2017

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  Casel, Katrin; Fernau, Henning; Grigoriev, Alexander; Schmid, Markus L.; Whitesides, Sue Combinatorial Properties and Recognition of Unit Square Visibility Graphs. International Symposium on Mathematical Foundations of Computer Science (MFCS) 2017: 30:1-30:15
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.
  @inproceedings{DBLP:conf/mfcs/CaselFGSW17, abstract = {Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.}, author = {Casel, Katrin and Fernau, Henning and Grigoriev, Alexander and Schmid, Markus L. and Whitesides, Sue}, booktitle = {International Symposium on Mathematical Foundations of Computer Science (MFCS)}, crossref = {DBLP:conf/mfcs/2017}, editor = {Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean{-}Fran{\c{c}}ois}, pages = {30:1-30:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik}, series = {LIPIcs}, title = {Combinatorial Properties and Recognition of Unit Square Visibility Graphs}, volume = 83, year = 2017 }

2016

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  Friedrich, Tobias Scale-Free Networks, Hyperbolic Geometry, and Efficient Algorithms. Symposium on Mathematical Foundations of Computer Science (MFCS) 2016: 4:1-4:3

  Invited Talk
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  The node degrees of large real-world networks often follow a power-law distribution. Such scale-free networks can be social networks, internet topologies, the web graph, power grids, or many other networks from literally hundreds of domains. The talk will introduce several mathematical models of scale-free networks (e.g. preferential attachment graphs, Chung-Lu graphs, hyperbolic random graphs) and analyze some of their properties (e.g. diameter, average distance, clustering). We then present several algorithms and distributed processes on and for these network models (e.g. rumor spreading, load balancing, de-anonymization, embedding) and discuss a number of open problems. The talk assumes no prior knowledge about scale-free networks, distributed computing or hyperbolic geometry.
  @inproceedings{DBLP:conf/mfcs/Friedrich16, abstract = {The node degrees of large real-world networks often follow a power-law distribution. Such scale-free networks can be social networks, internet topologies, the web graph, power grids, or many other networks from literally hundreds of domains. The talk will introduce several mathematical models of scale-free networks (e.g. preferential attachment graphs, Chung-Lu graphs, hyperbolic random graphs) and analyze some of their properties (e.g. diameter, average distance, clustering). We then present several algorithms and distributed processes on and for these network models (e.g. rumor spreading, load balancing, de-anonymization, embedding) and discuss a number of open problems. The talk assumes no prior knowledge about scale-free networks, distributed computing or hyperbolic geometry.}, author = {Friedrich, Tobias}, booktitle = {Symposium on Mathematical Foundations of Computer Science (MFCS)}, note = {Invited Talk}, pages = {4:1-4:3}, title = {Scale-Free Networks, Hyperbolic Geometry, and Efficient Algorithms}, year = 2016 }

2015

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  Cord-Landwehr, Andreas; Lenzner, Pascal Network Creation Games: Think Global - Act Local. Mathematical Foundations of Computer Science (MFCS) 2015: 248-260
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bilo et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the Price of Anarchy.
  @inproceedings{DBLP:conf/mfcs/Cord-LandwehrL15, abstract = {We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bilo et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the Price of Anarchy.}, author = {Cord-Landwehr, Andreas and Lenzner, Pascal}, booktitle = {Mathematical Foundations of Computer Science (MFCS)}, pages = {248-260}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Network Creation Games: Think Global - Act Local}, volume = 9235, year = 2015 }