## Butkovič, Peter

Compute Distance To:
 Author ID: butkovic.peter Published as: Butkovič, Peter; Butkovič, P.; Butkovic, Peter; Butkovic, P.; Butkoviĉ, Peter more...less
 Documents Indexed: 51 Publications since 1978, including 1 Book 1 Contribution as Editor Co-Authors: 22 Co-Authors with 35 Joint Publications 632 Co-Co-Authors
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### Co-Authors

 17 single-authored 10 Cuninghame-Green, Raymond A. 7 Schneider, Hans 6 Sergeev, Sergeĭ Mikhaĭlovich 3 Gaubert, Stéphane 3 Maccaig, Marie 2 Aminu, Abdulhadi 2 Burkard, Rainer E. 1 Cechlárová, Katarína 1 Guterman, Alexander Èmilevich 1 Hegedűs, Gábor 1 Hevery, Ferdinand 1 Jones, Daniel C. 1 Lewis, Seth 1 Loiseau, Jean Jacques 1 McEneaney, William “Mac” M. 1 Murfitt, Louise 1 Plavka, Ján 1 Szabo, Peter 1 Tam, Bit-Shun 1 Tam, Kin Po 1 Wagneur, Edouard 1 Zimmermann, Karel
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### Serials

 14 Linear Algebra and its Applications 11 Discrete Applied Mathematics 3 IMA Journal of Management Mathematics 2 Journal of Optimization Theory and Applications 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Matrix Analysis and Applications 2 ELA. The Electronic Journal of Linear Algebra 1 Linear and Multilinear Algebra 1 Kybernetika 1 Theoretical Computer Science 1 Operations Research Letters 1 Optimization 1 Annals of Operations Research 1 Mathematical Programming. Series A. Series B 1 CEJOR. Central European Journal of Operations Research 1 Discrete Optimization 1 Springer Monographs in Mathematics
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### Fields

 37 Linear and multilinear algebra; matrix theory (15-XX) 26 Operations research, mathematical programming (90-XX) 12 Numerical analysis (65-XX) 9 Combinatorics (05-XX) 7 Computer science (68-XX) 5 Systems theory; control (93-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Convex and discrete geometry (52-XX)

