Maciej Sysło | University of Wroclaw (original) (raw)

Papers by Maciej Sysło

Research paper thumbnail of A tabu search approach to the jump number problem

Algebra and discrete mathematics, Nov 9, 2015

We consider algorithmics for the jump number problem, which is to generate a linear extension of ... more We consider algorithmics for the jump number problem, which is to generate a linear extension of a given poset, minimizing the number of incomparable adjacent pairs. Since this problem is NP-hard on interval orders and open on two-dimensional posets, approximation algorithms or fast exact algorithms are in demand. In this paper, succeeding from the work of the second named author on semi-strongly greedy linear extensions, we develop a metaheuristic algorithm to approximate the jump number with the tabu search paradigm. To benchmark the proposed procedure, we infer from the previous work of Mitas [Order 8 (1991), 115-132] a new fast exact algorithm for the case of interval orders, and from the results of Ceroi [Order 20 (2003), 1-11] a lower bound for the jump number of two-dimensional posets. Moreover, by other techniques we prove an approximation ratio of n/ log log n for 2D orders.

Research paper thumbnail of Hamiltonian cycles in skirted trees

Applicationes Mathematicae, 1987

Research paper thumbnail of E-learning w szkole

e-mentor, 2009

Krótkie spojrzenie za siebie pozwala stwierdzić, że większość" nowych" pojęć, które dzi... more Krótkie spojrzenie za siebie pozwala stwierdzić, że większość" nowych" pojęć, które dzisiaj pojawiają się w dyskusji na temat edukacji, takich jak: społeczeństwo bazujące na wiedzy, kształcenie ustawiczne, kształcenie na odległość, indywidualizacja kształcenia, a nawet e ...

Research paper thumbnail of Algorithm 36. Transitive closure of a graph

Applicationes Mathematicae, 1974

Research paper thumbnail of Discrete Optimization Algorithms: with Pascal Programs (Dover Books on Mathematics)

Research paper thumbnail of Computational experiments with some approximation algorithms for the travelling salesman problem

Applicationes Mathematicae, 1983

Research paper thumbnail of Preface, List of papers

Applicationes Mathematicae, 1987

Research paper thumbnail of Applied graph theory. Application of graph theory to numerical methods

Mathematica Applicanda, May 21, 1975

Research paper thumbnail of Computational complexity of problems of combinatorics and graph theory

Mathematica Applicanda, Feb 1, 1981

From the introduction: "The present article does not pretend to be a complete survey of all ... more From the introduction: "The present article does not pretend to be a complete survey of all or even of the most important algorithms in combinatorics and graph theory. The algorithms presented illustrate only general considerations involving the computational complexity of problems of combinatorics. It is assumed that the reader is acquainted with the fundamental algorithms of combinatorics and graph theory. The first part of the paper is an outline of basic computation models used in the analysis of combinatorial algorithms. In subsequent parts, problems for which optimal or `good' algorithms exist are discussed. Here problems connected with the class P are presented, i.e. the class of problems that can be solved by algorithms with polynomial complexity. A formal definition is given of the class P and the class NP, to which, with minor exceptions, all difficult problems—the knapsack problem, the scheduling problem, the problem of Hamiltonian circuits in graphs and networks, etc.—belong. The question whether P=NP is a fundamental problem in the analysis of the computational complexity of combinatorial algorithms. Contents: (1) Introduction; (2) Computational complexity of algorithms; (3) Computation models; (4) Ways of representing graphs, and the efficiency of algorithms; (5) Lower bounds of computational complexity; (6) Examples of optimal and `good' algorithms; (7) Problems with polynomial complexity; (8) Problems for which the existence of algorithms with polynomial complexity is not possible; (9) NP-complete problems; (10) Conclusion; Bibliography.

Research paper thumbnail of Remarks on addition processes of positive floating-point numbers

Applicationes Mathematicae, 1974

Research paper thumbnail of In-trees and plane embeddings of outerplanar graphs

Bit Numerical Mathematics, Mar 1, 1990

A notion of an in-tree is introduced. It is then used to characterize and count plane embeddings ... more A notion of an in-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.

Research paper thumbnail of Independent Covers in Plane Graphs

Research paper thumbnail of Algorithms 62-64. Graph-theoretic algorithms for sparse matrix transformations

Applicationes Mathematicae, 1978

Research paper thumbnail of Generalizations of the standard travelling salesman problem

Applicationes Mathematicae, 1980

Research paper thumbnail of Proceedings of the 3rd international conference on Informatics in Secondary Schools - Evolution and Perspectives: Informatics Education - Supporting Computational Thinking

Research paper thumbnail of Adjacency matrix equations and related problems: Research notes

Commentationes Mathematicae Universitatis Carolinae, 1983

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz COMMENTAT!ONES HATHEMATICAE UNIVERSITATIS CAROLINAE 24.2(1983) ADJACENCY MATRIX EQUATIONS AND RELATED PROBLEMSiRESEARCH NOTES MACIEJ M.SYStO Abstracts The purpose of this paper is to discuss some generalizations of the notion of regularity in graphs which are derived from matrix equations involving adjacency matrices.

