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Published May 14, 2023 | Version 1.00
Dataset Open

Dataset of Feasible, Edmonds' and Geographic Bi-vectors and Tri-vectors

  • 1. RUTCOR, Rutgers University
  • 2. University of Primorska, FAMNIT and IAM
  • 1. RUTCOR, Rutgers University
  • 2. University of Primorska, FAMNIT and IAM,

Description

The dataset consists of two sets of files in JSON format. Each file consists of an array of elements and each element is presented by a vector (it can be a bi-vector in the case of the first set or a tri-vector in the latter case). This vector is followed by the Euler characteristic of surface and a set of Edmonds’ realizations, described as a concatenation of two incidence matrices. Such bi-matrix gives rise to the corresponding graph, its dual, as well as one-to-one correspondence between their edges.

The first set consists of 7 files, each containing all possible bi-vectors with all Edmonds’ realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 7).

The bi-vectors are stored in files with the value of ell at the end:

  • edmonds-bi-vector-realization-ell2.json
  • edmonds-bi-vector-realization-ell3.json
  • edmonds-bi-vector-realization-ell4.json
  • edmonds-bi-vector-realization-ell5.json
  • edmonds-bi-vector-realization-ell6.json
  • edmonds-bi-vector-realization-ell7.json

The second set consists of 9 files, each containing all possible tri-vectors with all Edmonds’ realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 8). The last file (for ell 9, contains only one Edmond’s realization per vector (if existing) due to time complexity).

The tri-vectors are stored in files with the ell mentioned at the end:

  • edmonds-tri-vector-realization-ell2.json
  • edmonds-tri-vector-realization-ell3.json
  • edmonds-tri-vector-realization-ell4.json
  • edmonds-tri-vector-realization-ell5.json
  • edmonds-tri-vector-realization-ell6.json
  • edmonds-tri-vector-realization-ell7.json
  • edmonds-tri-vector-realization-ell8.json
  • edmonds-tri-vector-realization-ell9.json

A set of utilities show use cases:

  • Parsing functions with examples implemented in Sage:

edmonds_import.sage

  • Parsing functions with examples implemented in Java:

EdmondsReaderBivector.java

EdmondsReader.java

Files

edmonds_dataset.zip

Files (3.2 MB)

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