### Citations contained in zbMATH Open

45 Publications have been cited 746 times in 387 Documents Cited by Year
Max-linear systems. Theory and algorithms. Zbl 1202.15032
Butkovič, Peter
2010
Max-algebra: The linear algebra of combinatorics? Zbl 1022.15017
Butkovič, Peter
2003
Generators, extremals and bases of max cones. Zbl 1119.15018
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2007
The equation $$A \otimes x = B \otimes y$$ over $$(\max,+)$$. Zbl 1021.65022
Cuninghame-Green, R. A.; Butkovič, P.
2003
On visualization scaling, subeigenvectors and Kleene stars in max algebra. Zbl 1180.15027
Sergeev, Sergeĭ; Schneider, Hans; Butkovič, Peter
2009
Bases in max-algebra. Zbl 1059.15001
Cuninghame-Green, R. A.; Butkovič, P.
2004
Strong regularity of matrices – a survey of results. Zbl 0804.06017
Butkovič, Peter
1994
Reducible spectral theory with applications to the robustness of matrices in max-algebra. Zbl 1204.15019
Butkovič, P.; Cuninghame-Green, R. A.; Gaubert, S.
2010
A strongly polynomial algorithm for solving two-sided linear systems in max-algebra. Zbl 1090.68119
Butkovič, Peter; Zimmermann, Karel
2006
A condition for the strong regularity of matrices in the minimax algebra. Zbl 0602.90136
Butkoviĉ, Peter; Hevery, Ferdinand
1985
Recognizing weakly stable matrices. Zbl 1267.15024
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2012
Applications of max algebra to diagonal scaling of matrices. Zbl 1093.15009
Butkovic, Peter; Schneider, Hans
2005
Introduction to max-linear programming. Zbl 1169.90396
Butkovic, P.; Aminu, A.
2009
Simple image set of (max,+) linear mappings. Zbl 0976.15013
Butkovic, Peter
2000
Strong linear independence in bottleneck algebra. Zbl 0629.90093
Butkovič, Peter; Cechlárová, Katarína; Szabó, Peter
1987
Finding all essential terms of a characteristic maxpolynomial. Zbl 1033.90098
Burkard, Rainer E.; Butkovič, Peter
2003
Max algebra and the linear assignment problem. Zbl 1160.90630
Burkhard, Rainer E.; Butkovič, Peter
2003
Minimal $$(\max,+)$$ realization of convex sequences. Zbl 0921.93006
Gaubert, Stéphane; Butkovič, Peter; Cuninghame-Green, Raymond
1998
An elimination method for finding all solutions of the system of linear equations over an extremal algebra. Zbl 0545.90101
Butkovič, Peter; Hegedűs, Gábor
1984
An $$O(n^ 2)$$ algorithm for the maximum cycle mean of an $$n\times n$$ bivalent matrix. Zbl 0776.05070
Butkovic, P.; Cuninghame-Green, R. A.
1992
On matrix powers in max-algebra. Zbl 1131.15008
Butkovič, P.; Cuninghame-Green, R. A.
2007
Calculating essential terms of a characteristic maxpolynomial. Zbl 0982.90042
Butkovic, Peter; Murfitt, Louise
2000
On tropical supereigenvectors. Zbl 1334.15024
Butkovič, Peter
2016
Non-linear programs with max-linear constraints: a heuristic approach. Zbl 1248.90075
Aminu, A.; Butkovič, P.
2012
On integer eigenvectors and subeigenvectors in the max-plus algebra. Zbl 1267.15023
Butkovič, Peter; Maccaig, Marie
2013
Two cores of a nonnegative matrix. Zbl 1305.15073
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ; Tam, Bit-Shun
2013
On the integer max-linear programming problem. Zbl 1303.90063
Butkovič, Peter; MacCaig, Marie
2014
Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings. Zbl 1255.15031
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2012
On some properties of the image set of a max-linear mapping. Zbl 1179.15004
Butkovič, Peter; Tam, Kin Po
2009
On the regularity of matrices in min algebra. Zbl 0731.15012
Butkovič, P.; Cuninghame-Green, R. A.
1991
Sign-nonsingular matrices and matrices with unbalanced determinant in symmetrised semirings. Zbl 0951.15014
Gaubert, S.; Butkovic, P.
1999
On the job rotation problem. Zbl 1163.90704
Butkovič, Peter; Lewis, Seth
2007
Regularity of matrices in min-algebra and its time-complexity. Zbl 0820.15003
Butkovič, P.
1995
Necessary solvability conditions of systems of linear extremal equations. Zbl 0561.90096
Butkovič, Peter
1985
On special cases of the generalized max-plus eigenproblem. Zbl 1347.15014
Butkovič, Peter; Jones, Daniel
2016
On the coefficients of the max-algebraic characteristic polynomial and equation. Zbl 1249.90213
Butkovič, Peter
2003
On the dependence of the maximum cycle mean of a matrix on permutations of the rows and columns. Zbl 0679.15017
Butkovič, Peter; Plávka, Ján
1989
Finding a bounded mixed-integer solution to a system of dual network inequalities. Zbl 1157.15021
Butkovič, P.
2008
Discrete-event dynamic systems: The strictly convex case. Zbl 0826.93016
Cuninghame-Green, R. A.; Butkovič, P.
1995
On properties of solution sets of extremal linear programs. Zbl 0567.90066
Butkovič, P.
1984
A strongly polynomial method for solving integer max-linear optimization problems in a generic case. Zbl 1323.65067
Butkovic, P.; MacCaig, M.
2015
Extremal eigenproblem for bivalent matrices. Zbl 0855.65032
Cuninghame-Green, R. A.; Butkovič, P.
1995
On the linear assignment problem for special matrices. Zbl 1060.93067
Butkovič, P.; Cuninghame-Green, R. A.
2004
Permuted max-algebraic eigenvector problem is $$NP$$-complete. Zbl 1149.65024
Butkovič, P.
2008
A note on tropical linear and integer programs. Zbl 1436.90102
