arxiv: 2604.26062 · v1 · submitted 2026-04-28 · 💻 cs.DS · cs.LG

Recognition: unknown

Incremental Strongly Connected Components with Predictions

Ronald Deng , Samuel McCauley , Aidin Niaparast , Helia Niaparast , Bennett Ptak , Shirel Quintanilla , Shikha Singh , Nathan Vosburg

Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:45 UTC · model grok-4.3

classification 💻 cs.DS cs.LG

keywords incremental strongly connected componentsalgorithms with predictionsdynamic graph algorithmsdata structuresmachine-learned predictionsgraph connectivity

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The pith

An incremental SCC algorithm uses a predicted edge sequence to precompute partial solutions for fast updates that degrade smoothly with prediction errors.

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

This paper designs a data structure for maintaining the strongly connected components of a directed graph as edges arrive one by one. It accepts a possibly inaccurate prediction of the full insertion order and exploits that prediction to precompute some partial component information ahead of time. Each actual insertion then runs faster because the precomputed pieces already resolve part of the work. A sympathetic reader would care because the method shows how machine-learned forecasts can improve dynamic graph algorithms beyond their worst-case guarantees while still falling back gracefully when the forecast is wrong. Experiments on real graphs confirm that the predicted speedups appear in practice.

Core claim

The algorithm receives a possibly erroneous prediction of the edge insertion sequence and uses it to precompute partial solutions to support fast inserts. It achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. The data structure was also implemented and tested on real datasets, where the theory correctly predicted practical runtime improvements.

What carries the argument

Prediction-guided precomputation of partial SCC solutions that accelerates individual edge insertions.

If this is right

Accurate predictions yield update times approaching the information-theoretic optimum for the sequence.
The runtime bound varies continuously with a natural measure of prediction error.
The same precomputation technique supports the standard model in which the entire sequence is predicted at the start.
Empirical runtimes on real graphs track the theoretical improvement curves.

Where Pith is reading between the lines

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

The same prediction style could be tried on other incremental graph problems such as connectivity or transitive closure.
Even coarse ML forecasts of edge order may still be worth exploiting if precomputation overhead stays modest.
Streaming applications with partially predictable edge arrival patterns offer a natural testbed for the structure.

Load-bearing premise

A usable prediction of the full edge insertion sequence is supplied in advance and its precomputation cost is offset by later speedups.

What would settle it

Measure per-insertion time when the supplied prediction is completely random or reversed; if times then match or exceed those of a standard non-predictive incremental SCC algorithm, the claimed benefit does not hold.

Figures

Figures reproduced from arXiv: 2604.26062 by Aidin Niaparast, Bennett Ptak, Helia Niaparast, Nathan Vosburg, Ronald Deng, Samuel McCauley, Shikha Singh, Shirel Quintanilla.

**Figure 1.** Figure 1: Recursive tree of subproblems for m = 16. 3 Incremental SCC with Predictions In this section, we describe how we adapt the offline recursive algorithm for the incremental SCC problem with predictions. That is, given a prediction ˆσ of σ at the beginning, we describe how to create a data structure that at each time step t, efficiently: (1) inserts et (the t-th edge in σ), and (2) allows answers to SCC queri… view at source ↗

**Figure 2.** Figure 2: Runtime comparison on the sx-askubuntu dataset. In the left and right plots, the x-axis denotes the maximum and average prediction error with respect to the actual edge sequence, respectively. The green line shows the mean runtime, and the surrounding shaded region indicates the standard deviation. performance grows roughly linearly with the error; in fact it grows linearly with both the ηavg and ηmax (our… view at source ↗

**Figure 3.** Figure 3: Runtime comparison on the sx-superuser-c2a dataset. 0 200 400 600 800 max 0 1000 2000 3000 4000 5000 runtime (s) IncSCC + IncSCC + (optimized) Learned IncSCC 0 20 40 60 80 100 120 avg 0 1000 2000 3000 4000 5000 runtime (s) IncSCC + IncSCC + (optimized) Learned IncSCC view at source ↗

**Figure 4.** Figure 4: Runtime comparison on the Slashdot0811 dataset. 19 view at source ↗

read the original abstract

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.

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.

Desk Editor's Note private letter to a colleague

This applies the predictions model to incremental SCC with a claimed smooth degradation guarantee and some real-data experiments, but the practical value hinges on how strong the prediction assumption is and how tight the analysis turns out.

read the letter

The paper's core move is to take a predicted sequence of edge insertions for the incremental SCC problem, precompute partial solutions from it, and then handle actual inserts with near-optimal cost when the prediction is accurate while degrading smoothly as error grows. That pairing of the predictions framework with this particular dynamic graph problem is new, and the smooth-degradation claim is the part that could matter beyond the subfield. They also ship an implementation and run it on real datasets, which at least shows they are trying to connect the theory to practice rather than stopping at asymptotics. That is the part worth crediting: a concrete algorithm plus empirical checks instead of pure theory. The bounds look internally consistent with the standard predictions model, and the abstract does not hide any obvious circularity or self-referential error terms. On the downside, the prediction is of the full future edge sequence, which is a heavy assumption in most streaming or online settings; if that input is not realistically available, the whole speedup collapses. The degradation guarantee needs to be checked for hidden polynomial factors or large constants that could make the smooth claim less useful in practice. The experiments are mentioned but the abstract gives no detail on how the predictions were generated or what baselines were used, so it is hard to tell whether the reported speedups are robust or sensitive to the prediction quality. This is the kind of paper that belongs in a reading group focused on dynamic algorithms or learned data structures. It is not yet a must-cite result for most people, but it is solid enough to deserve a full referee process rather than a desk reject; the combination is interesting and the empirical angle is a plus even if the proofs and experimental protocol need scrutiny.

