Patent Publication Number: US-11031092-B2

Title: Taxonomic annotation of variable length metagenomic patterns

Description:
BACKGROUND 
     Technical Field 
     The present invention relates generally to genomes and, in particular, to taxonomic annotation of variable length metagenomic patterns. 
     Description of the Related Art 
     Genome databases are growing everyday with hundreds of thousands of organisms. Hence, it can be an onerous task to trawl through the database. Accordingly, there is a need for a way to efficiently annotate metagenome databases for pattern classification purposes. 
     SUMMARY 
     According to an aspect of the present invention, a computer-implemented method is provided for metagenomic pattern classification. The method includes pre-processing, by a processor, a taxonomy tree associated with a genome database to extract taxonomy related information therefrom. The genome database includes a plurality of genome sequences. The method further includes building, by the processor, a suffix tree on the genome database. The method also includes annotating, by the processor, nodes in the suffix tree, using a plurality of right maximal patterns derived from the extracted taxonomy related information as annotations, such that each of the plurality of right maximal patterns in the suffix tree points to a respective one of a plurality of nodes in the taxonomy tree and such that a leaf node in the taxonomy tree represents a respective sample organism. The annotations are configured to function as classifications for the plurality of genome sequences. 
     According to another aspect of the present invention, a computer program product is provided for metagenomics pattern classification. The computer program product includes a non-transitory computer readable storage medium having program instructions embodied therewith. The program instructions are executable by a computer to cause the computer to perform a method. The method includes pre-processing, by a processor, a taxonomy tree associated with a genome database to extract taxonomy related information therefrom. The genome database includes a plurality of genome sequences. The method further includes building, by the processor, a suffix tree on the genome database. The method also includes annotating, by the processor, nodes in the suffix tree, using a plurality of right maximal patterns annotated from the extracted taxonomy related information, such that each of the plurality of right maximal patterns in the suffix tree points to a respective one of a plurality of nodes in the taxonomy tree and such that a leaf node in the taxonomy tree represents a respective sample organism. The annotations are configured to function as classifications for the plurality of genome sequences. 
     According to yet another aspect of the present invention, a computer processing system is provided for classification of genomic patterns. The system includes a processor. The processor is configured to pre-process a taxonomy tree associated with a genome database to extract taxonomy related information therefrom. The genome database includes a plurality of genome sequences. The processor is further configured to build a suffix tree on the genome database. The processor is also configured to annotate nodes in the suffix tree, using a plurality of right maximal patterns derived from the extracted taxonomy related information as annotations, such that each of the plurality of right maximal patterns in the suffix tree points to a respective one of a plurality of nodes in the taxonomy tree and such that a leaf node in the taxonomy tree represents a respective sample organism. The annotations are configured to function as classifications for the plurality of genome sequences. 
     These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following description will provide details of preferred embodiments with reference to the following figures wherein: 
         FIG. 1  shows an exemplary processing system to which the present invention may be applied, in accordance with an embodiment of the present invention; 
         FIG. 2  shows an exemplary system to which the present invention can be applied, in accordance with an embodiment of the present invention; 
         FIGS. 3-4  show an exemplary method for indexing genome databases with taxonomy using variable length patterns, in accordance with an embodiment of the present invention; 
         FIG. 5  shows an exemplary taxonomic database to which the present invention can be applied, in accordance with an embodiment of the present invention; 
         FIG. 6  shows an exemplary generalized suffix tree, in accordance with an embodiment of the present invention; 
         FIG. 7  shows an exemplary generalized suffix array, in accordance with an embodiment of the present invention; and 
         FIG. 8  shows an exemplary generalized bidirectional Burrows-Wheeler Transform (BWT), in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention is directed to taxonomic annotation of variable length patterns in a metagenomic database. For the purpose of the invention, the terms “metagenomics(s)”, “metatranscriptomic(s)”, “genomic(s)” can interchangeably refer to the following: a set of sequences annotated by taxonomic information. 
