XML Reconstruction View Selection in XML Databases: Complexity Analysis and Approximation Scheme

TL;DR

This paper formalizes the problem of selecting XML reconstruction views to optimize query performance, proves its NP-hardness, and introduces a fully polynomial-time approximation scheme for it.

Contribution

It is the first to formalize and analyze the complexity of XML reconstruction view selection and provides an approximation algorithm.

Findings

The problem is NP-hard.

A fully polynomial-time approximation scheme (FPTAS) is developed.

The scheme efficiently approximates optimal view selection under size constraints.

Abstract

Query evaluation in an XML database requires reconstructing XML subtrees rooted at nodes found by an XML query. Since XML subtree reconstruction can be expensive, one approach to improve query response time is to use reconstruction views - materialized XML subtrees of an XML document, whose nodes are frequently accessed by XML queries. For this approach to be efficient, the principal requirement is a framework for view selection. In this work, we are the first to formalize and study the problem of XML reconstruction view selection. The input is a tree $T$, in which every node $i$ has a size $c_i$ and profit $p_i$, and the size limitation $C$. The target is to find a subset of subtrees rooted at nodes $i_1,\cdots, i_k$ respectively such that $c_{i_1}+\cdots +c_{i_k}\le C$, and $p_{i_1}+\cdots +p_{i_k}$ is maximal. Furthermore, there is no overlap between any two subtrees selected in the solution. We prove that this problem is NP-hard and present a fully polynomial-time approximation scheme (FPTAS) as a solution.