Abstract
Deletion propagation is widely studied for single view but rarely for multiple views. We study the deletion propagation problem for multiple views called <small>Mdp</small> . We investigate the complexity and algorithms of <small>Mdp</small> in depth for key-preserving conjunctive queries. We characterize the structure of the set of queries to derive new results. On aspect of combined complexity, for two key-preserving views, it is NP-hard to find an approximation within a constant ratio for <small>Mdp</small> . This implies, if the number of queries and the dimension of every query are unbounded, it is hard to find a good approximation for <small>Mdp</small> even under the key preservation condition. On aspect of data complexity, for two key-preserving views, it is NP-hard to approximate <small>Mdp</small> within a ratio <inline-formula><tex-math notation="LaTeX">$k-2-\epsilon$</tex-math></inline-formula> for any <inline-formula><tex-math notation="LaTeX">$\epsilon >0$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$k>4$</tex-math></inline-formula> , if the dimension of each individual query is at most <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> . On aspect of upper bound, we design a linear programming based approximation algorithm. This implies that, under the key preservation condition, <small>Mdp</small> can be approximated within a ratio <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula> if each query has a dimension at most <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula> and the set of input queries is tree-like. In addition, we show that the approximation ratio can be improved as <inline-formula><tex-math notation="LaTeX">$2\sqrt{n}$</tex-math></inline-formula> when <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> the size of <inline-formula><tex-math notation="LaTeX">$I$</tex-math></inline-formula> is smaller than <inline-formula><tex-math notation="LaTeX">$d^2$</tex-math></inline-formula> . At last, a dynamic programming based algorithm is proposed to solve the strict star-like case in polynomial time. The strict star-like case is more restrictive than tree-like case under the key preservation condition.
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More From: IEEE Transactions on Knowledge and Data Engineering
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