Computers and Intractability: A Guide to the Theory of NP-Completeness by Michael R. Garey and David S. Johnson — Summary, Key Ideas & Quotes

At the heart of the book is a rigorous explanation of NP-completeness—a class of problems for which no efficient (polynomial-time) solution is known, but for which proposed solutions can be quickly checked. The authors clarify the distinction between P (problems solvable quickly) and NP (problems verifiable quickly), and introduce the concept of NP-complete problems as the hardest problems in NP. If any NP-complete problem can be solved efficiently, then all problems in NP can be.

A central methodological tool in the book is the idea of reductions—transforming one problem into another in a way that preserves computational difficulty. Garey and Johnson systematically show how reductions are used to prove that new problems are NP-complete, building a web of relationships that map the landscape of computational hardness.