Illustration of Algorithm 3 from paper:

Reconstructing a suffix array By F. Franek & B. Smyth

Slide 1

INDEX LSA LCP

INDEX X

1

19 2

5

13 16

4

3

1 9

0

2

2 10

1

6

14 17

1

11 7

3 12

8

3

15

18

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18a b c a a b c d a b c c a b d a b e a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18

1 1 3 3 2 2 0 2 2 1 1 0 2 1 1 0 3 0

19

19

Slide 2

The permutation of the alphabet for this example is defined by

p[a]=ap[b]=cp[c]=dp[d]=bp[e]=e

Slide 3

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

Next SlideSlide 4

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

Next SlideSlide 5

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

Next SlideSlide 6

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

Next SlideSlide 7

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

IDENTIFY AND EXTRACT FAMILY

Next SlideSlide 8

0 (PREV of start)

stack

start=19

2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 139 10 12 1 0 14 8 15 5 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 9 5 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

IDENTIFY AND EXTRACT FAMILY

31

39

253-family

Next SlideSlide 9

0 (PREV of start)

stack

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 5 9 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

SORT THE FAMILY

31

39

253-family 3

135

29

LCP sort of t-family:preserve the last and every k>=tchange every k < t to t

Next SlideSlide 10

0 (PREV of start)

stack

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 5 9 13 16 2 10

6 14 17 3 12 11 7 8 15 18

INDEXmod LCP

NEXTTAIL

4 (PREV of 1)

FLATTEN THE FAMILY

Nothing to flatten, it is already flat

Next SlideSlide 11

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1313 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 45 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 13 16 2 10 6 14 17

3 12 11 7 8 15 18

1

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

0 (PREV of start)

stack

4 (PREV of 1)

endnext

Should we pop? NO

Next SlideSlide 12

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1313 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 45 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 13 16 2 10 6 14 17

3 12 11 7 8 15 18

1

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

next end

0 (PREV of start)

stack

4 (PREV of 1)

Next SlideSlide 13

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1313 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 45 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 13 16 2 10 6 14 17

3 12 11 7 8 15 18

1

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

next end

0 (PREV of start)

stack

4 (PREV of 1)

Next SlideSlide 14

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1313 10 12 1 9 14 8 15 0 6 7 11 16 17 18 0 3 0 45 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 13 16 2 10 6 14 17

3 12 11 7 8 15 18

1

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

next end

0 (PREV of start)

stack

4 (PREV of 1)

31

213

0162-family

Next SlideSlide 15

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1316 10 12 13 9 14 8 15 0 6 7 11 1 17 18 0 3 0 45 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 16 2 10 6 14 17

3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

next end

0 (PREV of start)

stack

4 (PREV of 1)

31

213

0162-family 2

1331

016

Next SlideSlide 16

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 16 2 10 6 14

17 3 12 11 7 8 15 18

13 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

0 (PREV of start)

stack

4 (PREV of 1)

Next SlideSlide 17

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 16 2 10 6 14

17 3 12 11 7 8 15 18

13 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

0 (PREV of start)

stack

4 (PREV of 1)

Next SlideSlide 18

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 2 17 18 0 3 0 4

16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

0 (PREV of start)

stack

4 (PREV of 1)

nextend

Next SlideSlide 19

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 2 17 18 2 3 0 4

16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

0 (PREV of start)

stack

4 (PREV of 1)

nextend

Should we pop? YES

Next SlideSlide 20

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 2 17 18 0 3 0 4

16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

0 (PREV of start)

stack

nextend

Next SlideSlide 21

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 0 17 18 0 3 0 4

16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

0 (PREV of start)

stack

nextend

119

14

2131-family

Next SlideSlide 2

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 0 17 18 0 3 0 4

16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

0 (PREV of start)

stack

nextend

119

14

2131-family 1

1914

213

Next SlideSlide 23

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 2 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 16 2 10 6 14

17 3 12 11 7 8 15 18

13 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

0 (PREV of start)

stack

Next SlideSlide 24

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 16 2 10 6 14

17 3 12 11 7 8 15 18

13 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

0 (PREV of start)

stack

Next SlideSlide 25

start=19

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

0 (PREV of start)

stack

nextend

Should we pop? YES

Next SlideSlide 26

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

2

Next SlideSlide 27

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

Next SlideSlide 28

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

Next SlideSlide 29

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

Next SlideSlide 30

2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 135 10 12 13 9 0 8 15 16 6 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 10 6 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

22

210

162-family

Next SlideSlide 31

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 6 10 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

stack

nextend

19 (PREV of 2)

22

210

162-family 2

226

110

Next SlideSlide 32

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 6 10 14

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

19 (PREV of 2)

Nothing to flatten, it is already flat

Next SlideSlide 33

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

14 17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

19 (PREV of 2)

next end

Next SlideSlide 34

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

14 17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

19 (PREV of 2)

next end

Should we pop? NO

Next SlideSlide 35

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

14 17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

next end

Next SlideSlide 36

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 20 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

14 17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

next end

Next SlideSlide 37

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 0 0 20 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