Butkovič, Peter
2019
A note on tropical linear and integer programs. Zbl 1436.90102
Butkovič, Peter
2019
On tropical supereigenvectors. Zbl 1334.15024
Butkovič, Peter
2016
On special cases of the generalized max-plus eigenproblem. Zbl 1347.15014
Butkovič, Peter; Jones, Daniel
2016
A strongly polynomial method for solving integer max-linear optimization problems in a generic case. Zbl 1323.65067
Butkovic, P.; MacCaig, M.
2015
On the integer max-linear programming problem. Zbl 1303.90063
Butkovič, Peter; MacCaig, Marie
2014
On integer eigenvectors and subeigenvectors in the max-plus algebra. Zbl 1267.15023
Butkovič, Peter; Maccaig, Marie
2013
Two cores of a nonnegative matrix. Zbl 1305.15073
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ; Tam, Bit-Shun
2013
Recognizing weakly stable matrices. Zbl 1267.15024
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2012
Non-linear programs with max-linear constraints: a heuristic approach. Zbl 1248.90075
Aminu, A.; Butkovič, P.
2012
Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings. Zbl 1255.15031
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2012
Max-linear systems. Theory and algorithms. Zbl 1202.15032
Butkovič, Peter
2010
Reducible spectral theory with applications to the robustness of matrices in max-algebra. Zbl 1204.15019
Butkovič, P.; Cuninghame-Green, R. A.; Gaubert, S.
2010
On visualization scaling, subeigenvectors and Kleene stars in max algebra. Zbl 1180.15027
Sergeev, Sergeĭ; Schneider, Hans; Butkovič, Peter
2009
Introduction to max-linear programming. Zbl 1169.90396
Butkovic, P.; Aminu, A.
2009
On some properties of the image set of a max-linear mapping. Zbl 1179.15004
Butkovič, Peter; Tam, Kin Po
2009
Finding a bounded mixed-integer solution to a system of dual network inequalities. Zbl 1157.15021
Butkovič, P.
2008
Permuted max-algebraic eigenvector problem is $$NP$$-complete. Zbl 1149.65024
Butkovič, P.
2008
Generators, extremals and bases of max cones. Zbl 1119.15018
Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ
2007
On matrix powers in max-algebra. Zbl 1131.15008
Butkovič, P.; Cuninghame-Green, R. A.
2007
On the job rotation problem. Zbl 1163.90704
Butkovič, Peter; Lewis, Seth
2007
A strongly polynomial algorithm for solving two-sided linear systems in max-algebra. Zbl 1090.68119
Butkovič, Peter; Zimmermann, Karel
2006
Applications of max algebra to diagonal scaling of matrices. Zbl 1093.15009
Butkovic, Peter; Schneider, Hans
2005
Bases in max-algebra. Zbl 1059.15001
Cuninghame-Green, R. A.; Butkovič, P.
2004
On the linear assignment problem for special matrices. Zbl 1060.93067
Butkovič, P.; Cuninghame-Green, R. A.
2004
Max-algebra: The linear algebra of combinatorics? Zbl 1022.15017
Butkovič, Peter
2003
The equation $$A \otimes x = B \otimes y$$ over $$(\max,+)$$. Zbl 1021.65022
Cuninghame-Green, R. A.; Butkovič, P.
2003
Finding all essential terms of a characteristic maxpolynomial. Zbl 1033.90098
Burkard, Rainer E.; Butkovič, Peter
2003
Max algebra and the linear assignment problem. Zbl 1160.90630
Burkhard, Rainer E.; Butkovič, Peter
2003
On the coefficients of the max-algebraic characteristic polynomial and equation. Zbl 1249.90213
Butkovič, Peter
2003
Simple image set of (max,+) linear mappings. Zbl 0976.15013
Butkovic, Peter
2000
Calculating essential terms of a characteristic maxpolynomial. Zbl 0982.90042
Butkovic, Peter; Murfitt, Louise
2000
Sign-nonsingular matrices and matrices with unbalanced determinant in symmetrised semirings. Zbl 0951.15014
Gaubert, S.; Butkovic, P.
1999
Minimal $$(\max,+)$$ realization of convex sequences. Zbl 0921.93006
Gaubert, Stéphane; Butkovič, Peter; Cuninghame-Green, Raymond
1998
Regularity of matrices in min-algebra and its time-complexity. Zbl 0820.15003
Butkovič, P.
1995
Discrete-event dynamic systems: The strictly convex case. Zbl 0826.93016
Cuninghame-Green, R. A.; Butkovič, P.
1995
Extremal eigenproblem for bivalent matrices. Zbl 0855.65032
Cuninghame-Green, R. A.; Butkovič, P.
1995
Strong regularity of matrices – a survey of results. Zbl 0804.06017
Butkovič, Peter
1994
An $$O(n^ 2)$$ algorithm for the maximum cycle mean of an $$n\times n$$ bivalent matrix. Zbl 0776.05070
Butkovic, P.; Cuninghame-Green, R. A.
1992
On the regularity of matrices in min algebra. Zbl 0731.15012
Butkovič, P.; Cuninghame-Green, R. A.
1991
On the dependence of the maximum cycle mean of a matrix on permutations of the rows and columns. Zbl 0679.15017
Butkovič, Peter; Plávka, Ján
1989
Strong linear independence in bottleneck algebra. Zbl 0629.90093
Butkovič, Peter; Cechlárová, Katarína; Szabó, Peter
1987
A condition for the strong regularity of matrices in the minimax algebra. Zbl 0602.90136
Butkoviĉ, Peter; Hevery, Ferdinand
1985
Necessary solvability conditions of systems of linear extremal equations. Zbl 0561.90096
Butkovič, Peter
1985
An elimination method for finding all solutions of the system of linear equations over an extremal algebra. Zbl 0545.90101
Butkovič, Peter; Hegedűs, Gábor
1984
On properties of solution sets of extremal linear programs. Zbl 0567.90066
Butkovič, P.
1984
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### Cited by 355 Authors

