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Ricardo D. Katz

  1. Tropical linear programming and parametric mean payoff games.

    Ср, 01/19/2011 - 16:01 — SomNambul
    Authors: Sergei Sergeev, Stephane Gaubert, Ricardo D. Katz
    Subjects: Metric Geometry
    Abstract

    Tropical polyhedra have been recently used to represent disjunctive
    invariants in static analysis. To handle larger instances, tropical analogues
    of classical linear programming results need to be developed. This motivation
    leads us to study a general tropical linear programming problem.

  2. Tropical polar cones, hypergraph transversals, and mean payoff games.

    Пнд, 04/19/2010 - 15:01 — SomNambul
    Authors: Stephane Gaubert, Xavier Allamigeon, Ricardo D. Katz
    Subjects: Combinatorics
    Abstract

    We discuss the tropical analogues of several basic questions of convex
    duality. In particular, the polar of a tropical polyhedral cone represents the
    set of linear inequalities that its elements satisfy. We characterize the
    extreme rays of the polar in terms of certain minimal set covers which may be
    thought of as weighted generalizations of minimal transversals in hypergraphs.
    We also give a tropical analogue of Farkas lemma, which allows one to check
    whether a linear inequality is implied by a finite family of linear
    inequalities.

Math-arch

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