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arxiv: 2505.21052 · v2 · submitted 2025-05-27 · 💻 cs.IR

A Reduction-Driven Local Search for the Generalized Independent Set Problem

Yiping Liu , Yi Zhou , Zhenxiang Xu , Mingyu Xiao , Jin-Kao Hao This is my paper

Pith reviewed 2026-05-19 13:21 UTC · model grok-4.3

classification 💻 cs.IR
keywords Generalized Independent SetData Reduction RulesLocal Search AlgorithmLarge-Scale GraphsGraph OptimizationCombinatorial Optimization
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The pith

Integrating 14 reduction rules into local search solves the generalized independent set problem on graphs with over 260 million edges.

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

The paper establishes that 14 data reduction rules with optimality guarantees can be efficiently embedded into a local search algorithm for the generalized independent set problem. This problem adds vertex profits and edge penalties to the classic independent set task and arises in applications like forest planning and social network analysis. By using the reductions in preprocessing, solution initialization, and the search process itself, the resulting RLS algorithm finds better solutions than existing methods on most of 278 tested graphs. It also scales to instances far larger than what other solvers can handle.

Core claim

The authors show that a reduction-driven local search algorithm, which incorporates 14 optimality-preserving reduction rules throughout its execution, delivers superior solutions to the generalized independent set problem and remains effective on graphs exceeding 260 million edges, a scale at which all competing methods fail.

What carries the argument

The reduction-driven local search (RLS) that repeatedly applies 14 data reduction rules to shrink the graph while preserving the optimal generalized independent set value.

If this is right

  • The RLS provides practical solutions for large real-world instances in forest harvest planning and competitive facility location.
  • Data reduction is shown to be crucial for handling graphs with hundreds of millions of edges.
  • RLS achieves significantly better solutions than other solvers on the majority of tested graphs.
  • Generalized independent set instances that were previously unsolvable now admit high-quality solutions.

Where Pith is reading between the lines

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

  • If the reduction rules prove robust across domains, they could be generalized to related problems such as the maximum cut or prize-collecting variants.
  • Hybridizing these reductions with other metaheuristics might further improve performance on dynamic or streaming graph data.
  • Success on 260-million-edge graphs suggests the method could support analysis of very large social or biological networks.

Load-bearing premise

The 14 reduction rules remain fast to apply repeatedly inside the local search loop and continue to guarantee optimality for the original instance after reductions.

What would settle it

A graph with more than 260 million edges on which the RLS algorithm either exceeds practical runtime limits or returns a solution value lower than a known lower bound from another method would falsify the scalability and superiority claims.

read the original abstract

The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in fields such as forest harvest planning, competitive facility location, social network analysis, and even machine learning. However, solving the GIS problem in large-scale, real-world networks remains computationally challenging. In this paper, we explore data reduction techniques to address this challenge. We first propose 14 reduction rules that can reduce the input graph with rigorous optimality guarantees. We then present a reduction-driven local search (RLS) algorithm that integrates these reduction rules into the pre-processing, the initial solution generation, and the local search components in a computationally efficient way. The RLS is empirically evaluated on 278 graphs arising from different application scenarios. The results indicates that the RLS is highly competitive -- For most graphs, it achieves significantly superior solutions compared to other known solvers, and it effectively provides solutions for graphs exceeding 260 million edges, a task at which every other known method fails. Analysis also reveals that the data reduction plays a key role in achieving such a competitive performance.

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

3 major / 2 minor

Summary. The paper proposes 14 reduction rules for the Generalized Independent Set (GIS) problem, each claimed to preserve optimality. These rules are integrated into a Reduction-Driven Local Search (RLS) algorithm for preprocessing, initial solution generation, and the local search loop itself. The RLS is evaluated on 278 graphs from diverse applications, with claims of significantly superior solution quality over existing solvers for most instances and the ability to produce solutions for graphs exceeding 260 million edges where other methods fail. Data reduction is highlighted as key to the performance.

