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 polynomial-time solvable graph problem


Fast Parameterized Preprocessing for Polynomial-Time Solvable Graph Problems

Communications of the ACM

A holy grail of theoretical computer science, with numerous fundamental implications to more applied areas of computing such as operations research and artificial intelligence, is the question of whether NP is equal to P. Much of modern technology is based on the so-called Cobham-Edmonds' thesis (named after Alan Cobham and Jack Edmonds), which states that algorithmic problems can be feasibly computed on a computational device only if they can be computed in polynomial time. In a nutshell: P means "feasible" while NP-hard means "infeasible" to compute. Moving from theory to practice, and looking at problems more realistically, the size of the exponent in a polynomial-time algorithm matters a lot. In the era of big data, when n is, say, the number of users of Facebook or Twitter, an Θ(n3)– or even Θ(n2)-time algorithm might be too slow. In such applications where the input size n is very large, any practically efficient algorithm that solves a problem to optimality can only afford a linear or almost linear-time complexity.