Upload
charlotte-keon
View
29
Download
2
Embed Size (px)
DESCRIPTION
Computation Basics & NP-Completeness. 박상준. 컴퓨터로 문제풀기. Computational Efficiency? 컴퓨팅 Problem Solving Running Time 함수 -> 기본적인 스텝의 수 How the Analyzing goes?. Insersion-Sort. The running time of the algorithm is the sum of running times for each statements executed. Running time. - PowerPoint PPT Presentation
Citation preview
컴퓨터로 문제풀기• Computational Efficiency?• 컴퓨팅
– Problem Solving– Running Time– 함수 -> 기본적인 스텝의 수
• How the Analyzing goes?
Insersion-Sort
• The running time of the algorithm is the sum of running times for each statements executed
Running time
• T(n) is expressed as an2+bn+c for constants a,b,c; it is thus a quadratic function of n.
O-notation
• O(g(n))={f(n): there exist positive constants c and n0 such that 0 <=f(n)<= cg(n) for all n >= n0 }
• It is upper bound on the worst-case running time– an2+bn+c=O(n2 )
– We say “ The running time is O(n2 ) ”
Polynomial-time algorithms
• An algorithms that ,on inputs of size n their worst-case running time is O(nk) for some constant k.
• Complexity class P : the Set of decision problems that are solvable in polynomial time
NP-Completeness
• Although problem O(n100) looks intractable, there are very few practical problems that require such a high-degree polynomial time order
• P ≠ NP ? No one knows• For simplicity, the theory of NP-
completeness restricts attention to decision problems: those having a yes/no solution
Steiner Tree
• Instance: Graph G=(V,E), subset R⊆V, positive integer K <= |V|-1.
• Question: Is there a subtree of G that includes all the vertices of R and that contains on more than K edges?
The Maximum Clique Problem
• Clique : in undirected graph G=(V,E), a subset V’⊆V of vertices, each pair of which is connected by an edge in E
• Size of a clique is the number of vertices it contains.
• It is Exist, CLIQUE={<G,k>:G is a graph with a clique of size k}?