Greed is good: approximating independent sets in sparse and bounded-degree graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Greedily finding a dense subgraph
Journal of Algorithms
Massive Quasi-Clique Detection
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Mining market data: a network approach
Computers and Operations Research
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In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, f-QIS, consists of, given a graph and a non-decreasing function f, finding a maximum size subset Q of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to f(|Q|). For this problem, we show an exact solution method that runs within time $O^*(2^{\frac{d-27/23}{d+1}n})$ on graphs of average degree bounded by d. For the most specifically defined γ-QIS and k-QIS problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.