Significance. If the optimality guarantees and the efficiency of repeated reductions hold, this would be a meaningful contribution to scalable methods for GIS, a problem arising in forest harvest planning, facility location, social networks, and machine learning. The scale of the experimental evaluation (278 instances, including very large graphs) and the direct embedding of reductions into the search procedure are strengths that could influence heuristic design for other NP-hard graph problems.

major comments (3)
  1. §3: The 14 reduction rules are asserted to come with rigorous optimality guarantees, yet the manuscript contains no proof sketches, derivation details, or references to an appendix containing the proofs. This is load-bearing for the central claim that reductions can be safely applied without compromising solution quality.
  2. §4.2 (algorithm description and pseudocode): The integration of the reduction rules inside the local-search improvement loop lacks any amortized complexity bound, incremental maintenance scheme, or per-rule cost analysis. Without this, it is unclear how the repeated application remains computationally cheap on instances with >260 million edges, directly affecting the scalability claim in the abstract.
  3. §5 (experimental results): The manuscript reports summary statistics and claims of superiority but does not include raw performance tables or per-instance breakdowns in the main text. This makes it difficult to verify the statement that RLS achieves 'significantly superior solutions' for most graphs.
minor comments (2)
  1. The objective function combining vertex profits and edge penalties could be stated more explicitly with a formal mathematical definition early in §2 to aid readability.
  2. Figure captions for the reduction illustrations would benefit from step-by-step annotations linking each panel to the corresponding rule.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for the thoughtful and constructive review. The comments have helped us identify areas where the manuscript can be strengthened. Below, we provide detailed responses to each major comment and outline the revisions we intend to make in the next version of the paper.

read point-by-point responses

  1. Referee: §3: The 14 reduction rules are asserted to come with rigorous optimality guarantees, yet the manuscript contains no proof sketches, derivation details, or references to an appendix containing the proofs. This is load-bearing for the central claim that reductions can be safely applied without compromising solution quality.

    Authors: We acknowledge the importance of providing evidence for the optimality guarantees. In the revised manuscript, we will incorporate concise proof sketches for all 14 reduction rules within Section 3. Full detailed proofs will be added to an appendix, with appropriate cross-references in the main text. This revision will substantiate the central claims regarding safe application of the reductions. revision: yes

  2. Referee: §4.2 (algorithm description and pseudocode): The integration of the reduction rules inside the local-search improvement loop lacks any amortized complexity bound, incremental maintenance scheme, or per-rule cost analysis. Without this, it is unclear how the repeated application remains computationally cheap on instances with >260 million edges, directly affecting the scalability claim in the abstract.

    Authors: We agree that additional analysis is needed to support the efficiency claims. We will revise Section 4.2 to include a discussion of the amortized complexity bounds for the reduction-driven local search. Specifically, we will detail the incremental maintenance scheme employed, which updates only affected parts of the graph after each local search move, and provide per-rule cost estimates. This will clarify how the approach scales to graphs with hundreds of millions of edges. revision: yes

  3. Referee: §5 (experimental results): The manuscript reports summary statistics and claims of superiority but does not include raw performance tables or per-instance breakdowns in the main text. This makes it difficult to verify the statement that RLS achieves 'significantly superior solutions' for most graphs.

    Authors: We understand the need for more detailed experimental data in the main text. In the revision, we will include a new table in Section 5 that provides per-instance breakdowns for a diverse subset of the 278 graphs, demonstrating the superiority on most instances. The complete raw data will be emphasized as available in the supplementary files, with a clear pointer in the text. revision: yes

Circularity Check

0 steps flagged

No circularity: new reduction rules and empirical validation form independent derivation

full rationale

The paper introduces 14 reduction rules with stated optimality guarantees, then embeds them into preprocessing, initialization, and local search within the RLS algorithm. Performance claims rest on direct empirical comparison across 278 instances rather than any quantity defined in terms of the algorithm's own outputs or prior self-citations. No equations reduce by construction to fitted parameters, no uniqueness theorems are imported from the same authors, and no ansatz is smuggled via citation. The derivation chain from rules to competitive solutions on large graphs is externally falsifiable via the reported experiments and does not collapse to self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard graph-theoretic assumptions and local-search meta-heuristics; the new content is the 14 reduction rules whose correctness is asserted but not derived in the visible text.

axioms (1)
  • domain assumption Standard definitions of vertex profits and edge penalties in the GIS formulation.
    Invoked in the problem statement and reduction-rule definitions.

pith-pipeline@v0.9.0 · 5735 in / 1268 out tokens · 43899 ms · 2026-05-19T13:21:51.204260+00:00 · methodology

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