This week the teaching activity is suspended, as requested by our Rector. Hence the classes of March 5 and 6 are canceled. Next class is Tue, March 10, regular time, but lectures will be given in streaming. More details follow.
You student, what can you do next for getting a lecture?
The advanced nature of this course focuses on developing algorithmic design skills, exposing the students to complex problems that cannot be directly handled by standard libraries (being aware that several basic algorithms and data structures are already covered by the libraries of modern programming languages), thus requiring a significant effort in problem solving. These problems involve all basic data types, such as integers, strings, (geometric) points, trees and graphs as a starting point. The syllabus is structured to highlight the applicative situations in which the corresponding algorithms can be successfully employed, making references to software applications and libraries. The level of detail in each argument can change year-by-year, and will be decided according to requests coming from other courses in the curriculum and/or specific issues arising in, possibly novel, applicative scenarios.
Suggested reading: some useful tips for scientific writing in English (first two sections) by J.S. Vitter.
Example of interaction: student and instructor discussing the report's content and structure.
Oral exam: topics discussed in class, please read the references in the notes.
Caveat: Several topics are the outcomes of recent advancements in the field, and thus the course material mostly consists in research papers or book chapters.
Randomization is a powerful tool to solve large-scale problems. After introducing the concept of randomized algorithms and hashing, we consider some applications, such as data streaming algorithms, a field emerged in the last decade. Here data flow as a stream and one-pass algorithms with limited memory can process it. We focus on the count-min sketch paradigm and its applications. [Note: to refresh the basic notions on counting and probability, please refer to Appendix C in Cormen-Leiserson-Rivest-Stein's book “Introduction to Algorithms”, 3rd ed., MIT Press. Concentration bounds are explained in these class notes.]
|Date||Topics||References and notes|
|18.02.2020||Playing with probability. Random indicator variables: secretary problem and random permuting (suggested reading: birthday paradox). Randomized quick sort.||[CLRS 5.1-5.3 (optional 5.4.1), par. 7.3] code|
|20.02.2020||Virus scan and stream analysis with Karp-Rabin fingerprints: randomized checking and pattern matching. Montecarlo and Las Vegas algorithms.||[RM par.7.4-7.6] code|
|21.02.2020||Universal hashing. Markov's inequality. Perfect hashing.||[CLRS 11.2, 11.3.3, CLRS 11.5 ] code|
|25.02.2020||Proxy caches and dictionaries with errors: Bloom filters.||Survey: except par.2.5-2.6 (optional: par.2.2)|
|27.02.2020||Worst-case constant-time lookup: Cuckoo hashing.||Notes Notes code|
|28.02.2020||Space-efficient implementation of Bloom filters using cuckoo hashing and succinct rank data structure.||Notes (first part)|
|03.03.2020||Space-efficient storage of sets with approximate memberships: upper and lower bounds.||Notes (second part)|
|10.03.2020||Distributed server and load balancing through hashing.||blog Sect.7 and 8.1|
|12.03.2020||Distributed server and load balancing through hashing (continued).||blog Sect.7 and 8.1|
|13.03.2020||Multiplicative universal hashing.||Sect. 2.3|
|17.03.2020||Data streaming and sketching algorithms: approximate counters (part 1).||Sect. 3-5|
|19.03.2020||Case study on hashing: rsync and file synchronization using hash functions.||slides|
|20.03.2020||Sketching algorithms: approximate counters (part 2).||Sect. 3-5|
|24.03.2020||Sketching algorithms: approximate counters (part 3).||Sect. 3-5|
|26.03.2020||Flajolet-Martin sketches for counting distinct elements.||notes|
|27.03.2020||Count-Min sketches for frequent elements.||sects.1-3, 4.1 Site Notes code|
|31.10.2020||Integer counters and range queries with Count-Min Sketches: implementation and analysis.||sects.3-4|