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Everything about Partition problem

NP-complete problem in computer science

In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called "the easiest hard problem". Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Partition problemA 5-minute orientation
  2. Skim a recent paper: Multi-manned assembly line balancing problem with dependent task times: a heuristic based on solving a partition problem with constraintsInfluential work since 2022
  3. Pick up a classic book: Unravelling the Kashmir KnotThe most-reprinted book on the subject
  4. Read the landmark paper: The partition problemCited 201 times
  5. Go sideways: Multiway number partitioningA closely related topic
  6. Go sideways: Largest differencing methodA closely related topic

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🗂️ The subject at a glance

  1. Examples
  2. Computational hardness
  3. Approximation algorithms
  4. Exact algorithms
  5. Hard instances and phase-transition
  6. Probabilistic version
  7. Variants and generalizations
  8. Applications

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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