Online Didactic Material for course "Ricerca operativa e Ottimizzazione"
Here you can find the complete list of the course material available online.
Description  Date  Size  Type  

00Graphs, linear algebraElements of graph theory and polyhedral geometry 

0.2 Polyhedral geometry  English
Elementary definitions of polyhedral geometri, a few things to know  English version 
05 mar 2019  208KB  
0.2 Polyhedral geometry  Italian
Elements of linear algebra and polyhedral geometry, Italian version 
05 mar 2019  324KB  
0.1 Elements of graph theory  Italian
Elements of graph theory: definitions, properties, examples 
05 mar 2019  845KB  
0.1 Elements of graph Theory  English
Graphs: basic definitions and properties 
05 mar 2019  790KB  
01Famous ProblemsA gallery of famous problems 

1.4 Linearization techniques in 01 LP
A method to formulate combinatorial optimization problems as 01 LP 
07 giu 2019  652KB  
1.3 01LP Formulations  Italian
Formulating combinatorial optimization problems as 01 Linear Programming 
05 mar 2019  395KB  
1.2 Linear relaxation: An exercise on the stable set...
Stable set formulations 
05 mar 2019  298KB  
1.2 01 LP formulations and LP relaxation  Italian
01 LP formulations and LP relaxation  Italian version 
05 mar 2019  2305KB  
1.1 Problem Gallery  Italian
A survey of some famous combinatorial optimization problems  Italian version 
05 mar 2019  4898KB  
1.1 A gallery of famous problems  English

05 mar 2019  4740KB  
02ComplexityFundamentals of computational complexity 

2.1 Elements of computational complexity  Italian

05 mar 2019  433KB  
2.1 Elements of computational complexity  English

05 mar 2019  429KB  
04CutsCuts in a graph. The max cut problem: a combinatorial algorithm for line graphs; VLSI circuit layout 

4.2 A VLSI circuit layout problem  English
Models for VLSI circuit layout (English version): PLA folding 
05 mar 2019  1262KB  
4.1 Simple max cut on linegraphs  English
An example of pure combinatorial algorithm: simple max cut on line graphs  English version 
05 mar 2019  660KB  
4.1 Max cut of a line graph  Italian
An example of pure combinatorial algorithm: simple max cut on line graphs  English version 
05 mar 2019  255KB  .zip  
05Dynamic ProgrammingDAGs and dynamic programming 

5.2 01 Knapsack  Italian
Dynamic programming for 01 knapsack and cover  Italian version 
05 mar 2019  414KB  
5.2 01 knapsack  English
Exercise: solving 01 knapsack via dynamic programming  English version 
05 mar 2019  217KB  
5.1 Dynamic programming  Italian
Directed acyclic graphs and recurrence  Italian version 
05 mar 2019  2493KB  
5.1 Dynamic programming  English
Acyclic digraphs and dynamic programming  English version 
05 mar 2019  2561KB  
03UnimodularityTotally unimodular matrices and applications 

3.1 Totally unimodular matrices  Italian
Totally unimodular matrices with applications to integer linear programming  Italian version 
05 mar 2019  438KB  
3.1 Totally unimodular matrices  English

05 mar 2019  412KB  
06MatroidsMatroids, and the greedy algorithm 

6.2 Spanning subgraphs  Italian
01 LP formulations of the spanning tree problem and the TSP, the separation problem 
05 mar 2019  1142KB  
6.2 Spanning subgraphs  Inglese
01 LP formulations of the spanning tree problem and the TSP, the separation problem 
05 mar 2019  1137KB  
6.1 Matroids  Italian
Matroids and the Greedy Algorithm  Italian version 
05 mar 2019  575KB  
6.1 Matroids  English
Matroids and the Greedy algorithm  English version 
05 mar 2019  714KB  
08Matching and around matchingMatching problems, Gallai's and Koenig's Theorems, algorithms for bipartite matching 

8.1 (Bipartite) Matching  Italian
Matching: generalities, weighted and unweighted bipartite matching  Italian version 
05 mar 2019  1290KB  
8.1 (Bipartite) matching  English
Matching: generalities, weighted and unweighted bipartite matching  English version 
05 mar 2019  996KB  
09ApproximationDeterministic algorithms with guaranteed approximation 

9.1 Approximation algorithms  Italian
Deterministic algorithms with guaranteed approximation factor  Italian version 
05 mar 2019  563KB  
9.1 Approximation algorithms  English
Deterministic algorithms with guaranteed approximation  English version 
05 mar 2019  647KB  
10Branch and BoundImplicit enumeration for combinatorial optimization 

