Overview
SA-IS Suffix Array Construction is a string indexing method for suffix array construction. It works by inducing suffix order from recursively sorted LMS substrings.
SpecializedSource checked
SA-IS Suffix Array Construction
SA-IS Suffix Array Construction addresses suffix array construction by inducing suffix order from recursively sorted LMS substrings.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Pattern Matching
- Difficulty
- Advanced
- Family
- String Indexing
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 4
- Code example
- Not ready
- Visualization
- Ready
- Aliases
- SA-IS
Core Concepts
suffix array constructionstring indexingrecursionsuffix structurepattern matching
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n + m)
Worst
O(n + m)
Space
O(n + m)
When to Use
- Use SA-IS Suffix Array Construction when solving suffix array construction and you want to benefit from inducing suffix order from recursively sorted LMS substrings.
- Choose it when O(n + m) average/worst-case time and O(n + m) memory match your workload profile.
- Prefer it over Ukkonen Suffix Tree Construction or Suffix Automaton LCS when the problem structure favors suffix array construction.
When Not to Use
- Avoid when preprocessing cost is larger than the savings for a one-off tiny input.
- Avoid when the alphabet or scoring assumptions do not match the sequence data.
What It Does
- Computes suffix array construction within String Indexing workloads (O(n + m) time, O(n + m) space).
- Works by inducing suffix order from recursively sorted LMS substrings.
- Maintains key invariants across suffix array construction, string indexing, recursion.
Use Cases
- Production and research workloads requiring suffix array construction via inducing suffix order from recursively sorted LMS substrings.
- String Indexing pipelines where O(n + m) time and O(n + m) space fit system constraints.
- Engineering comparisons against Ukkonen Suffix Tree Construction and Suffix Automaton LCS when tuning suffix array construction.
Inputs
- Text or sequence
- Pattern, index, or comparison sequence
Outputs
- Matches, alignment, index, or similarity value
Pseudocode
- 1.Preprocess the input alphabet, pattern/grammar rules, or symbol frequency tables for SA-IS Suffix Array Construction.
- 2.Construct the lookup automaton, suffix/shift index, or coding state (suffix array construction, string indexing).
- 3.Scan the input sequence by inducing suffix order from recursively sorted LMS substrings.
- 4.Emit matches, derivation nodes, or encoded tokens while advancing the state transition table.
- 5.Finalize trailing state and return the completed suffix array construction output.
Canonical Example
- Input
- Text or sequence configured for a representative suffix array construction test case
- Output
- Matches, alignment, index, or similarity value satisfying SA-IS Suffix Array Construction invariants
- Explanation
- SA-IS Suffix Array Construction processes the input by inducing suffix order from recursively sorted LMS substrings, tracking suffix array construction and string indexing to produce the verified suffix array construction result.
Implementation Notes
- Keep preprocessing output inspectable with short examples.
- Test repeated characters and overlapping matches.
- Document sentinel or alphabet assumptions.
Common Pitfalls
- Mishandling empty patterns, repeated characters, or sentinel symbols.
- Confusing preprocessing indexes with the query algorithm.
- Forgetting whether indexing is zero-based or one-based.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow inducing suffix order from recursively sorted LMS substrings on a small suffix array construction example.
Input:ABABABCABAB
Window:ABAB
Step 1 of 5: Preprocess the input alphabet, pattern/grammar rules, or symbol frequency tables for SA-IS Suffix Array Construction.
pattern-matching-mechanismNotes
SA-IS Suffix Array Construction operates in O(n + m) time and O(n + m) space within the String Indexing family. Often compared with Ukkonen Suffix Tree Construction and Suffix Automaton LCS.
Sources (2)
What each reference supports for this entry.
SA-IS Suffix Array Construction
PaperSpecific reference for SA-IS Suffix Array Construction's induced-sorting suffix array construction mechanism.
Open sourceAlgorithms on Strings, Trees, and Sequences
BookString algorithms reference for SA-IS Suffix Array Construction's pattern matching, suffix indexing, alignment, or sequence-processing mechanism.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Used byManber-Myers Suffix Array Construction
Pattern Matching · Core
Manber-Myers Suffix Array Construction uses SA-IS Suffix Array Construction as a subroutine, representation, or supporting idea while doubling prefix lengths and sorting suffix ranks iteratively.
Compare with thisRelationships
View full relationship pageSA-IS Suffix Array Construction uses Ukkonen Suffix Tree Construction as a subroutine, representation, or supporting idea while inducing suffix order from recursively sorted LMS substrings.
SA-IS Suffix Array Construction uses Suffix Automaton LCS as a subroutine, representation, or supporting idea while inducing suffix order from recursively sorted LMS substrings.
Related Algorithms
Tags
Pattern MatchingStringsDivide and Conquer