XML Functional Dependency and Schema Normalization

Abstract

Normalization theory is necessary for designing a good XML document. A good document means that it has minimal redundancy. The research on XML functional dependency and normalization is still an open problem. This paper first presents a path language of XML model, then proposes a new kind of XML functional dependency (XFD) that has stronger expression ability to XML functional dependency that can result in redundancies. In this paper, the problems of XFD logical implication and XFD closure are studied and a group of the corresponding inference rules is proposed. Based on the XFD, a kind of XML normal form (XNF) and an algorithm converting into XNF are also proposed in this paper.

Algorithms for Minimal Dependency Set and Membership Based on XML Functional Dependency and Multi-Valued Dependency

“…Executing the "while" loop repeatedly before Q′=∅ or Q′ has been the union set of some elements from BASIS. W:=∅; (10) for g i ∈BASIS do (11) {if g i ⊂Q′ then (12) {W:=W∪g i ;} (13) if Q′≠∅ and Q′≠W then do (14) {change-flag:= 'T'; (15) BASIS:= MB{BASIS∪Q′};}}} (16)return(BASIS) End…”

“…Since the size of BASIS is at most m, the time cost of the operation is O(m 2 ). The time complexity of the "for" loop is O(m 2 ) of step (10). In step (4), it is possible to examine whether n dependencies change the BASIS value or not.…”

“…OUTPUT: the minimal dependency set ∑ min of ∑. for every path p∈P do (10) if d is a XFD, then P→Q do (11) if DEP_MEMBERSHIP(∑,{P-p}→Q) then (12) ∑:=(∑-{ P→Q }∪{P-p}→Q)); (13) if d is a XMVD, then P→→Q do (14) if DEP_MEMBERSHIP(∑,{P-p}→→Q) then (15) ∑:=(∑-{ P→→Q }∪{P}-{p}→→Q)); (16) if (exist redundancy attribute on the right of d) (17) for every path q∈Q do (18) if d is a XFD, then P→Q do (19) ∑:=(∑-{ P→Q })∪{P→ q 1 , ..., P→ q m };…”

“…In recent years, scholars have done a lot of exploration and research on the normalization of XML database: the normalization based on functional dependency [7][8][9][10][11][12] and multi-valued dependency [13][14][15]. These research literatures analyze the effect on XML data and free redundancy from a single point of view such as XML functional dependency or XML multi-valued dependency.…”