10.2 branchandbound  Italian
Implicit enumeration for combinatorial optimization problems, Italian version 
05 mar 2019  1634KB  
10.2 Branchandbound  English
Implicit enumeration methods, English version 
05 mar 2019  1897KB  
10.1 Linear relaxation  Italian
Relations between an integer linear program and its continuous relaxation 
05 mar 2019  2243KB  
11Problems and answer keysAnswer key to official written tests 

answer key to written test  January 23rd, 2017
solutions to proposed exercises, Italian 
02 feb 2017  262KB  
written test  January 23rd, 2017
text only, Italian 
24 gen 2017  190KB  
answer keys  July 8th, 2014
July 8th, 2014  written test  problems and solutions, Italian version 
09 nov 2016  288KB  
answer keys  september 8th, 2014
answer keys  september 8th, 2014  Italian version 
12 dic 2015  333KB  
answer keys  september 24th, 2014
answer keys  september 24th, 2014  Italian version 
12 dic 2015  170KB  
answer keys  july 28th, 2014
answer keys  july 28th, 2014  Italian version 
14 mag 2015  217KB  
answer keys  july 8th, 2014
answer keys  july 8th, 2014  Italian version 
15 apr 2015  288KB  
answer keys  february 6th, 2014
answer keys  february 6th, 2014  Italian version 
15 apr 2015  303KB  
answer keys  december 3rd, 2014
answer keys  december 3rd, 2014  Italian version 
15 apr 2015  467KB  
answer keys  april 23rd, 2014
answer keys  april 23rd, 2014  Italian version 
15 apr 2015  146KB  
answer keys  june 19th, 2014
answer keys  june 19th, 2014  Italian version 
15 apr 2015  232KB  
11Problems and answer keys/written test 1505  may 12th, 2015midterm test problems and answer key  may 12th, 2015  Italian and English version 

midterm test  may 12th, 2015 (group B, text only) Italian...
midterm test  may 12th, 2015 (group B, text only) Italian version 
14 mag 2015  112KB  
midterm test  may 12th, 2015 (group B, text only) English...
midterm test  may 12th, 2015 (group B, text only) English version 
14 mag 2015  117KB  
midterm test  may 12th, 2015 (group A, text only) Italian...
midterm test  may 12th, 2015 (group A, text only) Italian version 
14 mag 2015  111KB  
midterm test  may 12th, 2015 (group A, text only) English...
midterm test  may 12th, 2015 (group A, text only) English version 
14 mag 2015  116KB  
answer keys  may 12th, 2015, group B  italian version
answer keys  may 12th, 2015, group B 
14 mag 2015  132KB  
answer keys  may 12th, 2015, group A  italian version
answer keys  may 12th, 2015, group A 
14 mag 2015  122KB  
11Problems and answer keys/written test 1506  June 24th, 2015final test, texts and solutions  June 24th, groups A, B  italian version 

final test  June 24th, 2015, group B
final test  June 24th, 2015, group B  Italian version 
30 giu 2015  131KB  
answer keys  June 24th, 2015, group B
answer keys  June 24th, 2015, group B  Italian version 
30 giu 2015  316KB  
final test  June 24th, 2015, group A
final test  June 24th, 2015, group A  Italian version 
26 giu 2015  130KB  
final test  June 24th, 2015, group A
final test  June 24th, 2015, group A  English version 
26 giu 2015  134KB  
answer keys  June 24th, 2015, group A
answer keys  June 24th, 2015, group A  Italian version 
25 giu 2015  319KB  
11Problems and answer keys/written test 1506  July 8th, 2015texts and solutions of written tests  July 8th 2015 

July 8th 2015 written test  texts
July 8th 2015 written test  texts, group A (Italian), B (Italian and English) 
09 lug 2015  173KB  
answer key  July 8th 2015
texts and solutions of written tests  July 8th 2015, groups A and B, Italian version 
09 lug 2015  139KB  
11Problems and answer keys/written test 1509  September 15th, 2015text and keys to retake test  September 15th, 2015, groups A and B  Italian version 

answer keys  September 15th, 2015
text and answer keys to retake test  September 15th, 2015, groups A and B  Italian version 
17 set 2015  186KB  
retake test  September 15th, 2015
Italian version 
16 set 2015  198KB  
11Problems and answer keys/written test 1511  November 12nd, 2015answer keys to midterm test  November 12nd, 2015  English version 

