1. Indexing Graphs for Path Queries with Applications in Genome Research
Presented by: Evan Stene
Spring 2017

2. Paper Information
Authors: Published In: IEEE/ACM Transactions on Computational Biology and Bioinformatics Date of Publication: January 2014
Jouni Sirén
Niko Välimäki
Veli Mäkinen
Department of Computer Science
University of Chile
Research Programs Unit
University of Helsinki

3. Background – Alignment
Part of process for converting the biological data to computer readable data (sequencing)
Reading is prone to error
Sequence to search (reference genome) will never match all queries exactly

4. Combining Reference Sequences
Fig. 1. Pattern AGCTGTGT matching the multiple alignment when allowing it to change row when necessary.
Mention that small variations can be used with a reference as well
Also that backtracking is the alternative and is slow

5. Background – Suffix Arrays
Array of all suffixes of a string in sorted in ascending lexicographic order
Allows finding subsequence s in O(|s|)
Closed form function exists to find letter prepending suffix
Useful for compressed indices
E.g using only sampled values

6. Background – Prefix Doubling
Sort suffixes by their prefixes (iteratively)
Each iteration uses prefixes of length 2i
Each step effectively groups similar prefixes
Suffixes not belonging to any group (unique prefix) are in sorted order
Requires up to lg(n) iterations

7. Background – Prefix Doubling Example
Index 1 2 3 4 5 6 7 8 9 10 11 12
String $ A B R C D #
SA1
( 1
11 )
( 2
9 )
( 3
10 )
SA2
8 )
SA3
SA4
Mention that # and $ are beginning/end of string markers
LF = C[T[SA[i] – 1]] + rank(SA[i]) where rank is within that letter
e.G
For finding AB at 8,9
T[SA[9] – 1] = A
C[A] = 1
Rank(SA4[9]) = 1 since it’s the first B

8. Motivation
Combine reference sequences to provide greater accuracy when aligning
Create a suffix array like structure using a directional acyclic graph (DAG)
Relate the closed form transformations of suffix arrays to the DAG
Compress the sorted graph to fit into local memory

9. Building the Graph G A C G T A – C T G G A C G T A – – – G
G A T G T A – C T G
G A C – T A C C T G
Use examples G, T, A from end back and C at pos 3
Fig. 4. A reverse deterministic automaton corresponding to the first 10 positions of the multiple alignment in Fig. 1.

10. Prefix Sorting
For each node v in graph A, create the following tuple and store in an array:
(from(v), w, rank(v))
One for each w
Sort each tuple according to its rank
For tuples with unique ranks, set rank(v) = (rank(v), 0)
All other tuples combine as follows:
Tuples with from(u) and w = from(v) can be combined with rank(u,v) = (rank(u), rank(v))
Sort by the newly formed tuples and reassign the rank by location in array
Merge nodes with same rank and from values
Use example 1st A node from previous slide
1st part doubling, 2nd part pruning
W is 0 if no successors
from(v) = first node in path (forming the prefix)
rank(v) = rank of prefix starting from v among all other prefixes
w = successor to the last node in path

11. Prefix Sorting – Adding the edges
Fig. 5. A prefix-sorted automaton built for the automaton in Fig. 4. The strings above nodes are prefixes p(v).
Use middle T as edge example, it belongs to 4 prefixes

12. GCSA
BWT is being stored in list of incoming edges

13. Graph as Array AGC < AGZ -> prefixes for nodes 0 and 1
Mention offset is not stored in this example
Figures by: Daehwan Kim

14. Searching Example
Figures by: Daehwan Kim

15. Example Continued…
Figures by: Daehwan Kim

16. Example Ends
Talk about how this had a unique match, if the range was still >1 the results are ambigous. Also if the range slips to 0 at any point, the query returns 0 or backtracking is required
Figures by: Daehwan Kim

17. Compression
Talk about how to get to a node using the bit vector and how to count the number of outgoing edges
The compression of the incoming edge letter is only possible on genomic data
The authors of the paper use separate bit vectors for each letter with a 1 indicating that it appears at that index
Figures by: Daehwan Kim

18. Comparison Human genome version is about 3.1 Bln bp.
Determinization = building the graph
Backbone = main reference sequence

19. Comparison 0 Errors = exact matching
Some of the errors in GCSA are due to difficulty mapping certain highly repetitive regions