====== Combinatorial Algorithms (RM35KOA) ======
Lecturers: [[https://rtime.felk.cvut.cz/~hanzalek/| Zdeněk Hanzálek]], [[https://usermap.cvut.cz/profile/c981a544-91ea-4279-8b58-2a6f387896d5| Antonín Novák]]
Lab teacher:
[[https://usermap.cvut.cz/profile/c981a544-91ea-4279-8b58-2a6f387896d5| Antonín Novák]]
[[https://cw.felk.cvut.cz/brute/|Brute]], [[https://intranet.fel.cvut.cz/cz/education/rozvrhy-ng.B222/public/html/predmety/70/15/p7015806.html|Timetable]]
===== Course overview =====
{{:courses:rm35koa:mixed-criticality-bnb.png?200 |}}
This course focuses on the problems and algorithms of combinatorial optimization (often called discrete optimization). We emphasize the practical use of optimization techniques and algorithms based on graphs, integer linear programming, heuristics, approximation algorithms, and state-space search methods. You will learn how to formulate the problem using existing formalisms, and you will obtain experience with the existing algorithms solving them.
We demonstrate the use of combinatorial optimization algorithms on a large variety of real-life applications, e.g., logistics, transportation, planning of human resources, scheduling in production lines, message routing, and scheduling in parallel computers.
===== Exam results =====
{{ :courses:ko:23_05_29_ko_koa_exam_1.pdf | Exam 1 (29.5.2023) results}} (password is the animal displayed at the "Theodor taking a walk" private instance of HW1 (in Czech, lowercase)
{{ :courses:ko:23_06_10_ko_koa_exam_2.pdf | Exam 2 (10.6.2023) results}} (heslo je manželka zvířete z hesla v prvním termínu (vše malé, bez diakritiky))
===== Lectures =====
^ Week No. ^ Dates ^ Title ^ Lecturer ^ Handouts ^ Notes^
| 1 | 20.2.-26.2. | Introduction of Basic Terms, Example Applications | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/Basic_e.pdf]] | [[https://youtu.be/G1mKKyGpp_k|Intro]] |
| 2 | 27.2.-5.3. | Computational Complexity | AN | [[https://rtime.felk.cvut.cz/~novakan9/KOA/Complexity_e.pdf]] | |
| 3 | 6.3.-12.3. | Integer Linear Programming - Algorithms | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/ILP_e.pdf]] | [[https://youtu.be/hX9KE0DJJD4|ILP-I]] |
| 4 | 13.3-19.3. | Integer Linear Programming - Problem Formulations | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/ILP_e.pdf]] | [[https://youtu.be/90hs0gTgdHI|ILP-II]] |
| 5 | 20.3.-26.3. | Shortest Paths | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/SPT_e.pdf]] | [[https://youtu.be/90hs0gTgdHI?t=4516|SP-I]] \\ [[https://youtu.be/LCTwYILbmEY?t=44 | SP-II ]] \\ [[https://youtu.be/eFLIzXDeJ6U?t=33 | SP-III ]] |
| 6 | 27.3.-2.4. | Problem Formulation by Shortest Paths | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/SPT_e.pdf]] | **Test 1.** |
| 7 | 3.4.-9.4. | Flows and Cuts - Algorithms and Problem Formulation | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/Flows_e.pdf]] | [[https://youtu.be/eFLIzXDeJ6U?t=5687 | Flows-I]] \\ [[https://youtu.be/xK3xiyEfG-k | Flows-II]] \\ [[https://youtu.be/71B1FMVVX_o?t=34 | Flows-III]]|
| 8 | 10.4. public holiday | | | | |
| 9 | 17.4.-23.4. | Bipartite Matching. Multi-commodity Network Flows | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/Flows_e.pdf]] | |
| 10 | 24.4.-30.4. | Knapsack Problem, Pseudo-polynomial and Approximation Algorithms | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/knapsack_e.pdf]] | [[https://youtu.be/71B1FMVVX_o?t=3422 | Knapsack-I ]] |
| 11a | 1.5. public holiday | | | | |
| 11b | 4.5. replacement for #11a. | Traveling Salesman Problem and Approximation Algorithms | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/TSP_e.pdf]] | [[https://youtu.be/p9qiafTnd6Q?t=25 | TSP-I]] |
| 12a | 8.5. public holiday | | | | |
| 12b | 9.5. replacement for #12a. | Mono-processor Scheduling | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/sched_e.pdf]] | **Test 2.** [[https://youtu.be/p9qiafTnd6Q?t=6439 | Sched-I]] \\ [[https://youtu.be/idc516WZZ1I?t=41 | Sched-II ]] \\ [[https://youtu.be/MjekjcErKPc?t=21|Sched-III]] \\ [[https://youtu.be/dhe54BPDNwo?t=67|Sched--IV]] |