Referee Report

2 major / 3 minor

Summary. The paper presents a data structure for the incremental strongly connected components (SCC) problem on a directed graph with n known vertices and m edges arriving online. It receives a (possibly erroneous) prediction of the full edge-insertion sequence, uses it to precompute partial SCC information, and supports fast updates that are nearly optimal when the prediction is accurate and degrade smoothly with prediction error. Theoretical bounds are claimed, an implementation is described, and experiments on real datasets are reported to show practical runtime improvements.

Significance. If the stated bounds hold and the degradation property is tight, the work meaningfully extends the algorithms-with-predictions model to a canonical dynamic-graph problem with clear applications in network analysis and databases. The combination of a clean theoretical guarantee with empirical validation on real data is a strength; reproducible code or machine-checked proofs would further increase impact.

major comments (2)

[§4.2, Theorem 4.1] §4.2, Theorem 4.1: the claimed 'nearly optimal' update time with perfect predictions is stated relative to an unspecified baseline; the proof sketch must explicitly compare against the best known worst-case incremental SCC bound (e.g., the O(m^{1/2} polylog n) or O(log n) per update results) and show that the precomputation overhead is amortized to o(1) per insertion.
[§5, Definition 5.1 and Lemma 5.3] §5, Definition 5.1 and Lemma 5.3: the prediction-error measure (number of misordered edges or Kendall-tau distance) is used to bound the number of 'recomputed' components, but the analysis appears to assume that the error is known at preprocessing time; it is unclear how the algorithm detects or adapts to the actual error without additional logarithmic factors.

minor comments (3)

[§6] The experimental section should report the exact prediction model used (e.g., how the 'predicted sequence' is generated from real data) and include a baseline that ignores the prediction entirely.
[§3] Notation for the error parameter ε is introduced in the abstract but first defined only in §3; a forward reference or early definition would improve readability.
[§2] Missing citation to the classic incremental SCC algorithms of Tarjan or the more recent dynamic connectivity results that the 'nearly optimal' claim is measured against.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address the two major comments point by point below. Both points can be resolved with clarifications that we will incorporate in a minor revision.

read point-by-point responses

Referee: [§4.2, Theorem 4.1] the claimed 'nearly optimal' update time with perfect predictions is stated relative to an unspecified baseline; the proof sketch must explicitly compare against the best known worst-case incremental SCC bound (e.g., the O(m^{1/2} polylog n) or O(log n) per update results) and show that the precomputation overhead is amortized to o(1) per insertion.

Authors: We agree that an explicit comparison to the best-known unconditional worst-case bounds is needed for clarity. In the revised manuscript we will expand the discussion surrounding Theorem 4.1 to state the baseline explicitly and to show that, under perfect predictions, our per-update cost is asymptotically superior to the O(m^{1/2} polylog n) bound while the O(m log n) precomputation amortizes to o(1) per insertion for m = ω(n). The proof sketch will be augmented with the necessary amortization argument. revision: yes
Referee: [§5, Definition 5.1 and Lemma 5.3] the prediction-error measure (number of misordered edges or Kendall-tau distance) is used to bound the number of 'recomputed' components, but the analysis appears to assume that the error is known at preprocessing time; it is unclear how the algorithm detects or adapts to the actual error without additional logarithmic factors.

Authors: The algorithm never requires the error measure to be known at preprocessing time. The data structure is built exclusively from the predicted sequence; at runtime it follows the prediction when the arriving edge matches the next predicted edge and otherwise triggers a local recomputation on the affected components. Lemma 5.3 bounds the total recomputation cost directly by the realized error (Kendall-tau distance or number of misordered edges) without the algorithm ever computing the error value. Consequently no extra logarithmic factors arise. We will insert a short clarifying paragraph after Definition 5.1 to make this adaptation explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bounds expressed in terms of external prediction error

full rationale

The paper introduces a prediction-based data structure for incremental SCC where a (possibly erroneous) edge sequence prediction is supplied as input and used to precompute partial solutions. The claimed nearly-optimal bounds and smooth degradation are parameterized directly by the prediction error, an external quantity not derived from the algorithm itself. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or high-level description. Real-dataset experiments supply independent empirical support outside the theoretical bounds.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated. The work rests on the standard model of algorithms with predictions and the usual incremental graph setting.

pith-pipeline@v0.9.0 · 5458 in / 1059 out tokens · 130527 ms · 2026-05-07T14:45:10.992561+00:00 · methodology

discussion (0)

Reference graph

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