BCB 567/CprE 548
Fall 2007
Exam 2
Solutions
1.
(a) This is true.
Consider that
LCP
[
i
] =
k
.
This means that suffix
SA
[
i
] and suffix
SA
[
i
+ 1] have a longest common prefix of length
k
.
This implies that suffixes
SA
[
i
] + 1 and
SA
[
i
+ 1] + 1 have a longest common prefix of
k

1.
This means
that the range minimum in the LCP array between indexes
INV
[
SA
[
i
] + 1] and
INV
[
SA
[
i
+ 1] + 1] is
k

1. However, for this to be true, there must be some entry
in the LCP array equal to
k

1.
(b) The maximum zero entries in the LCP is equal to the alphabet size (if you consider
the last entry of the LCP array) or alphabet size  1 if you do not. Think about a
dictionary and how many times the first letter changes.
Grading Notes:
Both Σ and Σ

1 received full credit. Because the alphabet size
can be at most
N
, the answers
N
or
N

1 received partial credit.
(c) The minimum number of occurrences is 6. For each incoming suffix link, there exists
some internal node with path label
cα
. Therefore,
cα
occurs at least twice. Because
there are 3 suffix links, we have at least 3
×
2 = 6 occurrences.
(d)
i. No, counter example: ABC and ABCAB
ii. No, counter example: ABC and ABCAB
iii. Yes
iv. No, counter example: ABC and ABCAB
2.
(a) –
(b) –
(c)
i. To find length 3 repeats in the lookup table, search for table entries with more
than one index.
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 Fall '06
 OLIVEREULENSTEIN
 Graph Theory, Following, Repeat sign, LCP, longest common prefix

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