最大团大作业
要求在这里。简要的来讲：
- 码代码（4分）
- 写报告ppt（2分）
- 简述该问题研究的历史和现状
- 阅读一篇指定论文，写出其算法实现**
关于NP-hard问题之间的转化，如果感兴趣可以参考之前算分课上做过的Karp那篇论文的报告。
Project分析
OJ上面的数据是顶点数N<=750,边数M<=250000。
N=20,30,40,60,80,100,200,300,400,500,750。
成绩按解的质量给分，例如找到顶点数为8的团，该测试点给8分。目前最高是156分。
随手找了一下：
寻找图中最大团的最好算法是什么算法（2016年为止）? - 知乎
里面提到的Bron-Kerbosch algorithm，CSDN上有一篇文章有成型的代码。拿来试了一下，速度不快，暂时只能输出最大团大小，不知道怎么输出编号。
要求里面提到的样例数据所在的网站打不开有时能打开，用Internet Archive保存的网页看了一下，有这些数据：
- frb30-15-clq.tar.gz ( 914 KB): 450 vertices - 5 instances, with both the maximum clique size and the chromatic number = 30
- frb35-17-clq.tar.gz ( 1599 KB): 595 vertices - 5 instances, with both the maximum clique size and the chromatic number = 35
- frb40-19-clq.tar.gz ( 2647 KB): 760 vertices - 5 instances, with both the maximum clique size and the chromatic number = 40
- frb45-21-clq.tar.gz ( 4085 KB): 945 vertices - 5 instances, with both the maximum clique size and the chromatic number = 45
- frb50-23-clq.tar.gz ( 6444 KB): 1150 vertices - 5 instances, with both the maximum clique size and the chromatic number = 50
- frb53-24-clq.tar.gz ( 7979 KB): 1272 vertices - 5 instances, with both the maximum clique size and the chromatic number = 53
- frb56-25-clq.tar.gz ( 9774 KB): 1400 vertices - 5 instances, with both the maximum clique size and the chromatic number = 56
- frb59-26-clq.tar.gz (11890 KB): 1534 vertices - 5 instances, with both the maximum clique size and the chromatic number = 59
页面还介绍了一些进展：
Dec.1, 2014: Using a stochastic local search solver (called ), Christopher D. Rosin at Amara Health Analytics found independent sets of size 99 on the frb100-40.mis instance, in under 24 hours of runtime on a Linux server with a 3.4GHz i7-4770 CPU. ULSA's single-threaded average time to find 99 on this CPU is 29.3 hours.
Mar. 20, 2010: Using a local search solver (called EWLS) on a 3GHz/4GB computer, Shaowei Cai and Kaile Su at Peking University found a vertex cover of 3902 vertices (or equivalently, an independent set of 98 vertices) for the above MIS benchmark of 4000 vertices. More specifically, the authors performed 100 independent trials on this instance. 4 runs find a 3902-sized vertex cover, or equivalently, a 98-sized independent set with the average time of 2823.05 seconds and the fastest one did so in 1239.87 seconds. Of the other 96 runs, 59 found a 3903-sized solution and 37 found a 3904-sized solution.
随手找了一下，发现了去年一组同学做的源代码，ID很熟悉，应该是我们这届的。他们的samples里面包括了这些文件，还写了个decode的Tool，可以直接拿来用。
库里面还有他们复现的算法NuMVC对应的Paper。
Reference中提到的一篇Paper：Cai, Shaowei, Kaile Su, and Abdul Sattar. "Local search with edge weighting and configuration checking heuristics for minimum vertex cover." Artificial Intelligence 175.9-10 (2011): 1672-1696.里面介绍得比较详细，也包括了「简述该问题研究的历史和现状」这一task的很多信息，可以细看一下。
update:
- 用的是DIMACS格式的数据，以ASCII编码而不是binary，和给的样例数据一致
- 有用到高级指令集，需要在编译的时候指明。OJ应该是支持的。
- Usage
去年的Reference Paper：EWLS
最大团问题分析
解法可分为两类：
- exact
- branch-and-bound algorithms
- Exact algorithms guarantee the optimality of the solutions they find, but may fail to give a solution within reasonable time for large instances.
- heuristic
- stochastic local search algorithms
- heuristic algorithms cannot guarantee the optimality of their solutions, they can solve large and hard MVC (MIS, MC) instances in the sense of giving optimal or near-optimal solutions within reasonable time
”成绩按解的质量给分“，即鼓励使用heuristic way