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CS 474

Algorithms II

CS 474 is the proof-heavy second half of the algorithms sequence, where the focus shifts from "can you sort and search" to designing and rigorously justifying algorithms on graphs and amortized data structures. You'll spend the term writing correctness proofs, doing amortized analyses (potential method on Fibonacci heaps, union-by-rank with path compression), and working through three projects plus two midterms that lean on Cormen-style reasoning rather than coding tricks. It builds directly on CS 473 and is the backbone for almost everything theoretical that follows, network flows, advanced graph theory, optimization, and any grad course that assumes you can read and produce an algorithmic proof.

Kredi3ECTS5FakülteFaculty of EngineeringBölümComputer EngineeringÖn koşulCS 473KoordinatörCevdet Aykanat

Haftalık müfredat 14 hafta

Hafta 114–20 Eyl
Veri yapılarını augment etme teknikleri
Augmenting Data Structures: augmenting red-black trees, dynamic order statistics, interval trees.
red-black treedynamic order statisticsinterval treeaugmentation
Hafta 221–27 Eyl
İleri priority queue implementation'ları
Advanced priority queue implementations: mergeable-heap operations, binomial heaps, fibonacci heaps, runtime analysis using potential method of analysis
binomial heapFibonacci heapmergeable-heap operationspotential method
Hafta 328 Eyl – 4 Eki
Disjoint Set'lerin Linked List Gösterimi
Data structures for disjoint sets: linked list representation, analysis of weighted union heuristic
disjoint setslinked listweighted union heuristic
Hafta 45–11 Eki
Disjoint Set Forest ve Path Compression
Data structures for disjoint sets: disjoint set forests, analysis of union-by-rank with path compression.
disjoint set forestsunion-by-rankpath compressionanalysis
Hafta 512–18 Eki
Graph, tree ve breadth-first search
Graphs and trees: definition, representation and notation. Breadth-First search: correctness of BFS, Breadth first trees
graphtreeBFSbreadth-first tree
Hafta 619–25 Eki
Depth First Search ve kenar sınıflandırması
Depth First search: timestamping vertices, parenthesis theorem, white-path theorem, edge classification.
Depth First Searchtimestampingparenthesis theoremwhite-path theorem
Hafta 726 Eki – 1 Kas
DAG'lerde topological sort algoritmaları
Topological sort of dags: DFS-based algorithm, proof of correctness, Kahn's algorithm
topological sortDAGDFSKahn's algorithm
Hafta 82–8 Kas
DFS ile strongly connected components
Strongly connected components, use of DFS, proof of correctness, component graph
strongly connected componentsDFSproof of correctnesscomponent graph
Hafta 99–15 Kas
Minimum spanning tree ve greedy algoritmalar
Minimum Spanning Tree (MST): generic MST, proof of correctness, two famous greedy algorithms: Kruskal’s and Prim. Fast implementations of Kruskal's and Prim algorithms.
minimum spanning treeKruskalPrimgreedy algorithm
Hafta 1016–22 Kas
Tek kaynaklı en kısa yollar
Single-Source Shortest Paths (SSSP): shortest paths and relaxation, SSSP on dags, Dijkstra’s algorithm for positive edge weigths, Bellman Ford algorithm for general case. How to use Belmann Ford algorithm for a system of difference constraints for solving the feasibility problem on a system of difference constraints.
SSSPDijkstraBellman-Forddifference constraints
Hafta 1123–29 Kas
Tüm çiftler için en kısa yollar (APSP)
All-pairs shortest paths (APSP) - two DP formulations leading to matrix multiplication and Floyd-Warshall algorithms.
all-pairs shortest pathsdynamic programmingmatrix multiplicationFloyd-Warshall
Hafta 1230 Kas – 6 Ara
Tüm çiftler için en kısa yollar
APSPs: transitive closure of a directed graph, Johnson’s algorithm for sparse graphs.
APSPtransitive closuredirected graphJohnson's algorithm
Hafta 137–13 Ara
Maximum flow: Ford-Fulkerson ve Edmonds-Karp
Maximum Flows: flow networks, Ford-Fulkerson method, residual networks, augmenting paths, max-flow mincut theorem, Edmonds-Karp algorithm
flow networkFord-Fulkersonaugmenting pathEdmonds-Karp
Hafta 1414–20 Ara
Maximum flow: bipartite matching ve push-relabel
Maximum Flows: bipartite graph matching, integrality theorem, push-relabel algorithms
bipartite matchingintegrality theorempush-relabel

Değerlendirme 100% · 4 adım

40%
30%
3%
27%
Midterm:Essay/written Midterm 40%
Final:Essay/written Final Exam 30%
In-class attendance Attendance 3%
Project Project 27%
en büyük tek kalem %40 · sınav ağırlığı %70 nasıl hesaplanıyor

Önerilen kaynaklar 2 kitap

📕
Zorunlu
Introduction to Algorithms
T. H. Cormen, C. E. Leiserson
R. L. Rivest · and C. Stein
📖
Önerilen
Applied and Algorithmic Graph Theory
G. Chartrand and O. R. Oellermann
1993 · McGraw-Hill

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