More Efficient Bottom Up Multipattern Matching in Trees
More Efficient Bottom Up Multipattern Matching in Trees
Jiazhen Cai
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Of course, any overallocation during preprocessing is not needed for matching and can be shed. domain/ f(x)=y preimage range / count noi/e- record for/? ir'{y}i array / is numeric code for x e D Fig. 5. Implementation of 5£_map/: D -^ R 3J. Abstract Algorithm Let F be the set of function symbols appearing in PF. For each fimction /e F, let i4 (/) be its arity. Let r be the set of Hoffmann and O'Donnell match sets. From the above discussion, we know that the following equations hold: (J) Y = {{v..., s]: s e PF \ s is a leaf ] u u /{range e/:/€ F \ A{f)>Q] n>={c, :/(c, c, )€ PF] \i'f = {{m, m r\ 0}]: m € T) 9/= {[[^1, .... Mk], m]:m^ e range |J. |, ... , /w* e range n* ) where m = {/(cj, ... , Ci^) e PF lc, 6 m, / = 1 ^) u {v} Because the preceding equations contain a cyclic dependency in which T depends on both PF and 6, \i depends on F, and 6 depends on \i and PF, it would seem that a costly fixed point iteration is needed to maintain these equations when PF is modified. Fortunately, this can be avoided with careful scheduling.
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