Everything About ___
Live briefing

Everything about Subset sum problem

Decision problem in computer science

The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum, and the question is to decide whether any subset of the integers sum to precisely . The problem is known to be NP-complete. Moreover, some restricted variants of it are NP-complete too, for example:The variant in which all inputs are positive. The variant in which inputs may be positive or negative, and. For example, given the set, the answer is yes because the subset sums to zero. The variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i.e.,. This special case of SSP is known as the partition problem. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Subset sum problemA 5-minute orientation
  2. Skim a recent paper: Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at riskInfluential work since 2022
  3. Pick up a classic book: Introduction to Probability and StatisticsThe most-reprinted book on the subject
  4. Read the landmark paper: The Multiple Subset Sum ProblemCited 79 times
  5. Go sideways: Multiple subset sumA closely related topic
  6. Go sideways: Partition problemA closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. Computational hardness
  2. Exponential time algorithms
  3. Pseudo-polynomial time dynamic programming solutions
  4. Polynomial time approximation algorithms

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics