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Advanced -> Approximation And Relaxation

Approximation ratios, LP/SDP relaxations, primal-dual methods, and the boundary between exact and near-optimal algorithms.

  • Topic slug: advanced/approximation-and-relaxation
  • Tutorial page: Open tutorial
  • Ladder page: Open ladder
  • Repo problems currently tagged here: 0
  • Repo companion pages: 2
  • Curated external problems: 5

Microtopics

  • approximation-ratio
  • LP-relaxation
  • SDP-relaxation
  • randomized-rounding
  • primal-dual-method
  • integrality-gap
  • local-search
  • inapproximability

Learning Sources

Source Type
MIT 6.854 approximation algorithms Course
CMU 15-854 Approximation Algorithms Course
Williamson-Shmoys Reference

Follow-Up Reading

Source Type
MIT 6.854 problem sets Course
CMU 15-854B Course

Repo Companion Material

Material Type
Optimization and duality tutorial related tutorial
Complexity and hardness ladder adjacent ladder

Curated External Problems

Core

Problem Source Difficulty Context Style Prerequisites Tags Why it fits
Problem Set 1 Dartmouth EO249 Theory Approximation Algorithms - - TSP; Cycle Cover; Euler Tour Great starter set for approximation constructions around TSP-style problems.
Problem Set 2 Dartmouth EO249 Theory Approximation Algorithms - - Set Cover; Submodular; Greedy Approximation Covers several core greedy-approximation paradigms in one assignment.
Problem Set 4 Dartmouth EO249 Theory Approximation Algorithms - - Facility Location; Integrality Gap; LP Relaxation Strong LP-gap and approximation-ratio practice.
Problem Set 5 Dartmouth EO249 Theory Approximation Algorithms - - Knapsack PTAS; Iterated Rounding; Laminar Families A particularly rich set on relaxation, rounding, and structure in approximation.
Problem Set 6 Dartmouth CS 49/149 Theory Approximation Algorithms - - Duality; Randomized Rounding; LP Excellent follow-up for duality and randomized-rounding based approximation design.

Repo Problems

No repo problem note is attached yet. Use the repo companion material above for this theory/process-heavy topic.

Regeneration

python3 scripts/generate_problem_catalog.py