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Improved Inapproximability For Submodular Maximization

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Per Austrin

Computational Complexity · Submitted 21 Apr 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739.

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arXiv ID1004.3777 (version 1)
Pith ID2S4DCEFE, Pith's permanent record of this paper and its review
CitationPer Austrin. "Improved Inapproximability For Submodular Maximization." arXiv:1004.3777 (2010). https://pith.science/paper/2S4DCEFE
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,484 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739. These results slightly improve previous results by Feige, Mirrokni and Vondr\'ak (FOCS 2007) who showed that these problems are NP-hard to approximate to within $3/4 + \epsilon \approx 0.750$ and $5/6 + \epsilon \approx 0.833$, respectively.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739. result 0.94 0.96 0.93 asserted 1.00
s1 These results slightly improve previous results by Feige, Mirrokni and Vondr\'ak (FOCS 2007) who showed that these problems are NP-hard to approximate to within $3/4 + \epsilon \approx 0.750$ and $5/6 + \epsilon \approx 0.833$, respectively. background 0.67 0.21 0.07 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • references and citing sentences
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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739. These results slightly improve previous results by Feige, Mirrokni and Vondr\'ak (FOCS 2007) who showed that these problems are NP-hard to approximate to within $3/4 + \epsilon \approx 0.750$ and $5/6 + \epsilon \approx 0.833$, respectively.

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