Tree Pattern Matching to Subset Matching in Linear Time

Tree Pattern Matching to Subset Matching in Linear Time

In this paper, we show an O(n + m) time Turing reduction from the tree pattern matching problem to another problem called the subset matching problem. Subsequent works have given efficient deterministic and randomized algorithms for the subset matching problem. Together, these works yield an O ( n log m+m ) time deterministic algorithm and an O(n logn + m) time Monte Carlo algorithm for the tre...

Tree Pattern Matching and Subset Matching in Deterministic O(n log3 n)-time

The main goal of this paper is to give an O(n log 3 n) time deterministic algorithm for the the Subset Matching problem. This immediately yields an algorithm of the same eeciency for the Tree Pattern Matching problem. We also give an O(n log 3 n= log log n) time randomized algorithm for these problems. Finally, we give a O(n log n(z + log n)) time deterministic algorithm for a useful specializa...

Linear Pattern Matching Algorithms

In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but sub-optimal algorithms. In this paper, we introduce an interesting data structure called a bi-tree. A linear time algorithm "for obtaining a compacted version of a bi-tree associated with a given string is pr...

A new algorithm for linear regular tree pattern matching

We consider the problem of linear regular tree pattern matching and describe a new solution based on a bottom up technique. Current bottom up techniques preprocess the patterns and construct a nite state tree pattern matching automaton for the purpose. Though matching time is linear in the size of the subject tree, the size of the automaton can be exponential in the sum of the sizes of all patt...

A Linear Time Pattern Matching Algorithm Between a String and a Tree