问题描述:就是在图中找最小的点集,使得覆盖所有边. 和独立集等价:独立集问题:在图中找最大的点集,使得点集内的所有点互不相连. 引理:顶点覆盖集和独立集互补. 上面这个引理使得这两个问题可以相互规约,从而这两个问题等价. 等价问题:给定图G和数k, 问G包含大小至少为k的独立集吗? 为什么等价:如果我们能在多项式时间内给出这个问题的答案,那么我们可以通过二分查找得到最大独立集的size为K.一个点如果是最大独立集中的点,等价于除去这个点后得到的图G'含有一个K-1大小的独立集.那么我们每次选取一…

2038. Minimum Vertex Cover Time limit: 1.0 secondMemory limit: 64 MB A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. A minimum vertex cover is a vertex cover with minimal…

Vertex Cover frog has a graph with nn vertices v(1),v(2),…,v(n)v(1),v(2),…,v(n) and mm edges (v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm))(v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm)). She would like to color some vertices so that each edge has at least…

传送门 Vertex Cover frog has a graph with n vertices v(1),v(2),…,v(n)v(1),v(2),…,v(n) and m edges (v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm))(v(a1),v(b1)),(v(a2),v(b2)),…,(v(am),v(bm)). She would like to color some vertices so that each edge has at leas…

这里将讲解一下npc问题中set cover和vertex cover分别是什么. set cover: 问题定义: 实例:现在有一个集合A,其中包含了m个元素(注意,集合是无序的,并且包含的元素也是不相同的),现在n个集合,分别为B1.B2.....Bn.并且这n个集合的并集恰好等于A集合,即:B1UB2UB3U...UBn=A. 问题:是否存在B集合的最小子集,且他们的并集也等于A集合? 例子:集合A={1,2,3,4,5},集合B={{1,2,3},{2,4},{3,4},{4,5}}.可…

Vertex Cover Problem's Link Mean: 给你一个无向图,让你给图中的结点染色,使得:每条边的两个顶点至少有一个顶点被染色.求最少的染色顶点数. analyse: 裸的最小点覆盖问题,二分图的最大匹配,直接套模版即可. Time complexity: O(N^2) view code…

Vertex Cover frog has a graph with \(n\) vertices \(v(1), v(2), \dots, v(n)\) and \(m\) edges \((v(a_1), v(b_1)), (v(a_2), v(b_2)), \dots, (v(a_m), v(b_m))\). She would like to color some vertices so that each edge has at least one colored vertex. Fi…

Muddy Fields Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 10044   Accepted: 3743 Description Rain has pummeled the cows' field, a rectangular grid of R rows and C columns (1 <= R <= 50, 1 <= C <= 50). While good for the grass,…

http://poj.org/problem?id=3041 Asteroids Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 12601   Accepted: 6849 Description Bessie wants to navigate her spaceship through a dangerous asteroid field in the shape of an N x N grid (1 <= N <…

有向图的最小路径覆盖=V-二分图最大匹配. Consider a town where all the streets are one-way and each street leads from one intersection to another. It is also known that starting from an intersection and walking through town's streets you can never reach the same inters…