Edit Profile (opens in new tab) Butkovič, Peter Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1202.15032Butkovič, Peter 181 2010 Max-algebra: The linear algebra of combinatorics? Zbl 1022.15017Butkovič, Peter 82 2003 Generators, extremals and bases of max cones. Zbl 1119.15018Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 42 2007 The equation \(A \otimes x = B \otimes y\) over \((\max,+)\). Zbl 1021.65022Cuninghame-Green, R. A.; Butkovič, P. 36 2003 On visualization scaling, subeigenvectors and Kleene stars in max algebra. Zbl 1180.15027Sergeev, Sergeĭ; Schneider, Hans; Butkovič, Peter 36 2009 Bases in max-algebra. Zbl 1059.15001Cuninghame-Green, R. A.; Butkovič, P. 31 2004 Strong regularity of matrices – a survey of results. Zbl 0804.06017Butkovič, Peter 29 1994 Reducible spectral theory with applications to the robustness of matrices in max-algebra. Zbl 1204.15019Butkovič, P.; Cuninghame-Green, R. A.; Gaubert, S. 26 2010 A strongly polynomial algorithm for solving two-sided linear systems in max-algebra. Zbl 1090.68119Butkovič, Peter; Zimmermann, Karel 21 2006 A condition for the strong regularity of matrices in the minimax algebra. Zbl 0602.90136Butkoviĉ, Peter; Hevery, Ferdinand 21 1985 Recognizing weakly stable matrices. Zbl 1267.15024Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 18 2012 Applications of max algebra to diagonal scaling of matrices. Zbl 1093.15009Butkovic, Peter; Schneider, Hans 17 2005 Introduction to max-linear programming. Zbl 1169.90396Butkovic, P.; Aminu, A. 15 2009 Simple image set of (max,+) linear mappings. Zbl 0976.15013Butkovic, Peter 15 2000 Strong linear independence in bottleneck algebra. Zbl 0629.90093Butkovič, Peter; Cechlárová, Katarína; Szabó, Peter 15 1987 Finding all essential terms of a characteristic maxpolynomial. Zbl 1033.90098Burkard, Rainer E.; Butkovič, Peter 14 2003 Max algebra and the linear assignment problem. Zbl 1160.90630Burkhard, Rainer E.; Butkovič, Peter 13 2003 Minimal \((\max,+)\) realization of convex sequences. Zbl 0921.93006Gaubert, Stéphane; Butkovič, Peter; Cuninghame-Green, Raymond 12 1998 An elimination method for finding all solutions of the system of linear equations over an extremal algebra. Zbl 0545.90101Butkovič, Peter; Hegedűs, Gábor 11 1984 An \(O(n^ 2)\) algorithm for the maximum cycle mean of an \(n\times n\) bivalent matrix. Zbl 0776.05070Butkovic, P.; Cuninghame-Green, R. A. 10 1992 On matrix powers in max-algebra. Zbl 1131.15008Butkovič, P.; Cuninghame-Green, R. A. 8 2007 Calculating essential terms of a characteristic maxpolynomial. Zbl 0982.90042Butkovic, Peter; Murfitt, Louise 8 2000 On tropical supereigenvectors. Zbl 1334.15024Butkovič, Peter 7 2016 Non-linear programs with max-linear constraints: a heuristic approach. Zbl 1248.90075Aminu, A.; Butkovič, P. 7 2012 On integer eigenvectors and subeigenvectors in the max-plus algebra. Zbl 1267.15023Butkovič, Peter; Maccaig, Marie 6 2013 Two cores of a nonnegative matrix. Zbl 1305.15073Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ; Tam, Bit-Shun 5 2013 On the integer max-linear programming problem. Zbl 1303.90063Butkovič, Peter; MacCaig, Marie 5 2014 Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings. Zbl 1255.15031Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 5 2012 On some properties of the image set of a max-linear mapping. Zbl 1179.15004Butkovič, Peter; Tam, Kin Po 5 2009 On the regularity of matrices in min algebra. Zbl 