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Graph Theory versus Minimum Rank for Index Coding

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Karthikeyan Shanmugam, Alexandros G. Dimakis, Michael Langberg

Information Theory · Submitted 17 Feb 2014

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

The authors' main claim The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number.

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arXiv ID1402.3898 (version 1)
Pith IDN3EB45YA, Pith's permanent record of this paper and its review
CitationAlexandros G. Dimakis, Karthikeyan Shanmugam, Michael Langberg. "Graph Theory versus Minimum Rank for Index Coding." arXiv:1402.3898 (2014). https://pith.science/paper/N3EB45YA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,560 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.36 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.98 · mentions code or data availability 0.02.

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

We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number. This is in striking contrast to minrank since prior work has shown that it can outperform the chromatic number by a polynomial factor in some cases. The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. contribution 0.55 0.95 0.27 asserted 1.00
s1 Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number. result 0.99 0.82 0.25 asserted 1.00
s2 This is in striking contrast to minrank since prior work has shown that it can outperform the chromatic number by a polynomial factor in some cases. background 0.43 0.05 0.09 asserted 0.98
s3 The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number. interpretation 0.95 0.50 0.90 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 0.98.

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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 obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number. This is in striking contrast to minrank since prior work has shown that it can outperform the chromatic number by a polynomial factor in some cases. The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number.

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3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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What it cites · 2 sentences without a confident label

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Cites as background 1 paper
  • Second, interference alignment alongside information theoretic approaches have been recently applied for index coding [ref] introducing new interesting techniques for code constructions.

    Critical Graphs in Index Coding · Introduction · 0.85

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