14 17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

19 (PREV of 2)

next end

22

114

0172-family

Next SlideSlide 38

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 17 12 13 9 10 8 15 16 0 7 11 1 2 18 0 0 0 140 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17 3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

stack

nextend

19 (PREV of 2)

next end

22

114

0171-family 1

1422

017

14

Next SlideSlide 39

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 2 18 0 0 0 140 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 6 10 17 3 12 11 7

8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

19 (PREV of 2)

14

Next SlideSlide 40

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 17 7 11 1 2 18 0 0 0 140 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2 6 10 17 3 12 11 7

8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

19 (PREV of 2)

14

Next SlideSlide 41

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

3 12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

19 (PREV of 2)

14

nextend

Should we pop? YES

Next SlideSlide 42

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

Next SlideSlide 43

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

Next SlideSlide 44

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

Next SlideSlide 45

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

Next SlideSlide 46

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

23

1122-family

Next SlideSlide 47

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

23

1122-family 2

31

12

Next SlideSlide 48

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

Nothing to flatten, it is already flat

Next SlideSlide 49

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

Next SlideSlide 50

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11 7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

Should we pop? NO

Next SlideSlide 51

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

11

Next SlideSlide 52

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

11

Next SlideSlide 53

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

11

Next SlideSlide 54

2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 135 6 11 13 9 10 0 15 16 0 7 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

7 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

11

23

111

071-family

Next SlideSlide 55

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 7 13 9 10 11 15 16 0 0 0 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

next end

7

23

111

071-family 2

317

011

Next SlideSlide 56

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 12 13 9 10 11 15 16 0 8 7 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

7

Next SlideSlide 57

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 12 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12 11 8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

7

Next SlideSlide 58

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

7

nextend

Next SlideSlide 59

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

8 15 18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

14 (PREV of 3)

7

nextend

Should we pop? YES

Next SlideSlide 60

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

Next SlideSlide 61

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

Next SlideSlide 62

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 18 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

Next SlideSlide 63

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

38

0153-family

Next SlideSlide 64

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

38

0153-family 3

80

15

Next SlideSlide 65

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 15 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 0 0 0 0 11 0 2 0 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15 18

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

Nothing to flatten, it is already flat

Next SlideSlide 66

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 18 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

next end

Next SlideSlide 67

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 18 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

18

13

9

5

INDEXmod LCP

NEXTTAIL

VERTICALIZE THE FAMILY

stack

nextend

14

nextend

3

7

nextend

3 (PREV of 8)

8

next end

Should we pop? YES

Next SlideSlide 68

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 18 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

8

next end

18

Next SlideSlide 69

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 18 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

8

next end

18

Next SlideSlide 70

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 8 13 9 10 11 18 16 0 0 7 1 3 0 0 0 0 140 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

13

9

5

INDEXmod LCP

NEXTTAIL

IDENTIFY AND EXTRACT FAMILY

stack

nextend

14

nextend

3

7

nextend

8

next end

18

0-family 1 2 3 0119 14 3 8 18

Next SlideSlide 71

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 18 13 9 10 11 14 16 0 0 7 1 3 0 0 0 0 80 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

2

6

10

17

12

11

15

13

9

5

INDEXmod LCP

NEXTTAIL

SORT THE FAMILY

stack

nextend

14

nextend

3

7

nextend

8

next end

18

0-family 1 2 3 0119 14 3 8 18

3 1 2 0119 8 14 3 18

Next SlideSlide 72

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 18 13 9 10 11 14 16 0 0 7 1 3 0 0 0 0 80 17 12 16 0 0 0 15 0 0 0 11 0 2 15 0 0 0 4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19

4

1

16

13

9

5

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

nextend nextendnext

endnext end

2

6

10

17

12

11

15

14 3

7

8 18

Next SlideSlide 73

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 18 13 9 10 11 14 16 0 0 7 1 3 0 8 0 0 40 17 12 0 0 0 0 15 0 0 0 11 0 2 15 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

nextendnext

endnext end

15

8

2

6

10

17

12

11

14 3

7

18

Next SlideSlide 74

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 18 13 9 10 11 15 16 0 0 7 1 3 14 8 0 0 40 17 12 0 0 0 0 0 0 0 0 11 0 2 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

nextendnext

end

158

2

6

10

17

14

12

11

3

7

18Next SlideSlide 75

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 18 13 9 10 11 15 16 0 0 7 1 2 14 8 3 0 40 0 12 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

nextend

158

2 6 10 1714

12

11

3

7

18

Next SlideSlide 76

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 12 13 9 10 11 15 16 0 0 7 1 2 14 8 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

158

2 6 10 1714 12 117 183

Next SlideSlide 77

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 12 13 9 10 11 15 16 0 18 7 1 2 14 8 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

FLATTEN THE FAMILY

158

2 6 10 1714 12 117 183

Next SlideSlide 78

2 2 1 3 2 1 3 2 1 0 1 2 1 0 0 0 0 135 6 12 13 9 10 11 15 16 0 18 7 1 2 14 8 3 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

19 4 1 1613 95

INDEXmod LCP

NEXTTAIL

DONE

158

2 6 10 1714 12 117 183

INDEXLSA

LCP4 13 1 5 9 16 8 15 14 2 6 10 17 3 12 7 11 18191 1 2 3 3 2 0 3 0 1 2 2 1 0 2 1 1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Slide 79

end