midterm test solution  November 12nd, 2015
midterm test solution  November 12nd, 2015  English version 
13 nov 2015  182KB  
midterm test  November 12nd, 2015
midterm test  November 12nd, 2015  English version, text only 
13 nov 2015  132KB  
11Problems and answer keys/written test 1601  January 26th, 2016answer keys to tests  January 26th, 2016, groups A and B  Italian version 

answer keys  January 26th, 2016  Italian
answer keys  January 26th, 2016  Italian version 
03 feb 2016  177KB  
answer keys  January 26th, 2016  English
answer keys  January 26th, 2016  groups A and B, English version 
03 feb 2016  182KB  
written test  January 26th, 2016  Italian
written test  January 26th, 2016  Italian version, text only 
27 gen 2016  192KB  
written test  January 26th, 2016  English
written test  January 26th, 2016  groups A and B, English text only 
27 gen 2016  200KB  
11Problems and answer keys/written test 1602  February 17th, 2016final test, text and answer key  Feb 17th, 2016  groups A and B 

answer keys  February 17th, 2016  Italian
answer keys  February 17th, 2016  groups A and B, Italian 
18 feb 2016  334KB  
answer keys  February 17th, 2016  English
answer keys  February 17th, 2016  groups A and B, English 
18 feb 2016  336KB  
final test  Feb 17th, 2016  text only, Italian
final test  Feb 17th, 2016  groups A and B, text only, Italian 
17 feb 2016  233KB  
final test  Feb 17th, 2016  text only, English
final test  Feb 17th, 2016  groups A and B,text only, English 
17 feb 2016  233KB  
11Problems and answer keys/written test 1604  April 21st, 2016April 21st, 2016  midterm test  problems and solutions, Italian version 

answer keys  April 21st, 2016
April 21st, 2016  midterm test  text and answer keys, Italian version 
09 nov 2016  234KB  
midterm test  April 21st, 2016
April 21st midterm test  text only 
09 nov 2016  163KB  
11Problems and answer keys/written test 1606  June 14th, 2016text and answer key to final test  June 14th, 2016 

text of final test  June 14th, 2016
text of final test  June 14th, 2016  Italian version 
09 nov 2016  180KB  
text of final test  June 14th, 2016
text of final test  June 14th, 2016  English version 
09 nov 2016  153KB  
answer key to final test  June 14th, 2016
answer key to final test  June 14th, 2016  Italian version 
09 nov 2016  225KB  
11Problems and answer keys/final test 1606  June 30th, 2016text and answer key to final test  June 30th, 2016 

text of final test  June 30th, 2016
text of final test  June 30th, 2016 
01 lug 2016  175KB  
answer key to final test  June 30th, 2016
answer key to final test  June 30th, 2016  Italian version 
01 lug 2016  247KB  
11Problems and answer keys/written test 1607  July 25th, 2016July 25th, 2016  written test  problems and solutions, Italian version 

written test  July 25th, 2016  text only
written test  July 25th, 2016  text only, Italian version 
26 lug 2016  347KB  
answer keys  July 25th, 2016
answer keys  July 25th, 2016  Italian version 
26 lug 2016  362KB  
11Problems and answer keys/written test 1609  September 15th, 2016text and answer key to final test  September 15th, 2016 

text of final test  September 15th, 2016
written test of September 15th, 2016  text only, Italian version 
19 set 2016  270KB  
answer key to final test  September 15th, 2016
written test of September 15th, 2016  text and answer key, Italian version 
19 set 2016  371KB  
11Problems and answer keys/written test 1611  November 8th, 2016text and answer key to final test  November 8th, 2016 

final test  November 8th, 2016  text only
final test  November 8th, 2016  text only, Italian version 
08 nov 2016  189KB  
final test  November 8th, 2016  text and answer key
final test  November 8th, 2016  text and answer key, Italian version 
08 nov 2016  326KB  
11Problems and answer keys/written test 1702  February 13th, 2017written test: text and answer key 

written test  February 13th, 2017
written test of Feb 13th, 2017  text only, Italian version 
16 feb 2017  229KB  
answer key to written test  February 13th, 2017
written test of February 13th, 2017  solution of proposed exercises, Italian version 
16 feb 2017  304KB  
11Problems and answer keys/written test 1704  April 20th, 2017midterm test of April 20th, 2017  problems and solutions 

