Download presentation

Presentation is loading. Please wait.

Published byJeffrey Hodgetts Modified over 2 years ago

1
Parametrized Matching Amir, Farach, Muthukrishnan Orgad Keller

2
Orgad Keller - Algorithms 2 - Recitation 9 2 Definition: Two strings over the alphabet, parametrized match (p-match) if the following 3 conditions apply : Parametrized Match Relation

3
Orgad Keller - Algorithms 2 - Recitation 9 3 Conditions

4
Orgad Keller - Algorithms 2 - Recitation 9 4 We can see it as a bijection : Example

5
Orgad Keller - Algorithms 2 - Recitation 9 5 Parametrized Matching Input: Output: All locations where p-matches.

6
Orgad Keller - Algorithms 2 - Recitation 9 6 We can reduce the problem, to the same problem with (m-match). Given we’ll define : Observation

7
Orgad Keller - Algorithms 2 - Recitation 9 7 Now is over and is over and. We get the algorithm for p-match: Create Find all the places appears in (using KMP) Find all the places m-matches in (We’ll show later how) Return Observation

8
Orgad Keller - Algorithms 2 - Recitation 9 8 Why is that enough? In other words: Prove there is a p-match at location iff. We are left with the question: How do we solve step 3 efficiently? Exercise

9
Orgad Keller - Algorithms 2 - Recitation 9 9 Is m-match transitive? We can use KMP-like automaton method For each index in pattern, we want to find the longest suffix that m-matches the prefix. For instance: M-match

10
Orgad Keller - Algorithms 2 - Recitation 9 10 Failure Links Where to link the failure link from ? In KMP it is simple: If then link to. Otherwise go back again and repeat. In our case: If never appeared before, i.e. We link if. Otherwise, we link if such that, it holds that.

11
Orgad Keller - Algorithms 2 - Recitation 9 11 Failure Links Can we do this efficiently? We’ll build an array : So, if, we know hasn’t appeared before. Otherwise, we’ll know exactly where it had appeared last.

12
Orgad Keller - Algorithms 2 - Recitation 9 12 Building the Array We’ll hold a Balanced Binary Search Tree for the symbols of the alphabet. Initially it will be empty. We’ll go over the pattern. For each symbol, if it isn’t in the tree, we’ll add it with it’s index and update. Otherwise, we know exactly where it had last appeared, so we’ll update and then update the symbol in the tree with the new index. Time: where.

13
Orgad Keller - Algorithms 2 - Recitation 9 13 The Matching Itself We go forward in the automaton if either and. We’ll hold and update a balanced BST as we go over the text as well. Time: So overall algorithm time is Can we improve this further?

14
Orgad Keller - Algorithms 2 - Recitation 9 14 The Trick We’ll split the text into overlapping segments of size like this: So every match in the text must appear in whole in one of the segments. We’ll run the algorithm for each such segment. Time: where. Overall for all segments:

Similar presentations

OK

Costas Busch - LSU1 Deterministic Finite Automata And Regular Languages.

Costas Busch - LSU1 Deterministic Finite Automata And Regular Languages.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sectors of indian economy Ppt on condition based maintenance conference Ppt on seasons in india Ppt on pf and esi act Ppt on group development forming Ppt on building information modeling courses Ppt on magnetic field lines Ppt on symbols of french revolution Ppt on brain tumor detection Download ppt on global warming