New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

In this note we describe conditions under which, in idempotent functional analysis (see [1–3]), linear operators have integral representations in terms of idempotent integral of V. P. Maslov. We define the notion of nuclear idempotent semimodule and describe idempotent analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck (see, e.g., [4–6]). In [11], for the idempotent sem...

In this paper we consider a particular class of linear systems under the max-plus algebra and derive exponential upper bounds for the tail distribution of each component of the state vector in the case of Markov modulated input sequences. Our results are then applied to tandem queues with innnite buuers, Markov modulated arrivals and deterministic service times.

A complete description of the eigenspace structure for a given n × n Monge matrix in a max-plus algebra is presented. Based on the description, an O(n2) algorithm for computing the eigenspace dimension is formulated, which is faster than the previously known algorithms. © 2007 Elsevier B.V. All rights reserved. MSC: primary 04A72; secondary 05C50;15A33

GPUs are dedicated processors used for complex calculations and simulations and they can be effectively used for tropical algebra computations. Tropical algebra is based on max-plus algebra and minplus algebra. In this paper we proposed and designed a library based on Tropical Algebra which is used to provide standard vector and matrix operations namely Basic Tropical Algebra Subroutines (BTAS)...