     In an embodiment, the present invention can be used to annotate a pattern (of unknown origin) on a taxonomy, given the pattern (of unknown origin) and a reference database of sequences organized in a taxonomic tree. 
     In an embodiment, right maximal patterns are annotated, as opposed to k-mers. The use of right maximal patterns allows for the classification of patterns of any length as opposed to patterns having a fixed length k. 
     In an embodiment, the present invention can provide a lossless representation of taxonomic annotated sequences in an efficient amount of space that allows a time efficient pattern classification. In this way, data (sequence) identification, access, and classification times can be reduced, as well as the corresponding computing resources (e.g., processing, memory, bandwidth, etc.) implicated to search a genome database. 
     It is to be appreciated that the present invention can be used for a myriad of applications. For example, exemplary applications to which the present invention can be applied include, but are not limited to, any of the following: human microbiomes; related to human health; food safety; soil; microbiomes; and so forth. It is to be appreciated that the preceding applications to which the present invention can be applied are merely illustrative and, thus, the present invention can be used for other applications, as readily appreciated by one of ordinary skill in the art given the teachings of the present invention provided herein, while maintaining the spirit of the present invention. 
       FIG. 1  shows an exemplary processing system  100  to which the invention principles may be applied, in accordance with an embodiment of the present invention. The processing system  100  includes at least one processor (CPU)  104  operatively coupled to other components via a system bus  102 . A cache  106 , a Read Only Memory (ROM)  108 , a Random Access Memory (RAM)  110 , an input/output (I/O) adapter  120 , a sound adapter  130 , a network adapter  140 , a user interface adapter  150 , and a display adapter  160 , are operatively coupled to the system bus  102 . At least one Graphics Processing Unit (GPU)  194  is operatively coupled to the system bus  102 . 
     A first storage device  122  and a second storage device  124  are operatively coupled to system bus  102  by the I/O adapter  120 . The storage devices  122  and  124  can be any of a disk storage device (e.g., a magnetic or optical disk storage device), a solid state magnetic device, and so forth. The storage devices  122  and  124  can be the same type of storage device or different types of storage devices. 
     A speaker  132  is operatively coupled to system bus  102  by the sound adapter  130 . A transceiver  142  is operatively coupled to system bus  102  by network adapter  140 . A display device  162  is operatively coupled to system bus  102  by display adapter  160 . 
     A first user input device  152 , a second user input device  154 , and a third user input device  156  are operatively coupled to system bus  102  by user interface adapter  150 . The user input devices  152 ,  154 , and  156  can be any of a keyboard, a mouse, a keypad, an image capture device, a motion sensing device, a microphone, a device incorporating the functionality of at least two of the preceding devices, and so forth. Of course, other types of input devices can also be used, while maintaining the spirit of the present invention. The user input devices  152 ,  154 , and  156  can be the same type of user input device or different types of user input devices. The user input devices  152 ,  154 , and  156  are used to input and output information to and from system  100 . 
     Of course, the processing system  100  may also include other elements (not shown), as readily contemplated by one of skill in the art, as well as omit certain elements. For example, various other input devices and/or output devices can be included in processing system  100 , depending upon the particular implementation of the same, as readily understood by one of ordinary skill in the art. For example, various types of wireless and/or wired input and/or output devices can be used. Moreover, additional processors, controllers, memories, and so forth, in various configurations can also be utilized as readily appreciated by one of ordinary skill in the art. These and other variations of the processing system  100  are readily contemplated by one of ordinary skill in the art given the teachings of the present invention provided herein. 
     Moreover, it is to be appreciated that system  200  described below with respect to  FIG. 2  is a system for implementing respective embodiments of the present invention. Part or all of processing system  100  may be implemented in one or more of the elements of system  200 . 
     Further, it is to be appreciated that processing system  100  may perform at least part of the method described herein including, for example, at least part of method  300  of  FIGS. 3-4 . Similarly, part or all of system  200  may be used to perform at least part of method  300  of  FIGS. 3-4 . 
