97 citations · 431 across the 34 of their papers we have counts for
42 papers
Solving Linear Equations Over Maxmin- Systems
Muhammad Syifa'ul Mufid, Ebrahim Patel, Sergei Sergeev
Maxmin- dynamical systems were previously introduced as an ``all-in-one package'' that can yield a solely min-plus, a solely max-plus, or a max-min-plus dynamical system by vary…
Signed tropicalization of polar cones
Marianne Akian, Xavier Allamigeon, Stéphane Gaubert +1
We study the tropical analogue of the notion of polar of a cone, working over the semiring of tropical numbers with signs. We characterize the cones which arise as polars of sets o…
An algorithm for finding the scaled basis of the supereigenvector space in max-plus algebra
Hui-li Wang, Sergei Sergeev
We present an algorithm for finding a basis of the supereigenvector space in max-plus algebra. The main ideas of the new algorithm are: finding better generators by exploiting the…
Extremality criteria for the supereigenvector space in max-plus algebra
Sergei Sergeev, Hui-li Wang
We present necessary and sufficient criteria for a max-algebraic supereigenvector, i.e., a solution of the system with $A\in\overline{\mathbb{R}}…
Minimizing maximum lateness in two-stage projects by tropical optimization
Nikolai Krivulin, Serge\uı Sergeev
We are considering a two-stage optimal scheduling problem, which involves two similar projects with the same starting times for workers and the same deadlines for tasks. It is requ…
Extending CSR Decomposition to Tropical Inhomogeneous Matrix Products
Arthur Kennedy-Cochran-Patrick, Sergei Sergeev
This article presents an attempt to extend the CSR decomposition, previously introduced for tropical matrix powers, to tropical inhomogeneous matrix products. The CSR terms for inh…
Tropical pseudolinear and pseudoquadratic optimization as parametric mean-payoff games
Jamie Parsons, Sergei Sergeev, Huili Wang
We apply an approach based on parametric mean-payoff games to develop bisection and Newton schemes for solving problems of tropical pseudolinear and pseudoquadratic optimisation wi…
New bounds on the periodicity transient of the powers of a tropical matrix: using cyclicity and factor rank
Arthur Kennedy-Cochran-Patrick, Glenn Merlet, Thomas Nowak +1
Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for the periodicity threshold of the powers of a tropical matr…
Optimal Assignments with Supervisions
Adi Niv, Marie Maccaig, Sergei Sergeev
In this paper we provide a new graph theoretic proof of the tropical Jacobi identity, recently obtained in [AGN16]. We also develop an application of this theorem to optimal assign…
(K,L)-eigenvectors in max-min algebra
Martin Gavalec, Zuzana Nemcova, Sergei Sergeev
Using the concept of (K,L)-eigenvector, we investigate the structure of the max-min eigenspace associated with a given eigenvalue of a matrix in the max-min algebra (also known as…
A Bound for the Rank-One Transient of Inhomogeneous Matrix Products in Special Case
Arthur Kennedy Cochran Patrick, Sergei Sergeev, Štefan Berežný
We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length…
Tropical implementation of the Analytical Hierarchy Process decision method
Nikolai Krivulin, Sergei Sergeev
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-…
Tropical optimization techniques in multi-criteria decision making with Analytical Hierarchy Process
N. Krivulin, S. Sergeev
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-…
On the Tightness of Bounds for Transients of Weak CSR Expansions and Periodicity Transients of Critical Rows and Columns of Tropical Matrix Powers
Glenn Merlet, Thomas Nowak, Sergei Sergeev
We study the transients of matrices in max-plus algebra. Our approach is based on the weak CSR expansion. Using this expansion, the transient can be expressed by ,…
Reachability of eigenspaces for interval circulant matrices in max-algebra
Jan Plavka, Sergei Sergeev
A nonnegative matrix A is said to be strongly robust if its max-algebraic eigencone is universally reachable, i.e., if the orbit of any initial vector ends up with a max-algebraic…
X-simple image eigencones of tropical matrices
Jan Plavka, Sergei Sergeev
We investigate max-algebraic (tropical) one-sided systems where is an eigenvector and lies in an interval . A matrix is said to have -simple image…
Extremals of the supereigenvector cone in max algebra: a combinatorial description
Sergei Sergeev
We give a combinatorial description of extremal generators of the supereigenvector cone {x: Ax>=x} in max algebra.
Tropical linear algebra with the Lukasiewicz T-norm
Martin Gavalec, Zuzana Nemcova, Sergei Sergeev
The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be deve…
Characterizing matrices with -simple image eigenspace in max-min semiring
Jan Plavka, Sergei Sergeev
A matrix is said to have -simple image eigenspace if any eigenvector belonging to the interval is the unique solution…
The Markov chain tree theorem and the state reduction algorithm in commutative semirings
Buket Benek Gursoy, Steve Kirkland, Oliver Mason +1
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal a…
On sets of eigenvalues of matrices with prescribed row sums and prescribed graph
Gernot Michael Engel, Hans Schneider, Sergei Sergeev
Motivated by a work of Boros, Brualdi, Crama and Hoffman, we consider the sets of (i) possible Perron roots of nonnegative matrices with prescribed row sums and associated graph, a…
Weak CSR expansions and transience bounds in max-plus algebra
Glenn Merlet, Thomas Nowak, Sergei Sergeev
This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expa…
Generalizations of Bounds on the Index of Convergence to Weighted Digraphs
Glenn Merlet, Thomas Nowak, Hans Schneider +1
We study sequences of optimal walks of a growing length, in weighted digraphs, or equivalently, sequences of entries of max-algebraic matrix powers with growing exponents. It is kn…
On the dimension of max-min convex sets
Viorel Nitica, Sergei Sergeev
We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show t…