| 13 | 15.5.-21.5. | Scheduling on Parallel Processors | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/sched_e.pdf]] | |
| 14 | 22.5.-28.5. | Scheduling on Parallel Processors (cont.) | ZH | [[https://rtime.felk.cvut.cz/~hanzalek/KOA/sched_e.pdf]] | |
**Materials by topic**
^Title ^ Handouts ^ Stream^
|**Introduction** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/Basic_e.pdf]]| [[https://youtu.be/G1mKKyGpp_k|Intro]] |
|**Complexity** | [[https://rtime.ciirc.cvut.cz/~novakan9/KOA/Complexity_e.pdf]] | | |
|**Integer Linear Programming** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/ILP_e.pdf]]| [[https://youtu.be/hX9KE0DJJD4|ILP-I]] \\ [[https://youtu.be/90hs0gTgdHI|ILP-II]] |
| **Shortest paths** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/SPT_e.pdf]]| [[https://youtu.be/90hs0gTgdHI?t=4516|SP-I]] \\ [[https://youtu.be/LCTwYILbmEY?t=44 | SP-II ]] \\ [[https://youtu.be/eFLIzXDeJ6U?t=33 | SP-III ]] |
| **Network flows** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/Flows_e.pdf]]| [[https://youtu.be/eFLIzXDeJ6U?t=5687 | Flows-I]] \\ [[https://youtu.be/xK3xiyEfG-k | Flows-II]] \\ [[https://youtu.be/71B1FMVVX_o?t=34 | Flows-III]]|
|**Knapsack** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/knapsack_e.pdf]]| [[https://youtu.be/71B1FMVVX_o?t=3422 | Knapsack-I ]]|
|**Traveling Salesman Problem** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/TSP_e.pdf]]| [[https://youtu.be/p9qiafTnd6Q?t=25 | TSP-I]] |
|**Scheduling** |[[https://rtime.felk.cvut.cz/~hanzalek/KOA/sched_e.pdf]]| [[https://youtu.be/p9qiafTnd6Q?t=6439 | Sched-I]] \\ [[https://youtu.be/idc516WZZ1I?t=41 | Sched-II ]] \\ [[https://youtu.be/MjekjcErKPc?t=21|Sched-III]] \\ [[https://youtu.be/dhe54BPDNwo?t=67|Sched--IV]] |
===== Grading =====
Students may receive a total of 100 points. The final exam is worth 50% of the grade, while the other 50% can be obtained during the semester.
The points are distributed according to the following table.
| **Category** || **Maximum points** | ::: |
| **Semester** | Homeworks (3 assignments) | 15 | ::: |
| ::: | Theoretical tests (two tests, 10 points each)| 20 | ::: |
| ::: | Semester project | 15 | **Minimum points** |
| ::: | **Total semester** 1) | 50 | 30 |
| **Final exam** 2) | Written part | 40 | 20 |
| ::: | Oral exam | 10 | 0 |
| **Total** || 100 | 50 |
1) To get an ungraded assessment the following requirements have to be met:
* successfully solve all homework assignments (i.e., accepted by BRUTE evaluation as correct)
* obtain at least 30 from 50 points
The last date of awarding the ungraded assessments is **28. 5. 2023**. If you fail to fulfill the requirements by then, you will also fail the entire class.
2) Only the students, who obtained the ungraded assessment are allowed to take the exam.
The exam constitutes of the written part (40 points) and oral exam (10 points).
To pass the written exam, it is necessary to get at least 20 points.
The oral exam is **mandatory**.
**Final grading scale**:
^Points ^[0,50) ^[50,60) ^[60,70) ^[70,80) ^[80,90) ^[90,100]^
|Grade | F | E | D | C | B | A |
==== Assessment recognition ====
The following applies only to students who got an ungraded assessment in the previous year (all other students have to undergo the course from scratch).
Although the assessments are not fully recognized, the students may opt-in to transfer some points from the previous year to the current one (they may also undergo the course from scratch to get a higher number of points).
The following rules apply
- Theoretical tests, practical test and the homeworks have to be repeated.
- Students may transfer points from the semester project. If the grading table of the course changes between the years, the points are scaled accordingly. It is also possible to work on the same topic to increase/decrease the number of received points.
- The minimum number of points required to get an ungraded assessment is always taken from the current year grading table.