       FIG. 2  shows an exemplary system  200  to which the present invention can be applied, in accordance with an embodiment of the present invention. The system  200  includes a computer processing system  210  (e.g., computer processing system  100 ) and a set of other computer processing systems  220 . In an embodiment, one or more of the computer processing systems  210  and  220  can be configured as servers. 
     The computer processing system  210  includes a genome database D 211  and an associated taxonomy tree    212 . The computer processing system  210  can be configured to perform pre-processing on the genome database D  211  and the associated taxonomy tree    212 . The pre-processing can involve building and annotating a suffix tree  213  for use in searching the genome database D  211  for an input pattern to be classified/correlated. The computer processing system  210  can be configured to receive patterns to be classified from any of the other computer processing systems  220 , classify such patterns using the suffix tree  213 , and send a classification therefor to the other computer processing systems  220 . The classifications are in the form of space efficient annotations as described in further detail herein below. 
     The computer processing system  210  further includes at least a processor  291 , a memory  292 , and a transceiver  293 . Moreover, the other computer processing systems  220  at least include a processor  291 , a memory  292 , a transceiver  293 , and a database  294 . The processor  291  and memory  292  of the computer processing system  210  can be configured to perform indexing of the genome database D  211  with taxonomy    212  using maximal patterns. The processor  291  and the memory  292  of the other computer processing systems can be configured to provide patterns to be classified. The transceivers  293  in any of the systems  210  and  220  can be configured to send and receive patterns. The databases  294  of the other computer processing systems  220  can store patterns to be classified as well as classifications for patterns already classified. 
     In the embodiment shown in  FIG. 2 , the elements thereof are interconnected by a network(s)  201 . However, in other embodiments, other types of connections can also be used. Moreover, in an embodiment, at least one of the elements of system  200  is processor-based (in the shown example, all are processor-based). Further, while one or more elements may be shown as separate elements, in other embodiments, these elements can be combined as one element. The converse is also applicable, where while one or more elements may be part of another element, in other embodiments, the one or more elements may be implemented as standalone elements. Moreover, one or more elements of  FIG. 2  can be implemented in a cloud configuration including, for example, in a distributed configuration. Additionally, one or more elements in  FIG. 2  may be implemented by a variety of devices, which include but are not limited to, Digital Signal Processing (DSP) circuits, programmable processors, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs), Complex Programmable Logic Devices (CPLDs), and so forth. These and other variations of the elements of system  200  are readily determined by one of ordinary skill in the art, given the teachings of the present invention provided herein, while maintaining the spirit of the present invention. 
       FIGS. 3-4  show an exemplary method  300  for indexing genome databases with taxonomy using variable length patterns (right maximal patterns), in accordance with an embodiment of the present invention. In an embodiment, steps  310 - 340  of method  300  can be considered to correspond to a pre-processing phase or stage, while steps  350 - 360  can be considered to correspond to a classification phase or stage. 
     At step  310 , provide a genome database D and an associated taxonomy tree T. The genome database D includes genome sequences. The genome sequences can have different lengths. 
     At step  320 , preprocess the taxonomy tree   to extract taxonomy related information therefrom. The taxonomy related information can include, but is not limited to, any of the following: Lowest Common Ancestor (LCA) queries; and any function of the right maximal pattern and the LCA. The taxonomy related information is extracted at step  320  for later use (at step  340 ). 
     At step  330 , build a suffix tree or trie on the genome database D. The suffix tree can be built using, for example, any of the following: (1) a (bi-directional) FM-index; (2) an (enhanced) suffix array; and (3) a (compressed) suffix tree. The preceding structures are merely illustrative and, thus, other structures can also be used to build the suffix tree, while maintaining the spirit of the present invention. 
     At step  340 , annotate each node in the suffix tree using right maximal patterns derived and/or otherwise formed from the taxonomy related information (extracted at step  320 ). The resultant annotated suffix tree provides a medium upon which to perform quick searches in order to obtain classifications for input sequences to be searched. Hence, the proposed invention improves the functionality of the genome database Das well as the computer processing system that includes the genome database D. 