midterm test of April 20th, 2017  answer key
midterm test of April 20th, 2017  answer key, Italian version 
23 apr 2017  248KB  
midterm test of April 20th, 2017  text only
midterm test of April 20th, 2017  text only, Italian version 
20 apr 2017  101KB  
11Problems and answer keys/written test 1706  June 21st 2017written test, June 21st 2017  text and answer key, Italian version 

written test of June 21st, 2017  answer key
written test of June 21st, 2017  answer key, Italian version 
23 giu 2017  203KB  
written test of June 21st, 2017, group B
written test of June 21st, 2017, group B  text only, Italian version 
23 giu 2017  132KB  
written test of June 21st, 2017, group A
written test of June 21st, 2017, group A  text only, Italian version 
23 giu 2017  132KB  
11Problems and answer keys/final test 1707  July 5th, 2017final test  July 5th, 2017: tests and answer key 

written test of July 5th, 2017  text only
written test of July 5th, 2017  text only, Italian version 
08 lug 2017  179KB  
11Problems and answer keys/written test 1707  July 17th, 2017problems and answer key to the written test of July 17th, 2017 

answer key to written test, July 17th, 2017
answer key to written test, July 17th, 2017  Italian version 
18 lug 2017  354KB  
written test, July 17th, 2017  text only
written test, July 17th, 2017  text only, Italian version 
18 lug 2017  203KB  
11Problems and answer keys/written test 1709  September 12th, 2017written test of September 12th, 2017  text and solution, Italian version 

written test of September 12th, 2017  solution
written test of September 12th, 2017  solution, groups A and B, Italian version 
16 set 2017  216KB  
written test of September 12th, 2017  text only
written test of September 12th, 2017  text only, groups A and B, Italian version 
16 set 2017  121KB  
11Problems and answer keys/written test 1802  February 6, 2018written test, questions and answer key 

written test, Feb 6th 2018  text only
written test, Feb 6th 2018  text only, Italian version 
12 feb 2018  129KB  
written test, Feb 6th 2018  answer key
written test, Feb 6th 2018  answer key, Italian version 
12 feb 2018  147KB  
11Problems and answer keys/written test 1802  February 20th, 2018written test of February 20th, 2018, problems and answer key 

Answer key to written test of Feb 20th, 2018  Italian
Written test of Feb 20th, 2018  Italian text with answer key 
20 feb 2018  187KB  
written test of Feb 20th, 2018  Italian
written test of Feb 20th, 2018  Italian text 
20 feb 2018  121KB  
written test of Feb 20th, 2018  English
written test of Feb 20th, 2018  English text 
20 feb 2018  128KB  
11Problems and answer keys/midterm test 1804  April 19th, 2018problems and answer key to the midterm test of April 19th, 2018 

midterm test solution  April 19th, 2018
midterm test solution  April 19th, 2018, Italian 
22 apr 2018  166KB  
midterm test of April 19th, 2018  eng
midterm test of April 19th, 2018  English, text only 
22 apr 2018  105KB  
midterm test of April 19th, 2018  ita
midterm test of April 19th, 2018  Italian, text only 
22 apr 2018  138KB  
11Problems and answer keys/written test 1806  June 21st, 2018written test of June 21st, 2018: problems and answer key 

Written test of June 21st, 2018  answer key
Written test of June 21st, 2018  answer key, Italian version 
06 giu 2019  251KB  
Written test of June 21st, 2018  text only
Written test of June 21st, 2018  text only, Italian version 
23 giu 2018  188KB  
11Problems and answer keys/written test 1807  July 17th, 2018problems and answer key to the final test of July 17th, 2018 

answer key to written test  July 17th, 2018
answer key to written test of July 17th, 2018, Italian version 
06 giu 2019  256KB  
written test of July 17th, 2018  text only
written test of July 17th, 2018  Italian version, text only 
20 lug 2018  155KB  
11Problems and answer keys/written test 1807  July 26, 2018problems and answer key to the final test of July 26th, 2018 

final test, July 26th, 2018  text only
final test of July 26th, 2018  text only, Italian version 
26 lug 2018  2010KB  
final test July 26th, 2018  answer key
answer key to the final test of July 26th, 2018  Italian version 
26 lug 2018  2051KB  
11Problems and answer keys/written test 1809  September 4th, 2018problems and answer key of the written test of September 4th, 2018 

answer key to written test of September 4th, 2018
answer key to written test of September 4th, 2018  Italian version 
25 ott 2018  226KB  
written test of September 4th, 2018
written test of September 4th, 2018  text only, Italian version 
05 set 2018  146KB  
11Problems and answer keys/written test 1811  November 6th, 2018test problems  Nov 6th, 2018  English (only problems) and Italian (problems and solutions) 

