Improved Algorithmic Complexity for the 3SEQ Recombination Detection Algorithm
Speaker :
樂正、張耿健、張馭荃、葉光哲
Author : Ha Minh Lam 、 Oliver
Ratmann 、 Maciej F. Boni
Outline
Introduction
The proposed algorithm
Improvement
Experimental results and discussion
Outline
Introduction
The proposed algorithm
Improvement
Experimental results and discussion
Recombination
Three nucleotide( 核甘酸 ) sequences :
Informative Sites
The nucleotide in is identical to one parental sequence but different from
Not informative site
Double-breakpoint Recombinant
right-side is the most likely recombination breakpoint
Graph Representation
+1 +1 +1 -1 -1 -1 +1 +1 +1 +1 -1
� �
up-steps
down-steps
±1 ��������
Maximum descent
0 1 2 3 4 5 6 7 8 9 10 A:+1 +1 +1 -1 -1 -1 +1 +1 +1 +1 -1 B:+1 +2 +3 +2 +1 +0 +1 +2 +3 +4 +3
� �
Maximum descent =
l < r
In this case, Maximum descent = 3 at
Statistical Tests
Given three sequences
Null hypothesis : is not recombination of
the informative sites will become random permutation
Random Permutation
� �
Maximum descent = 3
� �
Statistical Tests
suppose that the maximum descent
�
is the probability that maximum descent for a random arrangement
Outline
Introduction
The proposed algorithm
Improvement
Experimental results and discussion
Some Notations
the probability that up-steps , down-steps , and the ma ximum descent is exactly
� �
�=8 ,�=5 ,�=4
Example
For there are permutations.
Md = 2 Md = 1 Md = 2
�1,2,0=0,�1,2,1= 1
3 , � 1,2,2= 2
3 , �1,2,3=0
Some Notations
the probability that up-steps , down-steps , and the ma ximum descent is
can be computed from
Some Notations
the probability that up-steps , down-steps , the maximu m descent is exactly and the minimum value is exactly unit below the origin
� �
�=8 ,�=5 ,�=4 , j=1
Some Notations
can be computed from
so we only need to concentrate on how to compute
Dynamic Programming
Transfer need time complexity
(1)
(2)
(3)
(4)
Dynamic Programming
Transfer need time complexity ) states
Time complexity ) Space complexity )
Outline
Introduction
The proposed algorithm
Improvement
Experimental results and discussion
Rewritten
��,�,�= ∑
�=0
�
��,�,�, �
¿ ��,�,�,0+ ∑
�=1
�−1
��,�,�, �+��,�,�,�
expanded by (1)
expanded by (4)
expanded by (3)
Recursive Relation
��,�,�
Can see this equation as the recursive function of We only need to know for which
Improvement
building dp table for
Original method
1. Time complexity )
2. Space complexity )
Improved method
1. Time complexity )
2. Space complexity )
Since for we only need to memorize those with
Complexity Analysis
for computing
Transfer need time complexity
) states
Time complexity ) Space complexity )
��,�,�
Complexity Analysis
for computing , overall
Time complexity ) Space complexity )