 32 Gaubert, Stéphane 28 Butkovič, Peter 23 Plavka, Ján 17 Krivulin, Nikolai K. 16 Wang, Xueping 15 Sergeev, Sergeĭ Mikhaĭlovich 14 Gavalec, Martin 12 Izhakian, Zur 11 Katz, Ricardo David 11 Peperko, Aljoša 10 Allamigeon, Xavier 10 Myšková, Helena 9 Akian, Marianne 9 Cechlárová, Katarína 9 Johnson, Marianne 8 de la Puente, Maria Jesus 8 Kambites, Mark 8 Schneider, Hans 8 Shu, Qianyu 8 Zimmermann, Karel 7 Hardouin, Laurent 7 Joswig, Michael 7 Maccaig, Marie 7 Tao, Yuegang 7 Tran, Ngoc Mai 7 Wang, Huili 6 Grigor’ev, Dmitriĭ Yur’evich 6 Maia, Carlos Andrey 6 Merlet, Glenn 6 Niv, Adi 6 Rowen, Louis Halle 5 Ćirić, Miroslav D. 5 Maragos, Petros 5 Shitov, Yaroslav Nikolaevich 5 Szabo, Peter 5 Tavakolipour, Hanieh 4 Cuninghame-Green, Raymond A. 4 De Schutter, Bart 4 Guterman, Alexander Èmilevich 4 Ignjatović, Jelena 4 Loho, Georg 4 Mason, Oliver 4 Niţică, Viorel 4 Wang, Cailu 3 Benchimol, Pascal 3 Blondel, Vincent D. 3 Fiedler, Miroslav 3 Gonçalves, Vinicius Mariano 3 Gursoy, Buket Benek 3 Hashemi, Behnam 3 Jones, Daniel C. 3 Mairesse, Jean 3 Majdzik, Paweł 3 Mohindru, Preeti 3 Müller, Vladimír 3 Nishida, Yuki 3 Nowak, Thomas 3 Peláez-Moreno, Carmen 3 Tan, Yijia 3 Tsiamis, Anastasios 3 Valverde-Albacete, Francisco José 3 van den Boom, Ton J. J. 3 Wagneur, Edouard 3 Watanabe, Sennosuke 3 Zhao, Shan 2 Aminu, Abdulhadi 2 Amiraslani, Amirhossein 2 Bapat, Ravindra Bhalchandra 2 Bezem, Marc 2 Bocewicz, Grzegorz 2 Burkard, Rainer E. 2 Castella, Dominique 2 Cottenceau, Bertrand 2 Fahrenberg, Uli 2 Fang, Shu-Cherng 2 Gad, Mahmoud 2 Ghalandarzadeh, Shaban 2 Hall, Frank J. 2 Hong, Hoon 2 Jamshidvand, Sedighe 2 Klüppelberg, Claudia 2 Komenda, Jan 2 Kubo, Susumu 2 Lahaye, Sébastien 2 Le Corronc, Euriell 2 Li, Pingke 2 Litvinov, Grigory Lazarevich 2 Liu, Guoping 2 Lu, Qi 2 Luo, Yan Feng 2 Morrison, Ralph 2 Nasrollahi Shirazi, Mahsa 2 Němcová, Zuzana 2 Nieuwenhuis, Robert 2 Olia, Fateme 2 Pereira, Rajesh 2 Plotnikov, P. V. 2 Podol’skiĭ, Vladimir Vladimirovich 2 Ponce, Daniela 2 Portier, Natacha ...and 255 more Authors
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### Cited in 101 Serials

