Is the Gröbner basis ideal for a sparse polynomial description where degrees of variables in monomials are either zero or one?

Current Research outlined in (July 2015 Current Trends on Gröbner Bases — The 50th Anniversary of Gröbner Bases, http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/). I number the outlining below by the factors found on the websites.

Outlining the 2015 Conference Contributed Talks

(1) algebraic geometry community (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/01-ruriko-yoshida.pdf)

(2) applied mathematicians such as factor analysis, Bayesian analysis and inverse problems (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/02-richards.pdf)

(3) applied mathematicians using Monte Carlo but found it hard to use Markov basis or Gröbner basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/03-satoshi-aoki.pdf)

(7) GreenGroebner package in Mathematica with boundary value problems for Mechanical Engineering, Kirchhoff Circular Plates problem, differential equations (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/07-Jane-Lue.pdf)

(8) Hypergeometric polynomials aka Jacobi polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/08-nobuki-takayama.pdf)

(9) GR cells, extensions, extension algebras, affine varities, monomial ideals -- looks algebraically demanding (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/09-alexandru-constantinescu.pdf)

(11) !!!!! GR basis, polytopes, adjacency matrices and graph theory (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/11-ohsugi.pdf)

(12) !!!!! GR basis, toric ideals, polytopes (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/12_akihiro_higashitani.pdf)

(13) !!!!! Neural codes, toric ideals, GRs (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/13_Gross.pdf)

(14) !!!!! Many Toric ideals generated by quadratic binomials posess no quadratic Grobner bases (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/14_akihiro_shikama.pdf)

(16) !!!!!! Polyomino ideals, tiling problems (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/16_ayesha_qureshi.pdf)

(18) !!!!!! Cover ideal of very well covered graph  http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/18-kyouko-kimura.pdf

(20) Ehrhart polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/20-akiyoshi-tsuchiya.pdf)

(24) ??? F-thresholds and GR (hard to see to which area related, http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/24-kazunori-matsuda.pdf)

Outlining the 2015 Conference Invited Talks (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/)

(I) !!!!!! Cocoa Software, GR, multivariate polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/bigatti.pdf)

(II) !!!!! Acyclic digraph, graph theory, covariance matrix, matrix algebra, vanishing ideal, GR basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/drton.pdf)

(III) !!!!! Tropicalisation: Pattern extraction, geometric to combinatorial, objects defined as ideals, GR basis, tropical varieties, Chan's algorithm (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/jensen.pdf)

(IV) !!!!!! Detecting binomality: matrix algebra, easy to undertand <3 (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/kahle.pdf)

(V) Non-commutative algebras (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/levadovskyy.pdf)

(VI) Equivariant GR (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/leykin.pdf)

(VII) Quadratic GR, Matroids, ... (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/michalek.pdf)

(VIII) ...

(IX) !!! Bouquet algebra and Toric ideals -- looks well presented with colours/annotation  (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/petrovic.pdf)

(X) !!!!! "The NBM [1] and LDP [2] algorithms are variants of the Buchberger-M¨oller algorithm for zero-dimensional ideals when the point coordinates are known up to a certain precision." -- Buchberger-M¨oller algorithm, vandermonde matrices, symbolic numeric approach, Newton like method to get f from NBM, Matlab code, algebraic statistics, Mahalanobis distance, -- http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/riccomagno.pdf -- applications contain robotics, image analysis.

(XI) !!!! Algebraic geometry to understand supersymmeric spaces in Physics: many Lagrangians optimizatons in Grobner bases: Mike Stillman, Bjarke Roune, software Macaulay2 "The code works for ideals in polynomial rings over finite prime fields. The result is not stashed in the ideal object. groebnerBasis(I, Strategy=>"MGB") -- or groebnerBasis(I, Strategy=>"F4")" -- open questions and looks intriquing! http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/stillman.pdf

(XII) Tensors: maximal minors form the GR basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/sturmfels.pdf)

(XIII) Algebraic and geometric perspective on exponential families: http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/uhler.pdf

(XIIII) Diffferential equations, wishart distribution .... http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/vidunas.pdf

(H) http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/wang.pdf

(HI) !!!!! Monomial ideal method in tree percolation, reliability of system, probabilities -- applied mathematics: http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/wynn.pdf


where I have bolded ideas looking relevant from Index of /~msj-si-2015/invited_talks_slides.