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Year 2022-2023

Announcements

  • The course will start on Feb. 22, 2023.

Schedule (work in progress)

  • Class hours: Mon 09‑11 (Fib-X1), Wed 09‑11 (Fib-L1), Fri 11-13 (Fib-L1)
  • MS Teams channel here, please subscribe
  • Office hours: remotely by appointment

Overview

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.

Exams

Written exam: weekly hands-on in classroom (attendance is highly suggested).

Oral exam: topics discussed in class, please read the references in the notes.

Syllabus: programma d'esame

Topics

  • Please see the topics listed below. Handouts are are available in the MS Teams channel.
Activity in class
  • The screen snapshots shown during the classes are available in the MS Teams channel.
Official forms for the course

Class schedule

Date Topics References and notes
22.02.2023 Introduction to the class. Course organization, schedule, and purpose.
24.02.2023 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
27.02.2023 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
01.03.2023 Universal hashing. Markov's inequality. Perfect hashing. [CLRS 11.2, 11.3.3, CLRS 11.5 ] code
03.03.2023 Weekly hands-on. see Teams drive
06.03.2023 Introduction to game theory. The theory of rational choice. Strategic games. The prisoner dilemma. Pollution game. Bach or Stravinsky. Matching Pennies. Stag hunt. (F. Geraci) see Teams drive
08.03.2023 Nash equilibrium. Review of example strategic games. Nash equilibrium of stag hunt with n players. Best response. Using best response to find the Nash equilibrium. (F. Geraci) see Teams drive
10.03.2023 Weekly hands-on. (F. Geraci) see Teams drive
13.03.2023 Game Theory. Improving and best response. Dominated actions. Vickrey auction (aka second price auction). Expected payoffs. (F. Geraci) see Teams drive
15.03.2023 Mixed strategy Nash equilibrium. Example: matching penny. Example: kicking penalty. Stable matching. (F. Geraci) see Teams drive
17.03.2023 Weekly hands-on. (F. Geraci) see Teams drive
20.03.2023 Worst-case constant-time lookup: Cuckoo hashing. Notes Notes code
22.03.2023 Proxy caches and dictionaries with errors: Bloom filters. Survey: except par.2.5-2.6 (optional: par.2.2)
24.03.2023 Weekly hands-on. see Teams drive
27.03.2023 Space-efficient storage of sets with approximate memberships: upper and lower bounds. Notes (second part)
29.03.2023 Distributed server and load balancing through hashing. blog Sect.7 and 8.1
31.03.2023 Weekly hands-on. see Teams drive
03.04.2023 Document resemblance with MinHash, k-sketches and the Jaccard similarity index. Azuma-Hoeffding bound. Triangle counting. paper paper Azuma-Hoeffding code
05.04.2023 Count-Min sketches for frequent elements. sects.1-3, 4.1 Site Notes code
14.04.2023 Weekly hands-on. see Teams drive
17.04.2023 The data stream model. Cardinality estimation. Linear counting. LogLog counters. (F. Geraci) see Teams drive
19.04.2023 Bloom filters (probabilistic deletion and counting). Count min sketch. Heavy hitters. The space saving algorithm. (F. Geraci) see Teams drive
21.04.2023 Weekly hands-on. (F. Geraci) see Teams drive
24.04.2023 Networked data and randomized min-cut algorithm for graphs. par.1.1
26.04.2023 Approximation in fine-grained algorithms and limitations. Case study: diameter in undirected unweighted graphs. notes
03.05.2023 Fine-grained algorithms. SETH conjecture and conditional lower bounds. Guaranteed heuristics. Case study: diameter in undirected unweighted graphs. notes sect. 2.3, 2.4, 3, 4
08.05.2023 Fixed-parameter tractable (FPT) algorithms. Kernelization. Bounded search tree. Case study: min-vertex cover in graphs. sect. 2.2.1, 3.1
10.05.2023 Randomized FPT algorithms: color coding and randomized separation. Case study: longest path in graphs and subgraph isomorphism. sect. 5.2, 5.3
12.05.2023 Local search, Greedy, Randomized: case study of max cut for graphs. Notes
15.05.2023 NP-hard problems: download file manager and the knapsack problem. Dynamic programming algorithms for Knapsack: Case 1: integer weights, complexity O(nW). Case 2: integer values, complexity O(n2vmax). Examples. General inapproximability results. Case study: travel salesman problem (TSP). 2-approximation algorithms for metric TSP. [CLRS 35.2] notes
17.05.2023 NP-hard problems: fully polynomial-time randomized approximation schemes (FPRASs). Case study: #knapsack problem. notes notes code
magistraleinformatica/ad/ad_22/start.txt · Ultima modifica: 03/07/2023 alle 12:07 (13 mesi fa) da Roberto Grossi