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arxiv: 2604.27548 · v2 · pith:3732IHEHnew · submitted 2026-04-30 · 💻 cs.DS

Smallest suffixient set maintenance in near-real-time

Dominik K\"oppl , Gregory Kucherov This is my paper

Pith reviewed 2026-07-01 08:10 UTC · model grok-4.3

classification 💻 cs.DS
keywords smallest suffixient setonline maintenancesuffix treestring repetitivenessdynamic algorithmsnear-real-time processingWeiner algorithm
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The pith

The smallest suffixient set can be maintained letter-by-letter with polyloglog worst-case time using suffix tree primitives.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a method to update the smallest suffixient set of a growing string in near-real-time. Letters arrive one at a time, and each addition costs only polyloglog time in the worst case. The approach works for both right-to-left and left-to-right addition orders. It relies on dynamic maintenance of a suffix tree to avoid full recomputation. If correct, this lets repetitiveness be tracked efficiently during streaming text processing without restarting from scratch each time.

Core claim

We study how to maintain the smallest suffixient set online in near-real-time, that is with small (in our case, polyloglog) worst-case time on processing each letter. Two frameworks are considered: when the text is given letter-by-letter in either a right-to-left or left-to-right direction. Our central algorithmic tool is Weiner's suffix tree algorithm and associated algorithmic primitives for its efficient implementation.

What carries the argument

Weiner's suffix tree algorithm, which supplies the primitives needed to support polyloglog-time updates to the smallest suffixient set.

If this is right

  • The repetitiveness measure updates correctly without full recomputation after each letter.
  • The same polyloglog bound holds for both left-to-right and right-to-left growth directions.
  • Near-real-time processing becomes feasible for long or streaming strings.
  • The method extends existing suffix tree maintenance to this new measure of repetitiveness.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar dynamic techniques might apply to other string repetitiveness measures beyond the smallest suffixient set.
  • Practical deployment could be tested by measuring observed update times on large real-world text streams.
  • The approach opens the possibility of integrating repetitiveness tracking into online compression or indexing pipelines.

Load-bearing premise

Weiner's suffix tree algorithm and its associated algorithmic primitives can be maintained and implemented efficiently enough to support the claimed polyloglog per-letter update time for the smallest suffixient set in the online letter-by-letter setting.

What would settle it

A concrete sequence of letter additions where the per-letter update time for the smallest suffixient set exceeds polyloglog in the worst case, or where the maintained set differs from the true smallest suffixient set.

read the original abstract

The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to maintain the smallest suffixient set online in near-real-time, that is with small (in our case, polyloglog) worst-case time on processing each letter. Two frameworks are considered: when the text is given letter-by-letter in either a right-to-left or left-to-right direction. Our central algorithmic tool is Weiner's suffix tree algorithm and associated algorithmic primitives for its efficient implementation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript studies online maintenance of the smallest suffixient set (a repetitiveness measure) for a string built letter-by-letter, considering both right-to-left and left-to-right arrival orders. It claims polyloglog worst-case time per update and identifies Weiner's suffix tree construction together with its algorithmic primitives as the central tool.

Significance. If the time bound is rigorously established, the work would supply the first near-real-time dynamic algorithm for this repetitiveness measure, enabling applications in streaming string processing and incremental compression where texts arrive online.

major comments (2)
  1. [Abstract and §1] Abstract and §1: the central polyloglog worst-case per-letter claim is stated without any recurrence, cost analysis, or reference to the specific dynamic primitives (e.g., link-cut trees or succinct representations) needed to convert the classic O(n) Weiner construction into an online structure whose per-update cost remains inside polyloglog.
  2. [§3] §3 (frameworks): the description of how the smallest suffixient set is extracted and maintained from the evolving suffix tree does not exhibit the auxiliary data structures or charging argument that would keep the per-letter overhead inside the stated bound when both the tree and the set must be updated simultaneously.
minor comments (1)
  1. [§2] Notation for the two arrival directions is introduced without a compact tabular comparison of the respective update primitives.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. The points raised concern the level of detail in presenting the time-bound analysis and auxiliary structures. We address each comment below and will revise the manuscript accordingly to strengthen the exposition.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1: the central polyloglog worst-case per-letter claim is stated without any recurrence, cost analysis, or reference to the specific dynamic primitives (e.g., link-cut trees or succinct representations) needed to convert the classic O(n) Weiner construction into an online structure whose per-update cost remains inside polyloglog.

    Authors: The abstract and §1 state the bound at a high level while referencing Weiner's construction and its algorithmic primitives. A detailed recurrence and explicit naming of dynamic structures (such as link-cut trees for path operations) appear in the technical sections that follow the framework. To improve accessibility, we will insert a short summary paragraph in §1 outlining the high-level recurrence and the role of the dynamic primitives. revision: yes

  2. Referee: [§3] §3 (frameworks): the description of how the smallest suffixient set is extracted and maintained from the evolving suffix tree does not exhibit the auxiliary data structures or charging argument that would keep the per-letter overhead inside the stated bound when both the tree and the set must be updated simultaneously.

    Authors: Section 3 presents the extraction and maintenance logic on top of the evolving suffix tree. The auxiliary structures (dynamic trees supporting the required operations) and the charging scheme that amortizes the simultaneous updates are described in the implementation subsections that follow. We agree that making the connection more explicit in the framework description itself would help; we will add a dedicated paragraph and a brief charging sketch to §3. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external Weiner algorithm

full rationale

The paper positions Weiner's suffix tree (1973) and its primitives as the central external algorithmic tool for maintaining the smallest suffixient set with polyloglog per-letter updates. No equations, self-citations, or claims in the abstract reduce the time bound or the set maintenance result to a self-definitional fit, a renamed known result, or a load-bearing self-citation chain. The approach is presented as building on an established, independent algorithm rather than deriving its efficiency from the paper's own inputs. This is the normal case of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract introduces no free parameters, additional axioms, or invented entities beyond standard algorithmic assumptions.

pith-pipeline@v0.9.1-grok · 5628 in / 1004 out tokens · 34616 ms · 2026-07-01T08:10:24.954173+00:00 · methodology

Review history (2 revisions) →

discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Computing Smallest Suffixient Arrays in Sublinear Time

    cs.DS 2026-06 unverdicted novelty 7.0

    Algorithm computes smallest suffixient arrays in sublinear time O((n log σ)/√log n + min(r, r-bar) log^ε n) when alphabet is small and BWT has few runs.

  2. Practical Linear-Time Computation of Smallest Suffixient Sets

    cs.DS 2026-06 unverdicted novelty 7.0

    A linear-time one-pass practical algorithm for building smallest suffixient sets is presented and empirically shown to dominate prior constructions.

Reference graph

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