CMU 15-451: Algorithm Design and Analysis
15-451 is CMU's advanced algorithms course — amortized analysis, network flow, linear programming and duality, NP-completeness and approximation, online and randomized algorithms — the senior-level capstone of the theory track after 15-210 and 15-251.
Fennie is independent and not affiliated with Carnegie Mellon University. This is an unofficial study guide.
Build my 15-451 study planWhat makes it hard
The problems require design under unfamiliarity at a higher bar than anything before: exams hand you problems that don't resemble homework and grade the algorithm, the proof, and the analysis together. The toolbox is broad and the course assumes you can deploy all of 210 and 251 without review — gaps from those courses resurface here with interest.
What you'll cover
- • Amortized and potential-function analysis
- • Network flow and matchings
- • Linear programming and duality
- • NP-completeness and reductions
- • Approximation algorithms
- • Online and randomized algorithms
The 15-451 study guide
How to study for CMU 15-451, step by step.
- 1
Rehab the prerequisite toolbox first
451 deploys 210's design patterns and 251's proof rigor without slowing down. Audit both honestly in week one — old gaps are the most common reason strong students struggle here.
- 2
Design cold, then calibrate against solutions
For every practice problem, produce your best algorithm and analysis before reading anything. The exam skill is original design under time, and it only builds through honest attempts.
- 3
Learn each technique's problem signature
What makes a problem smell like flow, like LP, like an amortized argument? Build the signature map deliberately — exams test the choice of tool as much as its execution.
- 4
Practice reductions in both directions
NP-completeness problems reward fluency in transforming problems into one another. Work many reductions and articulate the pattern of each — the gadget intuition is trainable.
- 5
Re-solve homework from a blank page before exams
Reproducing a design and its full analysis without notes is the closest rehearsal for exam conditions. If you can't re-derive it, you recognized it rather than learned it.
- 6
Train the toolbox with Fennie
Upload your 15-451 syllabus and Fennie's Daily Plan spaces design practice across every technique with prerequisite rehab built in, paced to the exam dates, plus quizzes from the actual course materials. Free to start.
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How Fennie helps with 15-451
Fennie's Daily Plans space 15-451's broad toolbox across the semester — every technique drilled past recognition into cold production, prerequisite gaps rehabbed early — synced to the exams. Chat through why a flow formulation works or where an amortized argument leaks, the design-and-justify skill this course grades.
FAQ
Is 15-451 hard?
It's the theory track's senior bar: exams present unfamiliar problems and grade design, proof, and analysis together, assuming 210 and 251 fluently. Students who practice cold design and keep the full toolbox deployable do well; recognition-level preparation gets exposed.
How does 15-451 differ from 15-210?
210 builds the foundation with its parallel cost framework; 451 goes wider and deeper — flow, LP duality, approximation, online algorithms — at a higher design difficulty, in a conventional sequential setting. Think of 451 as the course interviews and research both draw from.
How do I study for 15-451 exams?
Cold-design practice under time: unfamiliar problems, full algorithm-proof-analysis writeups, then line-by-line calibration against solutions. Build an explicit map of which problem features suggest which technique — tool selection is half of every exam question.
Pass 15-451 with a plan, not a cram
Upload your 15-451 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
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