I/O-algorithms, Spring 2006

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@cs.duke.edu

Lectures:

Third and Fourth quarter 2006, Thursday 13:15-16:00 in Shannon 159

Course Synopsis:

The class will cover a subset of the following:

Summary of Lectures:

 
Lec.
Date
Topic
Reading
1 (lec1.ppt)
Feb 2
 Introduction: Hierarchical memory, I/O-model, fundmental bounds
Sorting: Merge and distribution sort, lower bounds
[AV], [AL], [Alower]
2 (lec2.ppt)
 Feb 9
 Project 1: I/O-efficient merge sort
Searching: B-trees, weight-balanced B-trees, persistent B-trees 		[Anote] sec 1-4
3 (lec3.ppt)
 Feb 16
 Geometric data structures: Buffer trees [Anote] sec 5
4 (lec4.ppt)
 Feb 23
 Geometric data structures: Interval trees, priority search trees [Anote] sec 6+7
-
 Mar 2
 Cancelled
 -
5 (lec5.ppt)
 Mar 9
 Geometric data structures: Range trees, kdB-trees, O-trees
 [Anote] sec 8+9
6 (lec6.ppt)
 Mar 16
Geometric data structures: R-trees, PR-trees
Batched geometric problems: Distribution sweeping
Project 2: I/O-efficient heap and heap sort
[AdBHY] sec 1-2
[GTVV] sec 2.0-2.1
-
 Mar 23
 Break
 -
-
 Mar 30
 Break
 -
7
 Apr 6
 Graph algorithms: List ranking, algorithms on trees [Z] sec 2-4, [CGGTVV],sec 3-6, [Abuffer] sec 4.1, [ABDHM] sec 3.1-3.2
-
 Apr 13
Break (Easter)
 -
8
 Apr 20
 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 
9
 Apr 27
 Graph algorithms: Undirected Minimal Spanning Tree
Project 3: Theoretical homework
 [Z] sec 5, [ABT] sec 2,  [ABDHM] sec 3.4
10 (Brodal)
 May 4
Cache-oblivious algorithms: Model, Matrix multiplication, van Emde Boas Layout, dynamic search trees
 [FLPR] Sect.1, 2, 6, [BFJ] Sect. 3,
[ABF] Sect. 38.1, 38.2.1. 38.3.1
11 (Brodal)
 May 11
 Cache-oblivious algorithms: Sorting, priority queues, distribution sweeping [FLPR] Sect. 4, [ABF] Sect 38.2.2, 38.4.2, [BF] Sect. 2-3, [ABDHM] Sect. 2
12
 May 18
 Graph algorithms: Shortest paths, lower bounds [Z] sec 7, [KS] sec 2.2+3.3
[Z] sec 11,  [Aobbd] sec 2.3-lemma 2, [CGGTVV] sec. 2 
-
 May 25
 Break (Kr. himmelfartsdag)
-
 June 21
 Oral exam
 -

Course material:

The course will be based on original papers, survey papers and lecture notes (list 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. [AdBHY] The Priority R-Tree: A Practically Efficient and Worst-Case Optimal R-Tree. L. Arge, M. de Berg, H. Haverkort, and K. Yi. Proc. SIGMOD'04.
  6. [GTVV] External-Memory Computational Geometry. M.T. Goodrich, J-J. Tsay, D.E. Vengroff, and J.S. Vitter. Proc. FOCS'93.
  7. [Z] I/O-Efficient Graph Algorithms. N. Zeh. Lecture notes.
  8. [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
  9. [ABDHM] Cache-Obliviosu Priority Queue and Graph Algorithm Applications. L. Arge, M. Bender, E. Demaine, B. Holland-Minkley and I. Munro. Proc. STOC'02 (accepted for SICOMP)
  10. [Abuffer] The Buffer Tree: A Technique for Designing Batched External Data Structures. L. Arge. Algorithmica, 37:1-24, 2003.
  11. [BGVW] On External Memory Graph Traversal. A.L. Buchsbaum, M. Goldwasser, S. Venkatasubramanian, J.R. Westbrook, Proc. SODA'00.
  12. [MR] I/O-Complexity of Graph Algorithms. K. Munagala and A. Ranade. Proc. SODA'99.
  13. [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.
  14. [FLPR] Cache-Oblivious Algorithms. M. Frigo, C. E. Leiserson, H. Prokop and S. Ramachandran. Proc. FOCS'99.
  15. [ABF] Cache-Oblivious Data Structures. L. Arge, G. S. Brodal and R. Fagerberg. Chapter 38 in Handbook of Data Structures and
    Applications, CRC Press, 2004
  16. [BF] Cache Oblivious Distribution Sweeping. G.S. Brodal and R. Fagerberg. Proc. ICALP'02.
  17. [BFJ] Cache-Oblivious Search Trees via Binary Trees of Small Height. Gerth Stølting Brodal, Rolf Fagerberg, and Riko Jacob. In Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 39-48, 2002.
  18. [KS] Improved Algorithms and Data Structures for Solving Graph Problems in External Memory. V. Kumar and E.J. Schwabe. Tech. report version of paper in SPDP'96.
  19. [Aobbd] The I/O-Complexity of Ordered Binary-Decision Diagarm Manipulation. L. Arge. Full version of paper in Proc. ISAAC'95.

Prerequisites:

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

Projects:

Evaluation:

Oral exam is on June 21, 2006 in Turing-024 . The exam takes approximately 20 minutes, including evaluation. It will be a discussion of the reports on the three projects (and the material covered in class). The final grade - on the 13-scale - will be based on the project reports and the oral examination.

Examination list:

 1.  9:00 Rasmus Nygaard Andersen (3)
 2.  9:20 Bo Martin Sponholtz (3)
 3.  9:40 Martin Henning Jensen (3)
 4. 10:00 Anders Hessellund Jensen (1)
 5. 10:20 Mikkel Krøigård (2)

 6. 13:00 Rasmus Grønbæk (4)
 7. 13:20 Martin S. Kristensen (4)
 8. 13:40 Bo S. Carstensen (4)
 9. 14:00 Morten Revsbæk (5)
10. 14:20 Niels Døssing (5)
11. 14:40 Martin Olsen (5)

Credits:

10 ECTS

Lars Arge
Thu May 18, 2006