| __Challenging Benchmarks for Maximum Clique, Maximum Independent Set, Minimum Vertex Cover and Vertex Coloring - ...__ *(Site not responding. Last check: 2007-11-06)* |

| | Finding challenging benchmarks for the maximum **independent** **set** problem (or equivalently, the minimum vertex cover problem) is not only of significance for experimentally evaluating the algorithms of solving this problem but also of interest to the theoretical computer science community. |

| | To hide an **independent** **set** of size n in the instances of this graph model, we first select a vertex at random from each disjoint clique to form an **independent** **set** of size n, and then in the above process of generating random edges, no edge is allowed to violate this maximum **independent** **set**. |

| | Since a clique is an **independent** **set** in the complementary graph, the maximum **independent** **set** problem and the maximum clique problem (which is one of the first shown to be NP-hard and has been extensively studied in graph theory and combinatorial optimization) are essentially equivalent. |

| www.nlsde.buaa.edu.cn /~kexu/benchmarks/graph-benchmarks.htm (1556 words) |