Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Maximum independent set (MIS) is a fundamental problem in graph theory and it has important applications in many areas such as social network analysis, graphical information systems and coding theory. The problem is NP-hard, and there has been numerous studies on its approximate solutions. While successful to a certain degree, the existing methods require memory space at least linear in the size of the input graph. This has become a serious concern in view of the massive volume of today's fast-growing graphs.#R##N##R##N#,  study the MIS problem under the semi-external setting, which assumes that the main memory can accommodate all vertices of the graph but not all edges.  present a greedy algorithm and a general vertex-swap framework, which swaps vertices to incrementally increase the size of independent sets. Our solutions require only few sequential scans of graphs on the disk file, thus enabling in-memory computation without costly random disk accesses. Experiments on large-scale datasets show that our solutions are able to compute a large independent set for a massive graph with 59 million vertices and 151 million edges using a commodity machine, with a memory cost of 469MB and a time cost of three minutes, while yielding an approximation ratio that is around 99% of the theoretical optimum.
['Yu Liu', 'Jiaheng Lu', 'Hua Yang', 'Xiaokui Xiao', 'Zhewei Wei']
I am writing a research paper on a idea Towards maximum independent sets on massive graphs
[{"from": "human", "value": "I am writing a research paper on a idea Towards maximum independent sets on massive graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Maximum independent set (MIS) is a fundamental problem in graph theory and it has important applications in many areas such as social network analysis, graphical information systems and coding theory. The problem is NP-hard, and there has been numerous studies on its approximate solutions. While successful to a certain degree, the existing methods require memory space at least linear in the size of the input graph. This has become a serious concern in view of the massive volume of today's fast-growing graphs.#R##N##R##N#,  study the MIS problem under the semi-external setting, which assumes that the main memory can accommodate all vertices of the graph but not all edges.  present a greedy algorithm and a general vertex-swap framework, which swaps vertices to incrementally increase the size of independent sets. Our solutions require only few sequential scans of graphs on the disk file, thus enabling in-memory computation without costly random disk accesses. Experiments on large-scale datasets show that our solutions are able to compute a large independent set for a massive graph with 59 million vertices and 151 million edges using a commodity machine, with a memory cost of 469MB and a time cost of three minutes, while yielding an approximation ratio that is around 99% of the theoretical optimum."}]