Research paper thumbnail of Computational experiences with some transitive closure algorithms

Computing, Mar 1, 1975

Computational Experiences with Some Transitive Closure Algorithms. The paper contains results of ... more Computational Experiences with Some Transitive Closure Algorithms. The paper contains results of computational experiences with the following algorithms for finding the transitive closure of a digraph: (i) Warshall's algorithm [17], (ii) Purdom's algorithm [13], (iii) the modification of Yen's algorithm [14], and (iv) the new algorithms for finding the transitive closure [3, 4]. The tested digraphs were generated at random. The enclosed references contain all papers known to the authors concerning transitive closure algorithms. Reehnererfahrungen mit einigen Algorithmen fdr die transitive HiiUe eines gerichteten Graphen. Folgende Algorithmen wurden untersucht: 1. Warshall's Algo~thm [17], 2. Purdom's Algoritlun [13], 3. der modifizierte Algorithmus yon Yen [14], 4. der Algorithmus yon Dzikiewicz [3, 4]. Die getesteten Digraphen wurden durch einen Zufallsgenerator erzeugt. Das Literaturverzeichnis enth[ilt alle Ver6ffentlichungen fiber Algorithmen zur Bildung der transitiven Hfille, welche den Verfassern bekannt sind. Computing 15/1

Research paper thumbnail of Discrete Optimization Algorithms: With Pascal Programs

Research paper thumbnail of Webquest – activity for internet based learning

Research paper thumbnail of On some new types of greedy chains and greedy linear extensions of partially ordered sets

Discrete Applied Mathematics, Jun 1, 1995

Two new types of greedy chains, strongly and semi-strongly greedy, in posets are defined and thei... more Two new types of greedy chains, strongly and semi-strongly greedy, in posets are defined and their role in so|ring the jump number problem is discussed in this paper. Ifa poset P contains a strongly greedy chain C then C may be taken as the first chain in an optimal linear extension of P. If a poset P has no strongly greedy chains then it contains an optimal linear extension which starts with a semi-strongly greedy chain. Hence, every poser has an optimal linear extension which consist of strongly and semi-strongly greedy chains. Algorithmic issues of finding such linear extensions are discussed elsewhere (Syslo, 1987, 1988), where we provide a very efficient method for solving the jump number problem which is polynomial in the class of posets whose arc representations contain a bounded number of dummy arcs. In another work, the author has recently demonstrated that this method restricted to interval orders gives rise to 3/2-approximation algorithm for such posets.

Research paper thumbnail of A tabu search approach to the jump number problem

Algebra and discrete mathematics, Nov 9, 2015

We consider algorithmics for the jump number problem, which is to generate a linear extension of ... more We consider algorithmics for the jump number problem, which is to generate a linear extension of a given poset, minimizing the number of incomparable adjacent pairs. Since this problem is NP-hard on interval orders and open on two-dimensional posets, approximation algorithms or fast exact algorithms are in demand. In this paper, succeeding from the work of the second named author on semi-strongly greedy linear extensions, we develop a metaheuristic algorithm to approximate the jump number with the tabu search paradigm. To benchmark the proposed procedure, we infer from the previous work of Mitas [Order 8 (1991), 115-132] a new fast exact algorithm for the case of interval orders, and from the results of Ceroi [Order 20 (2003), 1-11] a lower bound for the jump number of two-dimensional posets. Moreover, by other techniques we prove an approximation ratio of n/ log log n for 2D orders.

Research paper thumbnail of Hamiltonian cycles in skirted trees

Applicationes Mathematicae, 1987

Research paper thumbnail of E-learning w szkole

e-mentor, 2009

Krótkie spojrzenie za siebie pozwala stwierdzić, że większość" nowych" pojęć, które dzi... more Krótkie spojrzenie za siebie pozwala stwierdzić, że większość" nowych" pojęć, które dzisiaj pojawiają się w dyskusji na temat edukacji, takich jak: społeczeństwo bazujące na wiedzy, kształcenie ustawiczne, kształcenie na odległość, indywidualizacja kształcenia, a nawet e ...

Research paper thumbnail of Algorithm 36. Transitive closure of a graph

Applicationes Mathematicae, 1974

Research paper thumbnail of Discrete Optimization Algorithms: with Pascal Programs (Dover Books on Mathematics)

Research paper thumbnail of Computational experiments with some approximation algorithms for the travelling salesman problem

Applicationes Mathematicae, 1983

Research paper thumbnail of Preface, List of papers

Applicationes Mathematicae, 1987

Research paper thumbnail of Applied graph theory. Application of graph theory to numerical methods

Mathematica Applicanda, May 21, 1975

Research paper thumbnail of Computational complexity of problems of combinatorics and graph theory

