## Lesson Diary A.y. 2021-2022

Wednesday September 22, 2021 (Lessons 1-2-3):

Introduction

The Routing Problem i.e. the Least Cost Path Problem (1)

• The routing Problem
• The shortest path Problem
• shortest paths: BFS
• The least cost path Problem
• the negative cycle issue
• least cost paths: introduction

Friday September 24, 2021:

No lesson

Wednesday September 29, 2021 (Lessons 4-5-6):

The Routing Problem i.e. the Least Cost Path Problem (2)

• The least cost path Problem
• Bellman-Ford algorithm
• Dijkstra algorithm
• Floyd-Warshall algorithm
• The Routing Problem on Interconnection Topologies
• the packet switching model
• the Butterfly network
• routing on the Butterfly network: the greedy algorithm

Friday October 1, 2021 (Lessons 7-8):

The Routing Problem i.e. the Least Cost Path Problem (3)

• The Routing Problem on Interconnection Topologies
• the concept of blocking network, non-blocking network and rearrangeable network
• the Benes network
• routing on the Benes network: the looping algorithm

The Problem of Laying out Interconnection Topologies i.e. the Grid Orthogonal Drawing Problem (1)

• The Thompson model
• The orthogonal grid drawing of graphs

Wednesday October 6, 2021 (Lessons 9-10-11):

The Problem of Laying out Interconnection Topologies i.e. the Grid Orthogonal Drawing Problem (2)

• Collinear Layout of the Complete network
• Layout of the Complete network
• Relation between bisection width and layout area
• Layout of the Butterfly network
• the Wise layout
• the Even & Even layout

Friday October 8, 2021 (Lessons 12-13):

The Problem of Laying out Interconnection Topologies i.e. the Grid Orthogonal Drawing Problem (3)

• Layout of the Butterfly network
• summary of the last lesson hour (the video went lost)
• comparison between the two methods
• Layout of the Hypercube network
• Collinear layout
• general layout
• The 3D layout problem

Wednesday October 13, 2021 (Lessons 14-15-16):

A parenthesis: Some problems in (co-)phylogeny (some theses' proposals)

The problem of worm propagation/prevention i.e. the Minimum Vertex Covering Problem (2)

• The problem
• worms
• damages caused by worms

Friday October 15, 2021 (Lessons 17-18):

The problem of worm propagation/prevention i.e. the Minimum Vertex Covering Problem (2)

• Model of the problem on graphs: minimum vertex cover
• definition
• ILP model
• a 2-approximation algorithm
• independent set and maximum matching in relation with vertex cover
• another approximation algorithm
• Konig-Egevary theorem (without proof)
• A related problem: eternal vertex problem

Wednesday October 20, 2021 (Lessons 19-20-21):

The Problem of Minimizing Boolean Circuits i.e. the Minimum Set Covering Problem

• The problem of minimizing boolean functions
• Model of the problem on graphs: the Minimum Set Cover Problem
• definition
• ILP formulation
• relation with the Minimum Vertex Covering Problem
• an O(log n)-approximation algorithm
• another approximation algorithm
• some related problems:
• Hitting set problem
• Edge Cover problem
• Set Packing problem
• Exact Cover problem

A Frequency assignment problem i.e. the L(h,k)-Labeling Problem (1)

• Introduction to the frequency assignment problems
• Direct and hidden collisions, interference graph

Friday October 22, 2021 (Lessons 22-23):

A Frequency assignment problem i.e. the L(h,k)-Labeling Problem (1)

• Introduction to the frequency assignment problems
• Direct and hidden collisions, interference graph
• L(h,k)-labeling and minimum span (1)
• The special case h=k in relation to the suqre of a graph
• Properties of the L(h,k)-labeling and their proofs
• Proof of NP-completeness for diameter 2 graphs (first part)

Wednesday October 27, 2021 (Lessons 24-25-26):

A Frequency assignment problem i.e. the L(h,k)-Labeling Problem (2)

• L(h,k)-labeling and minimum span (2)
• Proof of NP-completeness for diameter 2 graphs
• Lower bound of Delta+1 on lambbda
• Example: a graph requiring lambda=Delta squared - Delta
• Upper bound of Delta squared + 2 Delta
• Griggs and Yeh's conjecture
• Exact results: cliques
• Exact results: stars
• Exact results: trees
• Exact results: paths
• Exact results: cycles
• Exact results: grids

