8 research outputs found
Dynamic and Multi-functional Labeling Schemes
We investigate labeling schemes supporting adjacency, ancestry, sibling, and
connectivity queries in forests. In the course of more than 20 years, the
existence of labeling schemes supporting each of these
functions was proven, with the most recent being ancestry [Fraigniaud and
Korman, STOC '10]. Several multi-functional labeling schemes also enjoy lower
or upper bounds of or
respectively. Notably an upper bound of for
adjacency+siblings and a lower bound of for each of the
functions siblings, ancestry, and connectivity [Alstrup et al., SODA '03]. We
improve the constants hidden in the -notation. In particular we show a lower bound for connectivity+ancestry and
connectivity+siblings, as well as an upper bound of for connectivity+adjacency+siblings by altering existing
methods.
In the context of dynamic labeling schemes it is known that ancestry requires
bits [Cohen, et al. PODS '02]. In contrast, we show upper and lower
bounds on the label size for adjacency, siblings, and connectivity of
bits, and to support all three functions. There exist efficient
adjacency labeling schemes for planar, bounded treewidth, bounded arboricity
and interval graphs. In a dynamic setting, we show a lower bound of
for each of those families.Comment: 17 pages, 5 figure
Анализ проблем инновационного развития медицины в Украине
Проанализированы проблемы, тормозящие развитие инновационной деятельности в медицине Украины, и внесены предложения по их устранению.Проаналізовано проблеми, які стримують розвиток інноваційної діяльності в медицині України, і внесено пропозиції щодо їх усунення.The paper contains an analysis of barriers for innovation in the Ukrainian medical sector, with propositions for their elimination
Flexible Graph Connectivity
International audienceGraph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation problem (TAP) are all examples of fundamental well-studied network design tasks that postulate different initial states of the network and different assumptions on the reliability of network components. In this paper we motivate and study \emph{Flexible Graph Connectivity} (FGC), a problem that mixes together both the modeling power and the complexities of all aforementioned problems and more. In a nutshell, FGC asks to design a connected network, while allowing to specify different reliability levels for individual edges. While this non-uniform nature of the problem makes it appealing from the modeling perspective, it also renders most existing algorithmic tools for dealing with network design problems unfit for approximating FGC. In this paper we develop a general algorithmic approach for approximating FGC that yields approximation algorithms with ratios that are very close to the best known bounds for many special cases, such as 2-ECSS and TAP. Our algorithm and analysis combine various techniques including a weight-scaling algorithm, a charging argument that uses a variant of exchange bijections between spanning trees and a factor revealing min-max-min optimization problem