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Exploring Optimization Gaps in NP Problems: A Comprehensive Analysis

This work delves into the complexities of optimization gaps within various NP problems, focusing on critical aspects such as Gap-3SAT, Gap-CLIQUE, and Gap-Independent Set (Gap-IS). We explore the minimization techniques and probabilistic verification methods for proofs, including the pivotal role of the PCP theorem. Our analysis also highlights key reductions among NP-hard problems, providing insight into graph structures and their configurations (CSG) related to these gaps. This study is essential for researchers interested in computational complexity and optimization.

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Exploring Optimization Gaps in NP Problems: A Comprehensive Analysis

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  1. Promise Problems – Ilustrated *

  2. Optimization

  3. Gap-A[C,hC] (minimization)

  4. Gap-3SAT

  5. 7/8

  6. PCP Characterization of NP

  7. Probabilistic Checking of Proofs

  8. Gap-CLIQUE

  9. Gap Preserving Reduction f * *

  10. SATp CLIQUE    

  11. Constraints` Graph

  12. CSG

  13. CSG

  14. CSG

  15. Gap-IS

  16. qCSG

  17. Triplets` Unique T

  18. qCSG

  19. Gap-UG[, 1-] .

  20. Gap-MC[1-, 1-] .

  21. WWindex

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