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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.

Credit3ECTS5FacultyFaculty of EngineeringBölümComputer EngineeringPreCS 473

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%

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

Haftalık müfredat 14 hafta

Hafta 1
Augmenting Data Structures: augmenting red-black trees, dynamic order statistics, interval trees.
Hafta 2
Advanced priority queue implementations: mergeable-heap operations, binomial heaps, fibonacci heaps, runtime analysis using potential method of analysis
Hafta 3
Data structures for disjoint sets: linked list representation, analysis of weighted union heuristic
Hafta 4
Data structures for disjoint sets: disjoint set forests, analysis of union-by-rank with path compression.
Hafta 5
Graphs and trees: definition, representation and notation. Breadth-First search: correctness of BFS, Breadth first trees
Hafta 6
Depth First search: timestamping vertices, parenthesis theorem, white-path theorem, edge classification.
Hafta 7
Topological sort of dags: DFS-based algorithm, proof of correctness, Kahn's algorithm
Hafta 8
Strongly connected components, use of DFS, proof of correctness, component graph
Hafta 9
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.
Hafta 10
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.
Hafta 11
All-pairs shortest paths (APSP) - two DP formulations leading to matrix multiplication and Floyd-Warshall algorithms.
Hafta 12
APSPs: transitive closure of a directed graph, Johnson’s algorithm for sparse graphs.
Hafta 13
Maximum Flows: flow networks, Ford-Fulkerson method, residual networks, augmenting paths, max-flow mincut theorem, Edmonds-Karp algorithm
Hafta 14
Maximum Flows: bipartite graph matching, integrality theorem, push-relabel algorithms

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