Tropical Halfspaces
By Michael Joswig. 2003
59 citations recorded by the source corpus.
. As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring ( R , min , + ) . This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels [9] in a variety of contexts. The key tool to the understanding is a newly defined sign of the tropical determinant, which shares remarkably many properties with the ordinary sign of the determinant of a matrix. The methods are used to obtain an optimal tropical convex hull algorithm in two dimensions.
View Paper: https://www.semanticscholar.org/paper/21cf8cd1e67d746ffb78ca08082b8c5bff8f7353
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Stephane Gaubert
- Marianne Akian
- Peter Butkovic
- Ricardo D. Katz
- Alexander E. Guterman
- Sergeĭ Sergeev
- Hans Schneider
- V. Nitica
Citations in the corpus
- On visualization scaling, subeigenvectors and Kleene stars in max algebra (2008, background): “The interplay between max algebra (essentially equivalent to tropical algebra) and convexity, here explored via visualization, is also important for tropical convexity, see the papers [15,31,32], among many others.”
- Generators, extremals and bases of max cones (2006, background): “ted by) the emerging field of tropical geometry which develops basic concepts of max algebra in a different form and with different terminologyand applies these to finitely generated structures, see [DS],[Jos] and [BYu]. In particular, Proposition 11 can also be seen as a minor extension of [Jos, Propos”
- Max-linear Systems: Theory and Algorithms (2010, methodology): “Our presentation follows the lines of [43] and con rms the results of [69] developed for subspaces of R [ f"g : Some of the results of this section have been proved in [60], [103], [105] and [147].”
- Tropical Cramer Determinants Revisited (2013, background): “Some results of [Plu90, Gau92] concerning systems of linear balances can be interpreted geometrically using the signed variant of tropical hyperplanes, considered by Joswig in [Jos05].”
- On the frontiers of polynomial computations in tropical geometry (2004, methodology): “rithmic problems (such as computing the tropical determinant) which can be efficiently solved using techniques from linear programming, polyhedral computation and combinatorial optimization (see, e.g., [10, 20]). For many tropical problems, their computational complexity has not been clarified yet. In ”
- Best approximation in max-plus semimodules☆ (2010, background): “Note that the sets of this form are exactly the “tropical half-spaces” studied in [15], where the apex of the half-space (6.”
- Minimal half-spaces and external representation of tropical polyhedra (2009, background): “4 of [26]) and disproving Conjecture 14 of [6].”