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An Algorithmic Solution of a Birkhoff Type Problem
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Star Coloring and Acyclic Coloring of Locally Planar Graphs
SIAM Journal on Discrete Mathematics
Mesh Algorithms for Solving Principal Diophantine Equations, Sand-glass Tubes and Tori of Roots
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Rainbow Induced Subgraphs in Proper Vertex Colorings
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Tree Matrices and a Matrix Reduction Algorithm of Belitskii
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Inflation Algorithms for Positive and Principal Edge-bipartite Graphs and Unit Quadratic Forms
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Experiences in Symbolic Computations for Matrix Problems
SYNASC '12 Proceedings of the 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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We study the complexity of Bongartz's algorithm for determining a maximal common direct summand of a pair of modules M, N over k-algebra Λ; in particular, we estimate its pessimistic computational complexity Orm6n2n + m log n, where m = dimkM ≤ n = dimkN and r is a number of common indecomposable direct summands of M and N. We improve the algorithm to another one of complexity Orm4n2n+m log m and we show that it applies to the isomorphism problem having at least an exponential complexity in a direct approach. Moreover, we discuss a performance of both algorithms in practice and show that the “average” complexity is much lower, especially for the improved one which becomes a part of QPA package for GAP computer algebra system.