On approximating the minimum independent dominating set
Information Processing Letters
Approximating the minimum maximal independence number
Information Processing Letters
A still better performance guarantee for approximate graph coloring
Information Processing Letters
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Graphs and Hypergraphs
Note: On the inapproximability of independent domination in 2P3-free perfect graphs
Theoretical Computer Science
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We consider the polynomial approximationbehavior of the problem of finding, in a graphwith weighted vertices, a maximal independent setminimizing the sum of the weights. In the spirit of a work ofHalldórson dealing with the unweighted case, weextend it and perform approximation hardness results by using areduction from the minimum coloring problem. In particular, aconsequence of our main result is that there does not exist anypolynomial time algorithm approximating this problem within a ratioindependent of the weights, unless P = NP. We bring also to the fore avery simple ratio ρ guaranteed by every algorithm while nopolynomial time algorithm can guarantee the ratio (1 − ε)ρ.The known hardness results for the unweighted case can be deduced. Wefinally discuss approximation results for both weighted andunweighted cases: we perform an approximation ratio that is valid forany algorithm for the former and propose an analysis of a greedyalgorithm for the latter.