0731.15012Butkovič, P.; Cuninghame-Green, R. A. 5 1991 Sign-nonsingular matrices and matrices with unbalanced determinant in symmetrised semirings. Zbl 0951.15014Gaubert, S.; Butkovic, P. 5 1999 On the job rotation problem. Zbl 1163.90704Butkovič, Peter; Lewis, Seth 4 2007 Regularity of matrices in min-algebra and its time-complexity. Zbl 0820.15003Butkovič, P. 4 1995 Necessary solvability conditions of systems of linear extremal equations. Zbl 0561.90096Butkovič, Peter 3 1985 On special cases of the generalized max-plus eigenproblem. Zbl 1347.15014Butkovič, Peter; Jones, Daniel 3 2016 On the coefficients of the max-algebraic characteristic polynomial and equation. Zbl 1249.90213Butkovič, Peter 3 2003 On the dependence of the maximum cycle mean of a matrix on permutations of the rows and columns. Zbl 0679.15017Butkovič, Peter; Plávka, Ján 3 1989 Finding a bounded mixed-integer solution to a system of dual network inequalities. Zbl 1157.15021Butkovič, P. 3 2008 Discrete-event dynamic systems: The strictly convex case. Zbl 0826.93016Cuninghame-Green, R. A.; Butkovič, P. 3 1995 On properties of solution sets of extremal linear programs. Zbl 0567.90066Butkovič, P. 2 1984 A strongly polynomial method for solving integer max-linear optimization problems in a generic case. Zbl 1323.65067Butkovic, P.; MacCaig, M. 2 2015 Extremal eigenproblem for bivalent matrices. Zbl 0855.65032Cuninghame-Green, R. A.; Butkovič, P. 2 1995 On the linear assignment problem for special matrices. Zbl 1060.93067Butkovič, P.; Cuninghame-Green, R. A. 1 2004 Permuted max-algebraic eigenvector problem is \(NP\)-complete. Zbl 1149.65024Butkovič, P. 1 2008 A note on tropical linear and integer programs. Zbl 1436.90102Butkovič, Peter 1 2019 A note on tropical linear and integer programs. Zbl 1436.90102Butkovič, Peter 1 2019 On tropical supereigenvectors. Zbl 1334.15024Butkovič, Peter 7 2016 On special cases of the generalized max-plus eigenproblem. Zbl 1347.15014Butkovič, Peter; Jones, Daniel 3 2016 A strongly polynomial method for solving integer max-linear optimization problems in a generic case. Zbl 1323.65067Butkovic, P.; MacCaig, M. 2 2015 On the integer max-linear programming problem. Zbl 1303.90063Butkovič, Peter; MacCaig, Marie 5 2014 On integer eigenvectors and subeigenvectors in the max-plus algebra. Zbl 1267.15023Butkovič, Peter; Maccaig, Marie 6 2013 Two cores of a nonnegative matrix. Zbl 1305.15073Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ; Tam, Bit-Shun 5 2013 Recognizing weakly stable matrices. Zbl 1267.15024Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 18 2012 Non-linear programs with max-linear constraints: a heuristic approach. Zbl 1248.90075Aminu, A.; Butkovič, P. 7 2012 Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings. Zbl 1255.15031Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 5 2012 Max-linear systems. Theory and algorithms. Zbl 1202.15032Butkovič, Peter 181 2010 Reducible spectral theory with applications to the robustness of matrices in max-algebra. Zbl 1204.15019Butkovič, P.; Cuninghame-Green, R. A.; Gaubert, S. 26 2010 On visualization scaling, subeigenvectors and Kleene stars in max algebra. Zbl 1180.15027Sergeev, Sergeĭ; Schneider, Hans; Butkovič, Peter 36 2009 Introduction to max-linear programming. Zbl 1169.90396Butkovic, P.; Aminu, A. 15 2009 On some properties of the image set of a max-linear mapping. Zbl 1179.15004Butkovič, Peter; Tam, Kin Po 5 2009 Finding a bounded