Maciej Sysło - Profile on Academia.edu (original) (raw)

Papers by Maciej Sysło

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.

Applicationes Mathematicae, 1987

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 ...

Discrete Optimization Algorithms: with Pascal Programs (Dover Books on Mathematics)

ABSTRACT

Applicationes Mathematicae, 1983

Applied graph theory. Application of graph theory to numerical methods

Mathematica Applicanda, May 21, 1975

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.

Applicationes Mathematicae, 1974

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.

Independent Covers in Plane Graphs

Applicationes Mathematicae, 1980

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

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.

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

Discrete Optimization Algorithms: With Pascal Programs

ABSTRACT

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.

From Algorithmic to Computational Thinking

Computational thinking, as coined by Jeannette Wing, is a fundamental skill for all to be able to... more Computational thinking, as coined by Jeannette Wing, is a fundamental skill for all to be able to live in today’s world, a mode of thought that goes well beyond computing and provides a framework for reasoning about problems and methods of their solution. It has a long tradition as algorithmic thinking which within computer science is a competence to formulate a solution of a problem in the form of an algorithm and then to implement the algorithm as a computer program. Computational thinking is not an adequate characterization of computer science as claimed by Peter Denning and he is right – it is a collection of key mental tools and practices originated in computing but addressed to all areas far beyond computer science. As an extension of algorithmic thinking, it includes thinking with many levels of abstraction as a problem solving approach inherently connected to computer science and addressed to all students to use computers and computing skills in solving problems in various school subjects coming from various scientific and applied areas. Computational thinking involves concepts, skills and competences that lie at the heart of computing, such as abstraction, decomposition, generalization, approximation, heuristics, algorithm design, efficiency and complexity issues and therefore it is clear that basic computer science knowledge helps to systematically, correctly, and efficiently process information, perform tasks, and solve problems. Although coming from computer science, computational thinking is not only the study of computer science, though computers play an essential role in the design of problems’ solutions. It is a very important and useful mode of thinking in almost all disciplines and school subjects as an insight into what can and cannot be computed. In this talk we shall discuss a new computing curriculum addressed to ALL students in K-12 in Poland which motivates them to use computational thinking in solving problems in various school subjects. Moreover its goal is to encourage and prepare students from early school years to consider computing and related fields as disciplines of their future study and professional career. To this end, the curriculum allows teachers and schools to personalize learning and teaching according to students’ interests, abilities, and needs. The new computing curriculum benefits a lot from our experience in teaching informatics in our schools for almost 30 years – the first curriculum was approved by the ministry of education in 1985, 20 years after the first regular classes on informatics were held in two high schools in Wrocław and in Warsaw. Today, informatics is an obligatory subject in middle school (grades 7-9) and high school (grades 10-12) and it will replace computer lessons (mainly on ICT) in elementary schools (grades 16). The new curriculum is also addressed to vocational education.

This thesis involves the application of computational techniques to various problems in graph the... more This thesis involves the application of computational techniques to various problems in graph theory and low dimensional topology. The first two chapters of this thesis focus on problems in graph theory itself; in particular on graph decomposition problems. The last three chapters look at applications of graph theory to combinatorial topology, focusing on the exhaustive generation of certain families of 3-manifold triangulations. Chapter 1 shows that the obvious necessary conditions are sufficient for the existence of a decomposition of the complete graph into cycles of arbitrary specified lengths. This problem was formally posed in 1981 by Brian Alspach, but has its origins in the mid 1800s. A complete discussion of problem, as well as a full solution, is presented in Chapter 1. This work has been published, see [34].

Discrete Mathematics, 1987

, where arc diagrams of posets have been successfully applied to solve the jump number problem fo... more , where arc diagrams of posets have been successfully applied to solve the jump number problem for N-free posets. Here, we consider arbitrary posets and, again making use of arc diagrams of posets, we define two special types of greedy chains: strongly and semi-strongly greedy. Every strongly greedy chain may begin an optimal linear extension (Theorem 1 and Corollary 1). If a poset has no strongly greedy chains, then it has an optimal linear extension which starts with a semi-strongly greedy chain (Theorem 2). Therefore, every poset has an optimal linear extension which consists entirely of strongly and semi-strongly greedy chains. This fact leads to a polynomial-time algorithm for the jump number problem in the class of posets whose arc diagrams contain a bounded number of dummy arcs. Pulleyblank [4]), some of its special instances can be efficiently solved by polynomial-time algorithms. A jump @i, Pi+l) in a linear extension L =p1p2.. . pm of P is greedy if pi is not covered in P by any element q E P-Li such that N-(q) G (PI, pz,. .. , pi}, where Li =plp2. .. pi. A linear extension L is greedy if all jumps in L are

Banach Center Publications, 1989

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.