     In an embodiment, step  340  includes one or more of steps  340 A-C. 
     At step  340 A, configure each maximal pattern to point to a node in the taxonomy tree  , where a leaf node in the taxonomy tree   is a sample organism. 
     At step  340 B, configure the annotations to function as classifications for the genome sequences. 
     At step  340 C, configure each of the annotations as a lossless representation of a respective one of the plurality of genome sequences. 
     At step  350 , receive a given pattern to be classified. The given pattern can be, but is not limited to, a read (pattern) from Next Generation Sequencing (NGS) data and so forth. 
     At step  360 , search for the given pattern in the suffix tree and retrieve the annotation therefor. In an embodiment, as noted above, the annotation includes and/or otherwise represents a classification of the given pattern. 
     At step  370 , perform an action responsive to the annotation/classification of the given pattern. The action can include, but is not limited to, any of the following: sequence alignment (e.g., using one or more ASICs or other specially programmed computing devices); microbiome based tasks (e.g., binning and/or profiling); metatranscripts abundance estimation; and so forth. 
     Herein, a method is described for annotating generalized suffix arrays and BWTs in order to answer lowest taxonomic unit (LTU) queries in constant time for patterns of arbitrary length. The annotation method is not confined to the specific application of LTUs and can be used for general-purpose annotation, as readily appreciated by one of ordinary skill in the art, given the teachings of the present invention provided herein. 
       FIG. 5  shows an exemplary taxonomic database  500  to which the present invention can be applied, in accordance with an embodiment of the present invention. 
     The taxonomic database (S,  )  500  includes a collection of strings S={s 0 , s 1 , . . . , s m-1 } of total length n over the ordered alphabet Σ={a, c, g, t} and a taxonomic tree  , i.e., a rooted tree with m leaves labeled by the indexes of strings in S and internal nodes referring to taxonomic units. The taxonomic database  500  further includes an id for each of the strings. Given a pattern string p over Σ, the problem is to retrieve the lowest taxonomic unit (LTU) in   where p occurs. The taxonomic database (S,  ) is given in advance and can be preprocessed. 
     The LTU between 1 and 3 is 5. The LTU between 0 and 4 is 6. 
       FIGS. 6-8  hereinafter show examples based on taxonomic database  500  for illustrative purposes. 
     Initially, we conceptualize taxonomic annotation on generalized suffix trees (GSTs) and thereafter show how to annotate generalized suffix arrays and bidirectional BWTs. 
     A description will now be given of a generalized suffix tree, in accordance with an embodiment of the present invention. 
     The description will be provided with respect to  FIG. 6 , which shows an exemplary generalized suffix tree  600 , in accordance with an embodiment of the present invention. For illustrative purposes, the generalized suffix tree  600  of strings S is annotated for LTU queries on taxonomic tree  . The involved database is database (S,  ) shown in  FIG. 5 . In  FIG. 6 , non-terminal nodes are depicted as circles, terminal nodes are depicted as squares, and LTU annotations are depicted inside pentagons. The LTU of pattern “a” is 6 while the LTU of pattern “aa” is 4. 
     A practical definition of generalized suffix tree is adopted that is based on terminal nodes in addition to leaves and branching internal nodes. The definition allows the present invention to work on arbitrary collections of strings without introducing sentinel characters, e.g., $. In what follows, we denote the l-th suffix of string s k  as S (k,l) :=s k [l] . . . s k [|s k |−1] where |s k | is the length of string s k . 
     The generalized suffix tree of S, abbreviated as GST(S), is a lexicographically ordered tree data structure having one node designated as the root. Each node v of GST(S) provides the following operations: 
     CLD(v) returns the nodes children of v; 
     SUF(v) returns a list of pairs s.t. pair (k, l) refers to suffix S (k,l) ; 
     LABEL(v) returns a string over Σ or the empty string if v is the root; 
     REPR(v) returns REBR(u)·LABEL(v) where u is the parent of v. 
     We say that: 
     Node v is a leaf if |CLD(v)|=0 and internal otherwise; and 
     Node v is terminal if |SUF(v)|≥1 and non-terminal otherwise. 
     The GST(S) has the following properties: 
     For each (k, l) in SUF(v), REPR(v) spells exactly S (k,l) ; 
     Each leaf is terminal; and 
     Each non-terminal node v is branching, i.e., |CLD(v)|≥2, and LABEL(w) for all w∈CLD(v) begin with distinct characters. 
     As each suffix in S is associated with one terminal node, GST(S) has at most n terminal nodes. Furthermore, because of the branching property, GST(S) has at most n−1 non-terminal nodes. Therefore, we have to annotate at most 2n−1 nodes. 
     We now describe the annotation of GST(S) to answer LTU queries in constant time given node v. We denote the lowest common ancestor (LCA) of nodes u and v in   by LC (u, v) and the iterated LCA as follows:
 