mixed-integer solution to a system of dual network inequalities. Zbl 1157.15021Butkovič, P. 3 2008 Permuted max-algebraic eigenvector problem is \(NP\)-complete. Zbl 1149.65024Butkovič, P. 1 2008 Generators, extremals and bases of max cones. Zbl 1119.15018Butkovič, Peter; Schneider, Hans; Sergeev, Sergeĭ 42 2007 On matrix powers in max-algebra. Zbl 1131.15008Butkovič, P.; Cuninghame-Green, R. A. 8 2007 On the job rotation problem. Zbl 1163.90704Butkovič, Peter; Lewis, Seth 4 2007 A strongly polynomial algorithm for solving two-sided linear systems in max-algebra. Zbl 1090.68119Butkovič, Peter; Zimmermann, Karel 21 2006 Applications of max algebra to diagonal scaling of matrices. Zbl 1093.15009Butkovic, Peter; Schneider, Hans 17 2005 Bases in max-algebra. Zbl 1059.15001Cuninghame-Green, R. A.; Butkovič, P. 31 2004 On the linear assignment problem for special matrices. Zbl 1060.93067Butkovič, P.; Cuninghame-Green, R. A. 1 2004 Max-algebra: The linear algebra of combinatorics? Zbl 1022.15017Butkovič, Peter 82 2003 The equation \(A \otimes x = B \otimes y\) over \((\max,+)\). Zbl 1021.65022Cuninghame-Green, R. A.; Butkovič, P. 36 2003 Finding all essential terms of a characteristic maxpolynomial. Zbl 1033.90098Burkard, Rainer E.; Butkovič, Peter 14 2003 Max algebra and the linear assignment problem. Zbl 1160.90630Burkhard, Rainer E.; Butkovič, Peter 13 2003 On the coefficients of the max-algebraic characteristic polynomial and equation. Zbl 1249.90213Butkovič, Peter 3 2003 Simple image set of (max,+) linear mappings. Zbl 0976.15013Butkovic, Peter 15 2000 Calculating essential terms of a characteristic maxpolynomial. Zbl 0982.90042Butkovic, Peter; Murfitt, Louise 8 2000 Sign-nonsingular matrices and matrices with unbalanced determinant in symmetrised semirings. Zbl 0951.15014Gaubert, S.; Butkovic, P. 5 1999 Minimal \((\max,+)\) realization of convex sequences. Zbl 0921.93006Gaubert, Stéphane; Butkovič, Peter; Cuninghame-Green, Raymond 12 1998 Regularity of matrices in min-algebra and its time-complexity. Zbl 0820.15003Butkovič, P. 4 1995 Discrete-event dynamic systems: The strictly convex case. Zbl 0826.93016Cuninghame-Green, R. A.; Butkovič, P. 3 1995 Extremal eigenproblem for bivalent matrices. Zbl 0855.65032Cuninghame-Green, R. A.; Butkovič, P. 2 1995 Strong regularity of matrices – a survey of results. Zbl 0804.06017Butkovič, Peter 29 1994 An \(O(n^ 2)\) algorithm for the maximum cycle mean of an \(n\times n\) bivalent matrix. Zbl 0776.05070Butkovic, P.; Cuninghame-Green, R. A. 10 1992 On the regularity of matrices in min algebra. Zbl 0731.15012Butkovič, P.; Cuninghame-Green, R. A. 5 1991 On the dependence of the maximum cycle mean of a matrix on permutations of the rows and columns. Zbl 0679.15017Butkovič, Peter; Plávka, Ján 3 1989 Strong linear independence in bottleneck algebra. Zbl 0629.90093Butkovič, Peter; Cechlárová, Katarína; Szabó, Peter 15 1987 A condition for the strong regularity of matrices in the minimax algebra. Zbl 0602.90136Butkoviĉ, Peter; Hevery, Ferdinand 21 1985 Necessary solvability conditions of systems of linear extremal equations. Zbl 0561.90096Butkovič, Peter 3 1985 An elimination method for finding all solutions of the system of linear equations over an extremal algebra. Zbl 0545.90101Butkovič, Peter; Hegedűs, Gábor 11 1984 On properties of solution sets of extremal linear programs. Zbl 0567.90066Butkovič, P. 2 1984 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year