Author
Daniël Paulusma
Other affiliations: University of Bergen, University of Cologne, French Institute for Research in Computer Science and Automation ...read more
Bio: Daniël Paulusma is an academic researcher from Durham University. The author has contributed to research in topics: Induced subgraph & Chordal graph. The author has an hindex of 31, co-authored 352 publications receiving 3958 citations. Previous affiliations of Daniël Paulusma include University of Bergen & University of Cologne.
Topics: Induced subgraph, Chordal graph, Line graph, Pathwidth, Graph power
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors survey known results on the computational complexity of k-coloring and k-COLORING for graph classes that are characterized by one or two forbidden induced subgraphs, and also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.
Abstract: For a positive integer k, a k-coloring of a graph inline image is a mapping inline image such that inline image whenever inline image. The COLORING problem is to decide, for a given G and k, whether a k-coloring of G exists. If k is fixed (i.e., it is not part of the input), we have the decision problem k-COLORING instead. We survey known results on the computational complexity of COLORING and k-COLORING for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.
128 citations
Posted Content•
TL;DR: In this article, the authors survey known results on the computational complexity of coloring and coloring for graph classes that are characterized by one or two forbidden induced subgraphs, and also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex.
Abstract: For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)
eq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring of $G$ exists. If $k$ is fixed (that is, it is not part of the input), we have the decision problem $k$-Colouring instead. We survey known results on the computational complexity of Colouring and $k$-Colouring for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex.
109 citations
TL;DR: In this paper, the nucleolus of a weighted matching game is derived based on a characterization of the least core, which may be of independent interest for the general case of weighted matching games.
Abstract: A matching game is a cooperative game defined by a graph G = (N, E). The player set is N and the value of a coalition S ⊆ N is defined as the size of a maximum matching in the subgraph induced by S. We show that the nucleolus of such games can be computed efficiently. The result is based on an alternative characterization of the least core, which may be of independent interest. The general case of weighted matching games remains unsolved.
108 citations
TL;DR: It is proved that for each k≥2 there is a k-colourable chordal graph G whose reconfiguration graph of the (k+1)-colourings has diameter Θ(|V|2).
Abstract: A k-colouring of a graph G=(V,E) is a mapping c:V?{1,2,?,k} such that c(u)?c(v) whenever uv is an edge. The reconfiguration graph of the k-colourings of G contains as its vertex set the k-colourings of G, and two colourings are joined by an edge if they differ in colour on just one vertex of G. We introduce a class of k-colourable graphs, which we call k-colour-dense graphs. We show that for each k-colour-dense graph G, the reconfiguration graph of the l-colourings of G is connected and has diameter O(|V|2), for all l?k+1. We show that this graph class contains the k-colourable chordal graphs and that it contains all chordal bipartite graphs when k=2. Moreover, we prove that for each k?2 there is a k-colourable chordal graph G whose reconfiguration graph of the (k+1)-colourings has diameter ?(|V|2).
105 citations
TL;DR: The conjecture that Kristiansen and Telle conjectured that the R-role assignment problem is an NP-complete problem for any simple connected graph R on at least three vertices is proved.
68 citations
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Book•
27 Jul 2015
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Abstract: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
1,544 citations
TL;DR: Wittgenstein's work remains, undeniably, now, that off one of those few few philosophers who will be read by all future generations as mentioned in this paper, regardless of whether it is true or not.
Abstract: Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
910 citations
Book•
20 Mar 2013TL;DR: This book builds on the author’s prior research in this area, and also his practical experience of developing algorithms for matching kidney patients to donors in the UK, for assigning medical students to hospitals in Scotland, and for allocating students to elective courses and projects.
Abstract: Preliminary Definitions, Results and Motivation Stable Matching Problems: The Stable Marriage Problem: An Update SM and HR with Indifference The Stable Roommates Problem Further Stable Matching Problems Other Optimal Matching Problems: Pareto Optimal Matchings Popular Matchings Profile-Based Optimal Matchings.
488 citations
29 May 2013
TL;DR: An extensive survey and categorization of state-of-the-art mapping methodologies and highlights the emerging trends for multi/many-core systems.
Abstract: The reliance on multi/many-core systems to satisfy the high performance requirement of complex embedded software applications is increasing. This necessitates the need to realize efficient mapping methodologies for such complex computing platforms. This paper provides an extensive survey and categorization of state-of-the-art mapping methodologies and highlights the emerging trends for multi/many-core systems. The methodologies aim at optimizing system's resource usage, performance, power consumption, temperature distribution and reliability for varying application models. The methodologies perform design-time and run-time optimization for static and dynamic workload scenarios, respectively. These optimizations are necessary to fulfill the end-user demands. Comparison of the methodologies based on their optimization aim has been provided. The trend followed by the methodologies and open research challenges have also been discussed.
435 citations
Book•
25 Oct 2011TL;DR: This talk introduces basic concepts from cooperative game theory, and in particular the key solution concepts: the core and the Shapley value, and introduces the key issues that arise if one is to consider the cooperative games in a computational setting.
Abstract: The theory of cooperative games provides a rich mathematical framework with which to understand the interactions between self-interested agents in settings where they can benefit from cooperation, and where binding agreements between agents can be made. Our aim in this talk is to describe the issues that arise when we consider cooperative game theory through a computational lens. We begin by introducing basic concepts from cooperative game theory, and in particular the key solution concepts: the core and the Shapley value. We then introduce the key issues that arise if one is to consider the cooperative games in a computational setting: in particular, the issue of representing games, and the computational complexity of cooperative solution concepts.
395 citations