LC ( u, . . . ,y,z )=LC ( u ,LC ( . . . ,LC ( y,z )))  (1)
 
     We define IDS(v)={k:(k, l)∈SUF(v)}. The LTU of node v with CLD(v)={w 0 , w 1 , . . . , w k-1 } is as follows:
 
LT ( v )=LC ( IDS ( v ),LT ( w   0 ),LT ( w   1 ), . . . ,LT ( w   k-1 ))  (2)
 
     Before annotating GST(S), we preprocess   to answer LCA queries in constant time. In practice, we reduce LCA queries to range minimum queries (RMQ). Subsequently, we compute LT  (for all nodes of GST(S) in a single post-order traversal. The annotation of GST(S) thus takes  (n) time. 
     A description will be given regarding a generalized suffix array, in accordance with an embodiment of the present invention. 
     The description will be provided with respect to  FIG. 7 , which shows an exemplary generalized suffix array  700 , in accordance with an embodiment of the present invention. For illustrative purposes, the generalized suffix array  700  of strings S is annotated for LTU queries on taxonomic tree  . The involved database is database (S,  ) shown in  FIG. 5 . Pattern “agtg” corresponds to a singleton with interval [2, 3) and its LTU is id[2]=0. Pattern “a” corresponds to a leftmost node with interval [0, 6) and its LTU is tax[5]=6. Pattern “at” is not on a singleton nor on a leftmost node, its interval is [3, 6) and its LTU is tax[3]=5. 
     The generalized suffix array (GSA) of strings S is a pair (id, pas):=gsa of tables of length n where id[i]=k,pos[i]=l and gsa[i]=(k, l). Table gsa represents a permutation of all pairs (k, l) referring to suffixes S (k,l)  in S. Pairs in gsa are ordered s.t. S gsa[i-1] &lt; lex  S gsa[i]  for all i∈[1; n). 
     Table gsa corresponds to the pre-order concatenation of SUF(v) for all terminal nodes v in GST(S). Each node v of GST(S) is univocally identified by a half-open interval [LB(v), RB(v)) on table gsa and it can be determined by binary searching REPR(v) on gsa. GST(S) corresponds to a recursive partitioning of gsa: the root node corresponds to interval [0, n); if v is an internal node with CLD(v)={w 0 , w 1 , . . . , w k-1 } then its children intervals are as follows:
 
[ LB ( v )|SUF( v )|;  RB ( w 0)), [ RB ( w   0 );  RB ( w   1 )), . . . ,[ RB ( w   k-1 );  RB ( v )).
 
     GSA(S) can be traversed in linear-time, bottom-up using the additional lcp table and top-down using lcp and child tables. If top-down traversal is bounded to relatively short patterns, a binary search on table gsa is a practical alternative. Similarly, GSA(S) supports pattern search in time  (|p| log n) using only table gsa,  (|p|+log n) using table lcp and  (|p|) using lcp and child tables. 
     We now describe our method to store and retrieve LTUs in constant time once we reach a node v. Traversal on GST(S) to compute LTUs is readily translated onto GSA(S). The problem is how to store and retrieve annotations in GSA(S). We say that leaf v is singleton if LB(v)=RB(v)−1. Furthermore, we say that a node v with parent u is leftmost if LB(u)=RB(v); we determine this condition in constant time by remembering the parent u of v while traversing GSA(S) top-down. Note that we define the root not to be leftmost. We introduce a table tax of size n to store the annotations of all non-singleton nodes. We annotate the LTU of node v as follows: 
     
       
         
           
             
               
                 
                   
                     
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     If v is singleton, its LTU is already annotated in table id at position LB(v). We show by induction on GST(S) that each non-singleton node v is annotated at an available slot in tax. Prior to annotation both tax[LB(v)] and tax[RB(v)−1] are available; after annotation one of these two slots remains available. 
     1. If v is a leaf. All slots in tax within interval [LB(v), RB(v)) are available and LB(v)&lt;RB(v)−1 as v is non-singleton. Hence, if v is leftmost tax[LB(v)] remains available, otherwise tax[RB(v)−1] remains available. 
     2. If v is an internal node with children CLD(v)={w 0 , w 1 , . . . , w k-1 }. Node w k-1  is not leftmost and tax[RB(w k-1 )−1] is supposed to be available by induction. As RB(w k-1 )=RB(v) then tax[RB(v)−1] is available. 
     (a) If v is non-terminal. We have |SUF(v)|=0, LB(w 0 )=LB(v) and w 0  is leftmost. By induction tax[LB(w 0 )] that is tax[LB(v)] is supposed to be available. 
     (b) If v is terminal. All slots in tax within interval [LB(v); LB(v)+SUF(v)) are available and SUF(v)≥1, so tax[LB(v)] is available. 
     After annotation, if v is leftmost tax[LB(v)]remains available, otherwise tax[RB(v)−1] remains available. 
     A description will now be given regarding a generalized Burrows-Wheeler Transform (GBWT) to which the present invention can be applied, in accordance with an embodiment of the present invention. 
     The description will be provided with respect to  FIG. 8 , which shows an exemplary generalized bidirectional Burrows-Wheeler Transform  800 , in accordance with an embodiment of the present invention. For illustrative purposes, the generalized bidirectional BWT  800  of strings S is annotated for LTU queries on taxonomic tree  . The involved database is database (S,  ) shown in  FIG. 5 . 
     Hereinafter, we denote by  s =s[|s|−1] . . . s[1]s [0] the reversed string s and by S the collection S with all strings reversed. We consider the ordered alphabet Σ $ ={$ 1 , . . . , $ m }∪Σ and append $ i  to each string s i ∈S. This is to insure that S is primitive, i.e., that no string in S is a power of some other string. 
     The GBWT of strings S is a table gbwt of length n with: 
     