Friday October 29, 2021 (Lessons 27-28-29):

A Frequency assignment problem i.e. the L(h,k)-Labeling Problem (3)

• L(h,k)-labeling and minimum span (3)
• Approximate results: outerplanar graphs
• Variations of the problem (1)
• oriented L(2,1)-labeling
• L(h1, ..., hk)-labeling
• backbone coloring
• multiple L(h,k)-labeling
• frequency assignment in GSM networks

Week November 2-5, 2021: Mid-term exams

Wednesday November 10, 2021 (Lessons 30-31-32): A Frequency assignment problem i.e. the L(h,k)-Labeling Problem (4)

• L(h,k)-labeling and minimum span (4)
• Variations of the problem (2)
• a parenthesis on the 4 color theorem

The minimum energy broadcast i.e. the minimum spanning tree (1)

• NP-completeness and inapproximability results (reduction from Min Set Cover)
• Relation between Min Broadcast and Min Spanning Tree (MST)

Friday November 12, 2021 (Lessons 33-34): The minimum energy broadcast i.e. the minimum spanning tree (2)

• The MST problem
• Kruskal algorithm
• Prim algorithm
• Boruvka algorithm

Wednesday November 17, 2021 (Lessons 35-36-37):

The minimum energy broadcast i.e. the minimum spanning tree (3)

• MST heuristics
• SPT heuristics
• BAIP heuristics
• approximation ratio for MST

The data mule problem i.e. the TSP (1)

• (Fixed) sensor networks
• The Data Mule problem
• The TSP
• NP-completeness
• inapproximability

Friday November 19, 2021 (Lessons 38-39):

The data mule problem i.e. the TSP (2)

• special cases: metric TSP and Euclidean TSP
• generalizations

The centralized deployment of Mobile sensors i.e. the perfect matching in Bipartite graphs (1)

• (mobile) sensor networks

Wednesday November 24, 2021 (Lessons 40-41-42):

The centralized deployment of Mobile sensors i.e. the perfect matching in Bipartite graphs (2)

• the problem of centralized deployment
• the problem on graphs: min weight matching in a bipartite graphs
• maximum matching in a bipartite graph
• P. Hall theorem (with proof)
• corollary to the P. Hall theorem
• searching an augmenting path
• Berge theorem on the augmenting paths
• algorithm based on Berge theorem
• Hopcroft & Karp algorithm

Friday November 26, 2021 (Lessons 43-44):

The centralized deployment of Mobile sensors i.e. the perfect matching in Bipartite graphs (3)

• Minimum weight perfect matching in bipartite graphs (cntd)
• augmenting paths
• an algorithm based on searching augmenting paths
• ILP formulation
• Maximum matching in general graphs
• blossoms
• lemma on the cycle contraction
• Edmonds algorithm (idea)
• Another application

Wednesday December 1, 2021 (Lessons 45-46-47):

Students' lessons

The Distributed Deployment of Sensors i.e. the Construction of a Voronoi Diagram (1)

• The problem
• A Possible Approach: Virtual Forces
• A Protocol Based on Voronoi Diagrams
• Voronoi Diagrams
• hypthesis of general position
• properties
• complexity
• the dual problem: Delaunay triangulation

Friday December 3, 2021 (Lessons 48-49):

Students' lessons [BKTL04], [BPT00], [Bal07], [AGK08], [Xal14]

The Distributed Deployment of Sensors i.e. the Construction of a Voronoi Diagram (2)

Wednesday December 8, 2021: HOLIDAY

Friday December 10, 2021 (Lessons 50-51):

Monitoring by UAVs i.e. what? (some theses' proposals)

Students' lessons [M95], [Cal15]

Wednesday December 15, 2021 (Lessons 52-53-54):

Students' lessons [HZ14], [YWD06], [NSM16], [ML18] (these lessons could be anticipated to Dec. 10 if the program is finished)

Friday December 17, 2021 (Lessons 55-56): mid-term exam

Wednesday December 22, 2021: no lesson (unless it becomes necessary)

This topic: Algoreti > WebHome1011 > DiarioDelleLezioni
Topic revision: r142 - 2021-12-02 - TizianaCalamoneri

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