 112 Linear Algebra and its Applications 24 Discrete Applied Mathematics 17 Fuzzy Sets and Systems 15 Linear and Multilinear Algebra 11 Kybernetika 10 Discrete Event Dynamic Systems 8 Communications in Algebra 8 Information Sciences 7 Journal of Algebra 7 Vestnik St. Petersburg University. Mathematics 6 Semigroup Forum 6 Discrete & Computational Geometry 5 Theoretical Computer Science 5 Optimization 5 International Journal of Algebra and Computation 4 Automatica 4 Systems & Control Letters 4 Journal of Symbolic Computation 4 Journal of Mathematical Sciences (New York) 3 Advances in Mathematics 3 Journal of Pure and Applied Algebra 3 SIAM Journal on Discrete Mathematics 3 MCSS. Mathematics of Control, Signals, and Systems 3 Annals of Operations Research 2 Discrete Mathematics 2 Journal of Combinatorial Theory. Series A 2 Journal of Optimization Theory and Applications 2 Operations Research Letters 2 Information and Computation 2 SIAM Journal on Matrix Analysis and Applications 2 SIAM Review 2 The Electronic Journal of Combinatorics 2 Discrete and Continuous Dynamical Systems 2 Vietnam Journal of Mathematics 2 Soft Computing 2 Journal of Combinatorial Optimization 2 International Journal of Applied Mathematics and Computer Science 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Fuzzy Optimization and Decision Making 2 Computational Management Science 2 Discrete Optimization 2 Special Matrices 2 Journal of Logical and Algebraic Methods in Programming 2 SIAM Journal on Applied Algebra and Geometry 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 International Journal of Control 1 International Journal of General Systems 1 Information Processing Letters 1 Journal of Mathematical Analysis and Applications 1 Bulletin of Mathematical Biology 1 Algebra Universalis 1 Applied Mathematics and Computation 1 Journal of Computer and System Sciences 1 Mathematics of Operations Research 1 Mathematische Zeitschrift 1 Networks 1 Proceedings of the American Mathematical Society 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Acta Mathematica Hungarica 1 Algorithmica 1 Formal Aspects of Computing 1 The Annals of Applied Probability 1 Discrete Mathematics and Applications 1 Journal of Global Optimization 1 Automation and Remote Control 1 Communications in Statistics. Theory and Methods 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Mathematical Imaging and Vision 1 Computational Complexity 1 Journal of Algebraic Combinatorics 1 Applied Mathematics. Series B (English Edition) 1 St. Petersburg Mathematical Journal 1 Filomat 1 Séminaire Lotharingien de Combinatoire 1 Doklady Mathematics 1 Positivity 1 Journal of Inequalities and Applications 1 Data Mining and Knowledge Discovery 1 Discrete Dynamics in Nature and Society 1 Journal of Discrete Mathematical Sciences & Cryptography 1 Acta Mathematica Sinica. English Series 1 Lobachevskii Journal of Mathematics 1 The Journal of Logic and Algebraic Programming 1 OR Spectrum 1 SIAM Journal on Applied Dynamical Systems 1 Journal of Algebra and its Applications 1 Journal of Mathematical Cryptology 1 Journal of Physics A: Mathematical and Theoretical 1 Electronic Journal of Statistics 1 Asian-European Journal of Mathematics 1 Afrika Matematika 1 S$$\vec{\text{e}}$$MA Journal 1 Journal of Theoretical Biology 1 Mathematical Sciences 1 Journal of Function Spaces 1 Research in the Mathematical Sciences 1 International Journal of Systems Science. Principles and Applications of Systems and Integration ...and 1 more Serials
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### Cited in 34 Fields

 258 Linear and multilinear algebra; matrix theory (15-XX) 83 Operations research, mathematical programming (90-XX) 69 Algebraic geometry (14-XX) 62 Associative rings and algebras (16-XX) 54 Numerical analysis (65-XX) 49 Computer science (68-XX) 48 Combinatorics (05-XX) 37 Systems theory; control (93-XX) 33 Convex and discrete geometry (52-XX) 22 Order, lattices, ordered algebraic structures (06-XX) 21 Group theory and generalizations (20-XX) 15 Field theory and polynomials (12-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Mathematical logic and foundations (03-XX) 10 Operator theory (47-XX) 8 General algebraic systems (08-XX) 8 Information and communication theory, circuits (94-XX) 7 Probability theory and stochastic processes (60-XX) 5 Number theory (11-XX) 5 Commutative algebra (13-XX) 5 Statistics (62-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Functional analysis (46-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Biology and other natural sciences (92-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Statistical mechanics, structure of matter (82-XX)