       
         
           
             
               
                 
                   
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     Function RANK(c, i) counts the number of occurrences of character c∈Σ $  in the half-open interval [0, i) of gbwt and LF as:
 
 LF ( c,i )=Σ a&lt;c RANK( a,n )+RANK( c,i )  (5)
 
     Similarly to GSA(S), each node v of GST(S) is univocally identified on GBWT(S) by a half-open interval [LB(v), RB(v)). This interval is now determined by searching REPR(v) backwards on gbwt using LF. For any two nodes u, v of GBWT(S) with REPR(v)=c REPR(u) and c∈Σ, it holds:
 
 LB ( v )= LF ( c,LB ( u )+ m )− m   (6)
 
 RB ( v )= LF ( c,RB ( u )+ m )− m   (7)
 
     We adjust the boundaries by m since we have introduced m characters $ in S. Function LF is answered in  (1) time using o(n|Σ|log|Σ|) extra bits on top of gbwt. Pattern p is searched backwards in  (|p|) time. 
     The bidirectional GBWT includes GBWT(S) and GBWT(S) and allows searching simultaneously a pattern p backwards on GBWT(S) and its reverse  p  on GBWT(S). Function LT counts the number of characters lexicographically smaller than c∈Σ $  in gbwt within interval [i; j):
 
LT( c,i,j )=Σ a&lt;c RANK( a,j )−Σ a&lt;c RANK( a,i )  (8)
 
     If u is a node on GBWT(S), u is its corresponding node on GBWT(S) s.t. REPR(u)= REPR (ū). Furthermore, if v is with REPR(v)=c REPR(u), the interval of node  v  with REPR( v )=c REPR(ū) is determined as follows:
 
 LB (   v   )= LB ( ū )+LT( c,LB ( u )+ m,RB ( u )+ m )  (9)
 
 RB (   v   )= LB (   v   )+ RB ( v )− LB ( v )  (10)
 
     We construct an unidirectional BWT to answer LTU queries using only table gbwt of GBWT( S ) plus tables id and tax of GBWT(S). If we search pattern  p  backwards on GBWT(S) and arrive on a node  v  with REPR( v )= p , then node v corresponds to the node reached by searching p backwards on GBWT(S) or forward on GSA(S). Therefore we can still access the annotation at node v using Equation 3. To fill tables id and tax, we traverse top-down GBWT( S ) backwards and annotate nodes on GBWT(S) forward. Top-down traversal is feasible in practice if it is bounded to relatively short patterns. 
     We remark that table id can be obtained as a byproduct of certain BWT construction algorithms instead of slicing table gsa. Furthermore, tables id and tax can be sparsified when the annotation is bounded to relatively short patterns. These and other variations are readily determined by one of ordinary skill in the art, given the teachings of the present invention provided herein, while maintaining the spirit of the present invention. 
     It is to be appreciated that various can be imposed on the preceding data structures or other data structures can be used, given the teachings of the present invention provided herein, while maintaining the spirit of the present invention. 
     The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. 
     The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. 
     Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as SMALLTALK, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention. 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
     These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     Reference in the specification to “one embodiment” or “an embodiment” of the present invention, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment”, as well any other variations, appearing in various places throughout the specification are not necessarily all referring to the same embodiment. 
     It is to be appreciated that the use of any of the following “/”, “and/or”, and “at least one of”, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as readily apparent by one of ordinary skill in this and related arts, for as many items listed. 
     Having described preferred embodiments of a system and method (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in the particular embodiments disclosed which are within the scope of the invention as outlined by the appended claims. Having thus described aspects of the invention, with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.