Mathematica Applicanda, Feb 1, 1981

From the introduction: "The present article does not pretend to be a complete survey of all ... more From the introduction: "The present article does not pretend to be a complete survey of all or even of the most important algorithms in combinatorics and graph theory. The algorithms presented illustrate only general considerations involving the computational complexity of problems of combinatorics. It is assumed that the reader is acquainted with the fundamental algorithms of combinatorics and graph theory. The first part of the paper is an outline of basic computation models used in the analysis of combinatorial algorithms. In subsequent parts, problems for which optimal or `good' algorithms exist are discussed. Here problems connected with the class P are presented, i.e. the class of problems that can be solved by algorithms with polynomial complexity. A formal definition is given of the class P and the class NP, to which, with minor exceptions, all difficult problems—the knapsack problem, the scheduling problem, the problem of Hamiltonian circuits in graphs and networks, etc.—belong. The question whether P=NP is a fundamental problem in the analysis of the computational complexity of combinatorial algorithms. Contents: (1) Introduction; (2) Computational complexity of algorithms; (3) Computation models; (4) Ways of representing graphs, and the efficiency of algorithms; (5) Lower bounds of computational complexity; (6) Examples of optimal and `good' algorithms; (7) Problems with polynomial complexity; (8) Problems for which the existence of algorithms with polynomial complexity is not possible; (9) NP-complete problems; (10) Conclusion; Bibliography.

Research paper thumbnail of Remarks on addition processes of positive floating-point numbers

Applicationes Mathematicae, 1974

Research paper thumbnail of In-trees and plane embeddings of outerplanar graphs

Bit Numerical Mathematics, Mar 1, 1990

A notion of an in-tree is introduced. It is then used to characterize and count plane embeddings ... more A notion of an in-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.

Research paper thumbnail of Independent Covers in Plane Graphs

Research paper thumbnail of Algorithms 62-64. Graph-theoretic algorithms for sparse matrix transformations

Applicationes Mathematicae, 1978

Research paper thumbnail of Generalizations of the standard travelling salesman problem

Applicationes Mathematicae, 1980

Research paper thumbnail of Proceedings of the 3rd international conference on Informatics in Secondary Schools - Evolution and Perspectives: Informatics Education - Supporting Computational Thinking

Research paper thumbnail of Adjacency matrix equations and related problems: Research notes

Commentationes Mathematicae Universitatis Carolinae, 1983

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz COMMENTAT!ONES HATHEMATICAE UNIVERSITATIS CAROLINAE 24.2(1983) ADJACENCY MATRIX EQUATIONS AND RELATED PROBLEMSiRESEARCH NOTES MACIEJ M.SYStO Abstracts The purpose of this paper is to discuss some generalizations of the notion of regularity in graphs which are derived from matrix equations involving adjacency matrices.

Research paper thumbnail of Computational experiences with some transitive closure algorithms

Computing, Mar 1, 1975

Computational Experiences with Some Transitive Closure Algorithms. The paper contains results of ... more Computational Experiences with Some Transitive Closure Algorithms. The paper contains results of computational experiences with the following algorithms for finding the transitive closure of a digraph: (i) Warshall's algorithm [17], (ii) Purdom's algorithm [13], (iii) the modification of Yen's algorithm [14], and (iv) the new algorithms for finding the transitive closure [3, 4]. The tested digraphs were generated at random. The enclosed references contain all papers known to the authors concerning transitive closure algorithms. Reehnererfahrungen mit einigen Algorithmen fdr die transitive HiiUe eines gerichteten Graphen. Folgende Algorithmen wurden untersucht: 1. Warshall's Algo~thm [17], 2. Purdom's Algoritlun [13], 3. der modifizierte Algorithmus yon Yen [14], 4. der Algorithmus yon Dzikiewicz [3, 4]. Die getesteten Digraphen wurden durch einen Zufallsgenerator erzeugt. Das Literaturverzeichnis enth[ilt alle Ver6ffentlichungen fiber Algorithmen zur Bildung der transitiven Hfille, welche den Verfassern bekannt sind. Computing 15/1

Research paper thumbnail of Discrete Optimization Algorithms: With Pascal Programs

Research paper thumbnail of Webquest – activity for internet based learning

Research paper thumbnail of On some new types of greedy chains and greedy linear extensions of partially ordered sets

Discrete Applied Mathematics, Jun 1, 1995

Two new types of greedy chains, strongly and semi-strongly greedy, in posets are defined and thei... more Two new types of greedy chains, strongly and semi-strongly greedy, in posets are defined and their role in so|ring the jump number problem is discussed in this paper. Ifa poset P contains a strongly greedy chain C then C may be taken as the first chain in an optimal linear extension of P. If a poset P has no strongly greedy chains then it contains an optimal linear extension which starts with a semi-strongly greedy chain. Hence, every poser has an optimal linear extension which consist of strongly and semi-strongly greedy chains. Algorithmic issues of finding such linear extensions are discussed elsewhere (Syslo, 1987, 1988), where we provide a very efficient method for solving the jump number problem which is polynomial in the class of posets whose arc representations contain a bounded number of dummy arcs. In another work, the author has recently demonstrated that this method restricted to interval orders gives rise to 3/2-approximation algorithm for such posets.