written test of Nov 6th, 2018  text only, English
written test of Nov 6th, 2018  text only, Italian version 
07 nov 2018  151KB  
written test of Nov 6th, 2018  text only, English
written test of Nov 6th, 2018  text only, English version 
07 nov 2018  154KB  
written test of Nov 6, 2018  problems and answer key
problems and answer key to the written test of Nov 6, 2018  Italian version 
07 nov 2018  198KB  
11Problems and answer keys/written test 1901  January 22nd, 2019problems and answer key to the written test of January 22nd, 2019 

answer key to written test  Jan 22nd, 2019
answer key to written test of Jan 22nd, 2019  Italian version 
23 gen 2019  220KB  
written test  Jan 22nd, 2019
written test, Jan 22nd 2019  Italian version, problems proposed 
23 gen 2019  154KB  
11Problems and answer keys/written test 1902  Feb 5th, 2019problems and solutions of the written test of Feb 5th, 2019 

answer key to written test of Feb 5th, 2019
answer key to written test of Feb 5th, 2019  Italian version 
07 feb 2019  145KB  
written test of Feb 5th, 2019
written test of Feb 5th, 2019  without solution, Italian version 
06 feb 2019  109KB  
11Problems and answer keys/written test 1902  Feb 19th, 2019text and answer key to final test of Feb 19th, 2019  Italian 

answer key to written test of Feb 19th, 2019
answer key to written test of Feb 19th, 2019, Italian 
23 feb 2019  190KB  
written test of Feb 19th, 2019
written test of Feb 19th, 2019  without solution, Italian 
23 feb 2019  112KB  
11Problems and answer keys/written test 1904  April 11th, 2019problems and solution of the intermediate test of April 11th, 2019 

answer key to written test of April 11th, 2019  English
answer key to written test of April 11th, 2019  English 
16 apr 2019  233KB  
answer key to written test of April 11th, 2019  Italian
answer key to written test of April 11th, 2019  Italian 
16 apr 2019  295KB  
written test of April 11th, 2019  Italian
intermediate test of April 11the, 2019  Italian, text only 
16 apr 2019  219KB  
written test of April 11th, 2019  English
intermediate test of April 11th, 2019  English, text without solution 
16 apr 2019  198KB  
11Problems and answer keys/written test 1906  June 13th, 209Problems and solutions of the final test of June 13th, 2019 

answer key to written test of June 13th, 2019  English

18 giu 2019  195KB  
answer key to written test of June 13th, 2019  Italian
answer key to written test of June 13th, 2019  Italian 
18 giu 2019  296KB  
written test of June 13th, 2019  Italian
written test of June 13th, 2019  Italian, text only 
13 giu 2019  146KB  
written test of June 13th, 2019  English
written test of June 13th, 2019  English, text only 
13 giu 2019  129KB  
11Problems and answer keys/written test 1906  June 26th, 2019problems and solutions of the final test of June 26th, 2019 

Answer key to written test of June 26th, 2019  Italian
Answer key to written test of June 26th, 2019  Italian 
26 giu 2019  249KB  
Written test of June 26th, 2019  Italian
Written test of June 26th, 2019  Italian, just the problems 
26 giu 2019  138KB  
11Problems and answer keys/written test 1907  July 9th, 2019text and answer key to final test of Jul 9th, 2019  Italian 

Answer key to written test of July 9th, 2019
Answer key to written test of July 9th, 2019  Italian 
14 lug 2019  423KB  
Written test of July 9th, 2019
Written test of July 9th, 2019  text only, Italian 
14 lug 2019  170KB  
11Problems and answer keys/written test 1909  September 17th, 2019text and answer key to final test of Sep 17th, 2019  Italian 

Answer key to written test, September 17th 2019
Answer key to written test, September 17th 2019, Italian 
18 set 2019  261KB  
written test, September 17th 2019
written test, September 17th 2019, text only, Italian 
18 set 2019  119KB  
07DualityDuality Theory in LP 

7.3 Zerosum games
Prisoner's dilemma (an economic view), portfolio optimization as an LP, dual analysis 
16 apr 2019  212KB  
7.2 Duality  English
Duality theory in LP  English version 
05 mar 2019  244KB  
7.1 Projections  English
Projections of a convex polyhedron, FourierVeronese Theorem and FourierMotzkin Method  English version 
05 mar 2019  979KB  
7.1 Duality in a nutshell  Italian
Duality theory in LP 
05 mar 2019  4359KB 