Lectures:

 

Lec.

Date

Topic

Reading

Slides

-

Jan 25

Cancelled

-

-

1

Feb 1

Introduction: Hierarchical memory, I/O-model, fundamental bounds
Sorting: Merge and distribution sort

Project 1: I/O-efficient merge-sort

[AV], [AL]

ppt, pdf

-

Feb 8

Cancelled

-

-

2

Feb 15

Cancelled (Lars sick)

-

-

3

Feb 22

Sorting: Lower bounds

Searching: B-trees, Weight-balanced B-trees

[Alower]

[Anote] sec 1-3

ppt, pdf

4

Mar 1

Guest lecture by Nodari Sitchinava

Batched geometric problems: Distribution sweeping

Parallel private-cache algorithms: Model, parallel distribution sweeping

[GTVV] sec 2.0-2.1

 

[AGNS], [ASZ]

pdf (slide 1-79 in detail and 80-109 overviewed)

5

Mar 8

Searching: Persistent B-trees, buffer trees

Project: I/O-efficient heap and heap sort

[Anote] sec 4-5
[FJKT]

ppt, pdf

-

Mar 15

Break

-

-

-

Mar 22

Break

-

-

-

Mar 29

Break

-

-

6

Apr 5

Geometric data structures: Interval trees, Priority search trees

[Anote] sec 6-7

ppt, pdf

7

Apr 12

Geometric data structures: Range trees, kdB-trees, O-trees

[Anote] sec 8-9

ppt, pdf

8

Apr 19

Geometric data structures: R-trees, PR-trees (+review of distribution sweeping)

Projekt 3: Theoretical homework

[AdBHY] sec 1-2

ppt, pdf

Apr 26

Easter break

-

-

9

May 3

Graph algorithms: List ranking, algorithms on trees

[Z] sec 2-4, [CGGTVV] sec 3-6, [ABDHM] sec 3.1-3.2

 

10

May 10

Graph algorithms: Directed DFS and BFS, undirected BFS

[Z] sec 6.1-6.2, [ABDHM] sec 3.3, [CGGTVV], sec 7, [BGVW], [MR] sec 5.1 

-

11

May 17

Graph algorithms: Undirected Minimal Spanning Tree (Lecturer: Gerth Brodal)

[Z] sec 5, [ABDHM] sec 3.4, [ABT] sec 2, [ABW] sec 5.1

-

12

May 24

Cache oblivious algorithms: Models, Matrix-Multiplication, Search trees, Sorting.  (Lecturer: Gerth Brodal)

[FLPR99] Sec 1,2,4,6, [BF02] Sec 1-2

pdf

-

June 22-23

Oral exam

-

-

Course material:

The course will be based on original papers, survey papers and lecture notes (list below will be extended as course progress):

  1. [AV] The Input/Output Complexity of Sorting and Related Problems. A. Aggarwal and J. Vitter. CACM 31 (9), 1988.
  2. [AL] External partition element finding, Lecture notes by L. Arge and M. G. Lagoudakis.
  3. [Alower] Lower bound on External Permuting/Sorting, Lecture notes by L. Arge.
  4. [Anote] External Memory Geometric Data Structures. L. Arge. Lecture notes.
  5. [GTVV] External-Memory Computational Geometry. M.T. Goodrich, J-J. Tsay, D.E. Vengroff, and J.S. Vitter. FOCS 1993.
  6. [AGNS] Fundamental parallel algorithms for private-cache chip multiprocessors. L. Arge, M.T. Goodrich, M. Nelson, N. Sitchinava. SPAA 2008
  7. [ASZ] Geometric algorithms for private-cache chip multiprocessors. D. Ajwani, N. Sitchinava, N. Zeh. ESA 2010.
  8. [FJKT] Heaps and Heapsort on Secondary Storage. R.Fadel, K.V. Jakobsen, J. Katajainen, J. Teuhola. TCS 220 (2), 1999.
  9. [Z] I/O-Efficient Graph Algorithms. N. Zeh. Lecture notes.
  10. [CGGTVV] External-Memory Graph Algorithms. Y-J. Chiang, M. T. Goodrich, E.F. Grove, R. Tamassia. D. E. Vengroff, and J. S. Vitter. Proc. SODA'95
  11.  [ABDHM] Cache-Oblivious Priority Queue and Graph Algorithm Applications. L. Arge, M. Bender, E. Demaine, B. Holland-Minkley and I. Munro. SICOMP, 36(6), 2007.
  12.  [BGVW] On External Memory Graph Traversal. A.L. Buchsbaum, M. Goldwasser, S. Venkatasubramanian, J.R. Westbrook, Proc. SODA'00.
  13.  [MR] I/O-Complexity of Graph Algorithms. K. Munagala and A. Ranade. Proc. SODA'99.
  14. [ABT] On External-Memory MST, SSSP and Multi-Way Planar Graph Separation. L. Arge, G. S. Brodal, and Laura Toma. Journal of Algorithms 53:186-206, 2004.
  15. [ABW] A functional approach/ to external graph algorithms. J. Abello, A. L. Buchsbaum, and J. Westbrook. Algorithmica, 32(3):437-458, 2002.
  16. [FLPR99] Cache-Oblivious Algorithms. M. Frigo, C. Leiserson, H. Prokop, and S. Ramachandran. Proc. FOCS '99.
  17. [BF02] Cache Oblivious Distribution Sweeping. G. S Brodal and R. Fagerberg. Proc. ICALP’02.

Prerequisites:

dADS1+2, dOpt+dKombSøg (can be followed in parallel), and an interest in algorithms.

Projects:

Evaluation:

Three projects and a 20 minute oral exam (on June 22-23 in Turing-014) including evaluation (discussion of the reports on the three projects and the material covered in class). The final grade will be based on the project reports and the oral examination.

 

Examination list:

June 22:

1.      9:00 Tore Frederiksen (1)

2.      9:20 Søren Frederiksen (1)

3.      9:40 Vaida Ceikute (1)

4.      10:00Carsten Sørensen (1)

5.      10:20 Jørgen Fogh (2)

6.      10:40 Jesper A. S. Nielsen (2)

7.      11:00 Andreas Koefoed-Hansen (2)

8.      11:20 Jeppe Schou (3)

9.      11:40 Anders Egerup Halager (3)

10.  12:00 Troels Toftebjerg Hansen (3)

11.  12:20 Mikkel Hougaard (3)

June 23:

1.      9:00 Esben Rasmussen (4)

2.      9:20 Kasper Kristensen (4)

3.      9:40 Asger Eriksen (4)

4.      10:00 Thibaut Goetghebuer-Planchon (5)

5.      10:20 Søren Chrestensen (5)

6.      10:40 Eivind Ortind Simonsen (5)

7.      11:00 Stefan Ravnholt Nielsen (5)

8.      11:20 Thomas Sylvest (5)

9.      12:40 Mads Sandberg Brun (6)

10.  12:00 Peter Sandberg Brun (6)

Credits:

10 ECTS

Lars Arge
Tue June 21, 2011