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Simple and fast linear space computation of L ongest c ommon s ubsequencesPowerPoint Presentation

Simple and fast linear space computation of L ongest c ommon s ubsequences

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### Simple and fast linear space computation of Longest common subsequences

Claus Rick, 1999

What is the LCS problem?

A A B A C

A B C

…Finding a sequence of greatest possible length that can be obtained

From both A and B by deleting zero or more (not necessarily adjacent) symbols.

Some boring history…

Lemma 1

Let p be the length of an LCS between strings A and B. Then for every match (i,j) the following holds:

- There is an LCS containing (i,j) if and only if (i,j) is on the kth forward contour and on the (p-k+1)st backward contour.

Really really last terms

Define sets Mi as:

M0= M

M1= M0\FC1

M2= M1\BC1

M2i-1=M2(i-1) \FCi

M2i=M2i-1\BCi

Complexity

Finding the dominant matches each contour:

O(min(m, (n-p))

Number of contours:

P

O(Min(pm, p(n-p)

The End

Simple and fast linear space computation of longest common subsequence

Written by:

Claus Rick,1999

Based on algorithm by:

D.Hirschberg, 1975

Cast:

Matrices

Lines

Arrows

Squares

Blue

Red

Brown

Grey

Black

String A

String B

Presentation: Uri Scheiner

No Dominant Matches were harmed during the making of this presentation

Appendix subsequence

What is the LCS

Lemma 1

Divided And Conquer

Define M…

Match

Lemma 2

Chain

Keep just Dominant…

Dominant Matches

FC

Lemma 3

BC

Complexity

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