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Polynomial-time algorithm for determining the graph isomorphism (v.2)

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Anatoly D. Plotnikov

Data Structures and Algorithms · Submitted 27 Apr 2016

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

The authors' main claim This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to $O(n^4)$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1610.05725 (version 2)
Pith IDV2URLCD4, Pith's permanent record of this paper and its review
CitationAnatoly D. Plotnikov. "Polynomial-time algorithm for determining the graph isomorphism (v.2)." arXiv:1610.05725 (2016). https://pith.science/paper/V2URLCD4
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The compiled record

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,818 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, we define the neighborhoods of the vertices. Next, we construct the auxiliary directed graph, spawned by the selected vertex. The vertices of the digraph are positioned by special characteristics --- vectors, which locate each vertex of the digraph relative the found neighborhoods. This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to $O(n^4)$.

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 develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. contribution 0.93 0.94 0.22 asserted 1.00
s1 Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. method 0.98 0.79 0.06 asserted 1.00
s2 For the selected vertex of the undirected graph, we define the neighborhoods of the vertices. method 1.00 0.88 0.02 asserted 0.98
s3 Next, we construct the auxiliary directed graph, spawned by the selected vertex. method 0.99 0.91 0.03 asserted 1.00
s4 The vertices of the digraph are positioned by special characteristics --- vectors, which locate each vertex of the digraph relative the found neighborhoods. method 1.00 0.87 0.04 asserted 1.00
s5 This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to $O(n^4)$. result 0.73 0.93 0.77 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.90.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the corresponding vertex in the other graph. For the selected vertex of the undirected graph, we define the neighborhoods of the vertices. Next, we construct the auxiliary directed graph, spawned by the selected vertex. The vertices of the digraph are positioned by special characteristics --- vectors, which locate each vertex of the digraph relative the found neighborhoods. This enabled to develop the algorithm for determining graph isomorphism, the runing time of which is equal to $O(n^4)$.

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

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