NP-completeness - Wikipedia
WEBIn computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a …
List of NP-complete problems - Wikipedia
WEBGraph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition …
P, NP, NP-Complete and NP-Hard Problems in Computer Science
WEBMar 18, 2024 · Graph Theory Learn how GPS systems find the shortest routes, how engineers design integrated circuits and more real-world uses of graphs
Introduction to NP-Complete Complexity Classes
WEBMay 15, 2024 · NP problems are a class of computational problems that can be solved in polynomial time by a non-deterministic machine and can be verified in polynomial time …
WEBA language L {0, 1}* is NP-complete if: 1. L NP, and 2. L p L for every L NP, i.e. L is NP-hard Lemma. If L is language s.t. L p L where L NPC, then L is NP-hard. If L NP, then L NPC. Theorem. If any NPC problem is p-time solvable, then P = NP.
WEBIn the first case, the answer to the problem is “yes”, and in the second case the answer is “no”. One could also formulate this in terms of a single Turing machine, in which the accept states are divided into “yes” states and ”no” states. Here are some examples of computable decision problems.
WEBNP = the set of decision problems solvable in nondeterministic polynomial time. The output of these problems is a YES or NO answer. Nondeterministic refers to the fact that a solution can be guessed out of polynomially many options in (1) time. If any guess is a YES instance, then the nondeterministic algorithm. O. will make that guess.
WEBThe INDSET problem is NP-complete. To prove this, we will find a polynomial-time reduction from 3SAT to INDSET. Goal: Given a 3CNF formula φ, build a graph G and number n such that φ is satisfiable iff G has an independent set of size n. How can we accomplish this?
WEBNaively, it takes O(n2) to check that every vertex is traversed exactly once and O(nm) to check that every edge in the path is in the graph. Show Hamiltonian Path is ∈ NP-Hard. We prove this by giving a Karp-reduction of Hamiltonian Cycle to Hamiltonian Path.
WEBLecture 17. Complexity and NP-completeness. Supplemental reading in CLRS: Chapter 34. As an engineer or computer scientist, it is important not only to be able to solve problems, but also to know which problems one can expect to solve efficiently.
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