Perron-Frobenius Theory and Max-Algebraic Combinatorics of Nonnegative Matrices

Research output

Research output per year 2012 2014 2015 2019

• 19 Article

Research output per year

Research output per year

Search results

• 2019

  A note on tropical linear and integer programs

  Butkovic, P., Mar 2019, In: Journal of Optimization Theory and Applications. 180, 3, p. 1011-1026 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Integer Program 100%
  • Linear Program 85%
  • Duality 79%
  • Objective Function 68%
  • Linear programming 67%
  1 Citation (Scopus)

  153 Downloads (Pure)
• 2018

  On integer images of max-plus linear mappings

  Butkovic, P., 20 Apr 2018, In: Discrete Applied Mathematics. 239, p. 62-74

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Polynomial Solutions 100%
  • Integer 65%
  • Polynomials 64%
  • Max-plus Algebra 61%
  • Job Scheduling 57%
  1 Citation (Scopus)

  141 Downloads (Pure)

• On two-sided Max-Linear equations

  Jones, D., 30 Jun 2018, (E-pub ahead of print) In: Discrete Applied Mathematics.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Linear equations 100%
  • Linear equation 72%
  • Polynomials 70%
  • Linear systems 55%
  • Nontrivial Solution 49%
  2 Citations (Scopus)

  206 Downloads (Pure)
• 2016

  On special cases of the generalized max-plus eigenproblem

  Butkovic, P. & Jones, D., 4 Aug 2016, (E-pub ahead of print) In: S I A M Journal on Matrix Analysis and Applications. 37, 3, p. 1002–1021 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Eigenproblem 100%
  • Generalized Eigenproblem 42%
  • Max-plus Algebra 40%
  • Generalized Eigenvalue 36%
  • Saddlepoint 27%
  5 Citations (Scopus)

  244 Downloads (Pure)

• On tropical supereigenvectors

  Butkovic, P., Jun 2016, In: Linear Algebra and its Applications. 498, p. 574–591

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Eigenvector 100%
  • Max-plus Algebra 80%
  • Nontrivial Solution 54%
  • Subspace 38%
  • Characterization 28%
  8 Citations (Scopus)

  192 Downloads (Pure)
• 2015

  A strongly polynomial method for solving integer max-linear optimization problems in a generic case

  Butkovic, P. & Maccaig, M., 2015, In: Journal of Optimization Theory and Applications. 165, 3, p. 941-963 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Polynomial Methods 100%
  • Linear Optimization 97%
  • Integer 79%
  • Polynomials 78%
  • Optimization Problem 73%
  1 Citation (Scopus)

  114 Downloads (Pure)

• Extremals of the supereigenvector cone in max algebra : a combinatorial description

  Sergeev, S., 15 Aug 2015, In: Linear Algebra and its Applications. 479, p. 106-117

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Max-algebra 100%
  • Cone 53%
  • Generator 49%
  7 Citations (Scopus)

  200 Downloads (Pure)

• On the dimension of max–min convex sets

  Nitica, V. & Sergeev, S., 15 Jul 2015, In: Fuzzy Sets and Systems. 271, p. 88-101

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Algebra 100%
  • Convex Sets 87%
  • Linear systems 86%
  • Rank of a matrix 66%
  • Strong Regularity 66%
  1 Citation (Scopus)

  153 Downloads (Pure)

• The Markov Chain Tree Theorem in commutative semirings and the State Reduction Algorithm in commutative semifields

  Benek Gursoy, B., Kirkland, S., Mason, O. & Sergeev, S., 1 Mar 2015, In: Linear Algebra and its Applications. 468, p. 184-196

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Semifield 100%
  • Semiring 82%
  • Markov chain 62%
  • Stochastic Matrix 30%
  • Theorem 30%
  1 Citation (Scopus)

  178 Downloads (Pure)

• Tropical linear algebra with the Łukasiewicz T-norm

  Gavalec, M., Němcová, Z. & Sergeev, S., 1 Oct 2015, In: Fuzzy Sets and Systems. 276, p. 131-148

