3 Hardness of Approximation
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Coloring Graph Powers: Graph Product Bounds and Hardness of Approximation
We consider the question of computing the strong edge coloring, square graph coloring, and their generalization to coloring the k power of graphs. These problems have long been studied in discrete mathematics, and their “chaotic” behavior makes them interesting from an approximation algorithm perspective: For k = 1, it is well-known that vertex coloring is “hard” and edge coloring is “easy” in ...
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Bansal and Sviridenko [4] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P = NP. We show that similar approximation hardness results hold for several 2and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asym...
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It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1. a simple and efficient algorithm that achieves an n−1/3-approximation; 2. NP-hardness of approximation to within (1− ε), for some small constant ε > 0; 3. SSE-hardness of approximatio...
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It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1. a simple and efficient algorithm that achieves an n-approximation; 2. NP-hardness of approximation to within (1 − ε), for some small constant ε > 0; 3. SSE-hardness of approximation t...
متن کاملApproximation Algorithms and Hardness for Domination with Propagation
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or v has a neighbor in S, or (2) v has a neighbor w such that w and all of its neighbors except v are power dominated. We show a hardness of approximation threshold o...
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تاریخ انتشار 2009