Andrzej Proskurowski - Academia.edu (original) (raw)

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Papers by Andrzej Proskurowski

Discrete Applied Mathematics, 2016

We introduce a new notion of Systems of Distant Representatives of families of subsets of a metri... more We introduce a new notion of Systems of Distant Representatives of families of subsets of a metric space. We are in particular interested in the computational complexity of deciding the existence of such systems, for dierent distance parameters and for various metric spaces. The problem contains as a subproblem the well known polynomial time solvable problem of Systems of Distinct Representatives (for discrete metric and distance parameter 1). We prove several NP-hardness results, e.g., for discrete metric and distance parameter 2, or for Euclidean metric spaces. We also show a direct connection to practically motivated and previously studied problems such as scheduling, distance constrained graph labeling, map labeling, disjoint representatives of hypergraphs and independent sets in graphs.

Proceedings of the 41st ACM technical symposium on Computer science education, 2010

Lecture Notes in Computer Science, 2011

Discrete Mathematics, 2019

Journal of Combinatorial Theory, Series B, 1985

ABSTRACT A maximal outerplane graph (mop) is a plane embedding of a graph in which all vertices l... more ABSTRACT A maximal outerplane graph (mop) is a plane embedding of a graph in which all vertices lie on the exterior face, and the addition of an edge between any two vertices would destroy this outerplanarity property. Removing the edges of the exterior face of a mop G results in the interior graph of G. We give a necessary and sufficient condition for a graph to be the interior graph of some mop.

International Journal of Parallel Programming, 1981

Adominating cycle of a graph lies at a distance of at most one from all the vertices of the graph... more Adominating cycle of a graph lies at a distance of at most one from all the vertices of the graph. The problem of finding the minimum size of such a cycle is proved to be difficult even when restricted to planar graphs. An efficient algorithm solving this problem is given for the class of two-connectedouterplanar graphs, in which all vertices lie on the exterior face in a plane embedding of the graph.

The idea of applying a dynamic programming strategy to evaluating certain objective functions on ... more The idea of applying a dynamic programming strategy to evaluating certain objective functions on trees is fairly straightforward. The road for this idea to develop into theories of width parameters has been not so straight. Hans Bodlaender has played a major role in the process of mapping out that road. In this sentimental journey, we will recount our collective road trip over the past decades.

Siam Journal on Discrete Mathematics, 1997

In this paper, we consider a large class of vertex partitioning problems and apply to them the th... more In this paper, we consider a large class of vertex partitioning problems and apply to them the theory of algorithm design for problems restricted to partial k-trees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications. We give a precise characterization of vertex partitioning problems,

SIAM Journal on Algebraic Discrete Methods

Discrete Applied Mathematics, Jan 15, 2005

Siam Journal on Discrete Mathematics, 1998

This paper addresses memory requirement issues arising in implementations of algorithms on graphs... more This paper addresses memory requirement issues arising in implementations of algorithms on graphs of bounded treewidth. Such dynamic programming algorithms require a large data table for each vertex of a tree-decomposition T of the input graph. We give a linear-time algorithm that finds the traversal order of T minimizing the number of tables stored simultaneously. We show that this minimum value is lower-bounded by the pathwidth of T plus one, and upper bounded by twice the pathwidth of T plus one. We also give a linear-time algorithm finding the depth-first traversal order minimizing the sum of the sizes of tables stored simultaneously.

Discrete Applied Mathematics, 2012

Siam Journal on Algebraic Discrete Methods, Jul 17, 2006