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626 results on '"Berghammer, Rudolf"'

14. A General Method for Representing Sets of Relations by Vectors

Author

Berghammer, Rudolf, Winter, Michael, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Glück, Roland, editor, Santocanale, Luigi, editor, and Winter, Michael, editor

Published
2023
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15. Algorithmic Counting of Zero-Dimensional Finite Topological Spaces With Respect to the Covering Dimension

Author

Berghammer, Rudolf, Börm, Steffen, and Winter, Michael

Subjects
Computer Science - Discrete Mathematics
Abstract

Taking the covering dimension dim as notion for the dimension of a topological space, we first specify thenumber zdim_{T_0}(n) of zero-dimensional T_0-spaces on {1,...,n}$ and the number zdim(n) of zero-dimensional arbitrary topological spaces on {1,\ldots,n} by means oftwo mappings po and P that yieldthe number po(n) of partial orders on {1,...,n} and the set P(n) of partitions of {1,...,n}, respectively. Algorithms for both mappings exist. Assuming one for po to be at hand, we use our specification of zdim_{T_0}(n) and modify one for P in such a way that it computes zdim_{T_0}(n) instead of P(n). The specification of zdim(n) then allows to compute this number from zdim_{T_0}(1) to zdim_{T_0}(n) and the Stirling numbers of the second kind S(n,1) to S(n,n). The resulting algorithms have been implemented in C and we also present results of practical experiments with them. To considerably reduce the running times for computing zdim_{T_0}(n), we also describe a backtracking approach and its parallel implementation in C using the OpenMP library.

Published
2020

29. Relational Characterisations of Paths

Author

Berghammer, Rudolf, Furusawa, Hitoshi, Guttmann, Walter, and Höfner, Peter

Subjects
Computer Science - Logic in Computer Science, F.3.1, F.3.2
Abstract

Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in many areas of mathematics and computing, researchers usually fall back to point-wise reasoning when it comes to arguments about paths in a graph. We present a purely algebraic way to specify different kinds of paths in relation algebras. We study the relationship between paths with a designated root vertex and paths without such a vertex. Since we stay in first-order logic this development helps with mechanising proofs.To demonstrate the applicability of the algebraic framework we verify the correctness of three basic graph algorithms. All results of this paper are formally verified using the interactive proof assistant Isabelle/HOL.

Published
2018

30. Experimental Investigation of Sufficient Criteria for Relations to Have Kernels

Author

Berghammer, Rudolf, Kulczynski, Mitja, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Fahrenberg, Uli, editor, Gehrke, Mai, editor, Santocanale, Luigi, editor, and Winter, Michael, editor

Published
2021
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31. Relational Computation of Sets of Relations

Author

Berghammer, Rudolf, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Fahrenberg, Uli, editor, Gehrke, Mai, editor, Santocanale, Luigi, editor, and Winter, Michael, editor

Published
2021
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43. A Relation-Algebraic Treatment of the Dedekind Recursion Theorem

Author

Berghammer, Rudolf, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Fahrenberg, Uli, editor, Jipsen, Peter, editor, and Winter, Michael, editor

Published
2020
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46. Solving Hard Control Problems in Voting Systems via Integer Programming

Author

Polyakovskiy, Sergey, Berghammer, Rudolf, and Neumann, Frank

Subjects
Computer Science - Computer Science and Game Theory
Abstract

Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control problems. Our ILP formulations are flexible in the sense that they can work with an arbitrary number of candidates and voters. Using the off-the-shelf solver Cplex, we show that our approaches can manipulate elections with a large number of voters and candidates efficiently.

Published
2014

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