Applicationes Mathematicae, 1987

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 ...

Discrete Optimization Algorithms: with Pascal Programs (Dover Books on Mathematics)

ABSTRACT

Applicationes Mathematicae, 1983

Applied graph theory. Application of graph theory to numerical methods

Mathematica Applicanda, May 21, 1975

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.

Applicationes Mathematicae, 1974

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.

Independent Covers in Plane Graphs

Applicationes Mathematicae, 1980

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

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.

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

Discrete Optimization Algorithms: With Pascal Programs

ABSTRACT

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.

From Algorithmic to Computational Thinking

Computational thinking, as coined by Jeannette Wing, is a fundamental skill for all to be able to... more Computational thinking, as coined by Jeannette Wing, is a fundamental skill for all to be able to live in today’s world, a mode of thought that goes well beyond computing and provides a framework for reasoning about problems and methods of their solution. It has a long tradition as algorithmic thinking which within computer science is a competence to formulate a solution of a problem in the form of an algorithm and then to implement the algorithm as a computer program. Computational thinking is not an adequate characterization of computer science as claimed by Peter Denning and he is right – it is a collection of key mental tools and practices originated in computing but addressed to all areas far beyond computer science. As an extension of algorithmic thinking, it includes thinking with many levels of abstraction as a problem solving approach inherently connected to computer science and addressed to all students to use computers and computing skills in solving problems in various school subjects coming from various scientific and applied areas. Computational thinking involves concepts, skills and competences that lie at the heart of computing, such as abstraction, decomposition, generalization, approximation, heuristics, algorithm design, efficiency and complexity issues and therefore it is clear that basic computer science knowledge helps to systematically, correctly, and efficiently process information, perform tasks, and solve problems. Although coming from computer science, computational thinking is not only the study of computer science, though computers play an essential role in the design of problems’ solutions. It is a very important and useful mode of thinking in almost all disciplines and school subjects as an insight into what can and cannot be computed. In this talk we shall discuss a new computing curriculum addressed to ALL students in K-12 in Poland which motivates them to use computational thinking in solving problems in various school subjects. Moreover its goal is to encourage and prepare students from early school years to consider computing and related fields as disciplines of their future study and professional career. To this end, the curriculum allows teachers and schools to personalize learning and teaching according to students’ interests, abilities, and needs. The new computing curriculum benefits a lot from our experience in teaching informatics in our schools for almost 30 years – the first curriculum was approved by the ministry of education in 1985, 20 years after the first regular classes on informatics were held in two high schools in Wrocław and in Warsaw. Today, informatics is an obligatory subject in middle school (grades 7-9) and high school (grades 10-12) and it will replace computer lessons (mainly on ICT) in elementary schools (grades 16). The new curriculum is also addressed to vocational education.

This thesis involves the application of computational techniques to various problems in graph the... more This thesis involves the application of computational techniques to various problems in graph theory and low dimensional topology. The first two chapters of this thesis focus on problems in graph theory itself; in particular on graph decomposition problems. The last three chapters look at applications of graph theory to combinatorial topology, focusing on the exhaustive generation of certain families of 3-manifold triangulations. Chapter 1 shows that the obvious necessary conditions are sufficient for the existence of a decomposition of the complete graph into cycles of arbitrary specified lengths. This problem was formally posed in 1981 by Brian Alspach, but has its origins in the mid 1800s. A complete discussion of problem, as well as a full solution, is presented in Chapter 1. This work has been published, see [34].

Discrete Mathematics, 1987

, where arc diagrams of posets have been successfully applied to solve the jump number problem fo... more , where arc diagrams of posets have been successfully applied to solve the jump number problem for N-free posets. Here, we consider arbitrary posets and, again making use of arc diagrams of posets, we define two special types of greedy chains: strongly and semi-strongly greedy. Every strongly greedy chain may begin an optimal linear extension (Theorem 1 and Corollary 1). If a poset has no strongly greedy chains, then it has an optimal linear extension which starts with a semi-strongly greedy chain (Theorem 2). Therefore, every poset has an optimal linear extension which consists entirely of strongly and semi-strongly greedy chains. This fact leads to a polynomial-time algorithm for the jump number problem in the class of posets whose arc diagrams contain a bounded number of dummy arcs. Pulleyblank [4]), some of its special instances can be efficiently solved by polynomial-time algorithms. A jump @i, Pi+l) in a linear extension L =p1p2.. . pm of P is greedy if pi is not covered in P by any element q E P-Li such that N-(q) G (PI, pz,. .. , pi}, where Li =plp2. .. pi. A linear extension L is greedy if all jumps in L are

Banach Center Publications, 1989