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Linear algebra 100%
  • T-norm 87%
  • Semiring 86%
  • Eigenproblem 32%
  • Equivalence 18%
  8 Citations (Scopus)

  191 Downloads (Pure)
• 2014

  Characterization of tropical hemispaces by (P,R)-decompositions

  Katz, R. D., Nitica, V. & Sergeev, S., 1 Jan 2014, In: Linear Algebra and its Applications. 440, p. 131-163

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Convex Sets 100%
  • Decompose 70%
  • Characterization 57%
  • Semifield 24%
  • Extreme Points 19%
  2 Citations (Scopus)

  136 Downloads (Pure)

• Generalizations of bounds on the index of convergence to weighted digraphs

  Merlet, G., Nowak, T., Schneider, H. & Sergeev, S., 11 Dec 2014, In: Discrete Applied Mathematics. 178, p. 121-134

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Digraph 100%
  • Walk 54%
  • Generalization 54%
  • Periodicity 53%
  • Exponent 21%
  8 Citations (Scopus)

  907 Downloads (Pure)

• On sets of eigenvalues of matrices with prescribed row sums and prescribed graph

  Engel, G. M., Schneider, H. & Sergeev, S., 15 Aug 2014, In: Linear Algebra and its Applications. 455, p. 187-209

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Perron Root 100%
  • Eigenvalue 62%
  • Nonnegative Matrices 54%
  • Graph in graph theory 45%
  • Modulus 28%
  5 Citations (Scopus)

  155 Downloads (Pure)

• On the integer max-linear programming problem

  Butkovic, P. & MacCaig, M., 10 Jan 2014, In: Discrete Applied Mathematics. 162, p. 128–141

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Linear programming 100%
  • Linear Program 83%
  • Integer 56%
  • Linear systems 49%
  • Interactive Systems 42%
  9 Citations (Scopus)

  177 Downloads (Pure)

• Weak CSR expansions and transience bounds in max-plus algebra

  Merlet, G., Nowak, T. & Sergeev, S., 15 Nov 2014, In: Linear Algebra and its Applications. 461, p. 163-199

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Max-plus Algebra 100%
  • Transience 90%
  • Digraph 21%
  • Cycle 15%
  • Replacement 11%
  7 Citations (Scopus)

  179 Downloads (Pure)
• 2013

  On integer eigenvectors and subeigenvectors in the max-plus algebra

  Butkovic, P. & MacCaig, M., 15 Apr 2013, In: Linear Algebra and its Applications. 438, p. 3408–3424

  Research output: Contribution to journal › Article › peer-review

  • Max-plus Algebra 100%
  • Eigenvector 62%
  • Integer 35%
  • Polynomial time 21%
  • Column space 20%
  7 Citations (Scopus)

  8 Downloads (Pure)

• Two cores of a nonnegative matrix

  Butkovic, P., Schneider, H., Sergeev, S. & Tam, B-S., 1 Oct 2013, In: Linear Algebra and its Applications. 439, 7, p. 1929–1954

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Max-algebra 100%
  • Nonnegative Matrices 98%
  • Non-negative 61%
  • Linear algebra 43%
  • Minkowski Sum 30%
  4 Citations (Scopus)

  343 Downloads (Pure)
• 2012

  Recognising weakly stable matrices

  Butkovic, P., Schneider, H. & Sergeev, S., 2012, In: SIAM Journal on Control and Optimisation. 50, 5, p. 3029-3051 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Eigenvector 100%
  • Eigenvalues and eigenfunctions 95%
  • Orbit 62%
  • Orbits 59%
  • Reachability 58%
  22 Citations (Scopus)

  221 Downloads (Pure)

• Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings

  Butkovic, P., Schneider, H. & Sergeev, S., 6 Feb 2012, In: Linear and Multilinear Algebra. 60, 10, p. 1191-1210 20 p.

  Research output: Contribution to journal › Article › peer-review

  • Max-algebra 100%
  • Z-matrix 98%
  • Semiring 73%
  • Matrix Equation 65%
  • Linear algebra 64%
  9 Citations (Scopus)

  3 Downloads (Pure)