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The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved. Here, quickly means an algorithm that solves the task and runs in polynomial time exists, meaning the task completion time is bounded above by a ...
The problem has been shown to be NP-hard (more precisely, it is complete for the complexity class FP NP; see function problem), and the decision problem version ("given the costs and a number x, decide whether there is a round-trip route cheaper than x") is NP-complete. The bottleneck travelling salesman problem is also NP-hard.
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2. Feedback vertex set [2][3]: GT7. Feedback arc set [2][3]: GT8.
NP-Problem Chaitin et al. showed that register allocation is an NP-complete problem. They reduce the graph coloring problem to the register allocation problem by showing that for an arbitrary graph, a program can be constructed such that the register allocation for the program (with registers representing nodes and machine registers ...
Under the assumption that P ≠ NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. [1] In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where ...
The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus. Categories: Conjectures. Lists of unsolved problems. Unsolved problems in computer science.
Computational complexity. In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. [1] Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the ...
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