Optimality program in segment and string graphs

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in $2^{O(n^{2/3}\log n)}$ by Fox and Pach [SODA'11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs) or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis). Among our results, we show that, quite surprisingly, 3-Coloring can also be solved in time $2^{O(n^{2/3}\log^{O(1)}n)}$ on string graphs while an algorithm running in time $2^{o(n)}$ for 4-Coloring even on axis-parallel segments (of unbounded length) would disprove the ETH. For 4-Coloring of unit segments, we show a weaker ETH lower bound of $2^{o(n^{2/3})}$ which exploits the celebrated Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent Dominating Set.Comment: 19 pages, 15 figure

As ocupações neolíticas em lapiás: o caso de Negrais (Sintra)

Novas perspectivas de leitura em torno do Complexo de Negrais (Sintra, Portugal) onde se verificou a associação de vários sítios a uma paisagem muito peculiar proporcionada pelos campos de lapiás. Estas fortificações rochosas calcárias criam um ambiente fechado com abrigos e caminhos labirínticos que foram ocupados desde inícios do Neolítico até finais do Calcolítico. Apesar de apenas contarmos com dados descontextualizados a longevidade da ocupação nos lapiás de Negrais funciona como indicador dos vários momentos cronológico-culturais do Neolítico e Calcolítico da Estremadura Meridional.New perspectives upon the arcaheological sites of Negrais (Sintra, Portugal) where several sites are associated in a peculiar surrounding the fields of "lapiás". These limestone rock formations create a closed environment with shelters, labyrinth paths that had been chosen by peasants since the early Neolithic till the late Chalcolithic. A specific study was made about two of the most significant sites: Barruncheiros and Pedraceiras.info:eu-repo/semantics/publishedVersio

Efficient convexity and domination algorithms for fine- and medium-grain hypercube computers

This paper gives hypercube algorithms for some simple problems involving geometric properties of sets of points. The properties considered emphasize aspects of convexity and domination. Efficient algorithms are given for both fine- and medium-grain hypercube computers, including a discussion of implementation, running times and results on an Intel iPSC hypercube, as well as theoretical results. For both serial and parallel computers, sorting plays an important role in geometric algorithms for determining simple properties, often being the dominant component of the running time. Since the time required to sort data on a hypercube computer is still not fully understood, the running times of some of our algorithms for unsorted data are not completely determined. For both the fine- and medium-grain models, we show that faster expected-case running time algorithms are possible for point sets generated randomly. Our algorithms are developed for sets of planar points, with several of them extending to sets of points in spaces of higher dimension.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41352/1/453_2005_Article_BF01758751.pd

Sozialplanzuschuesse in der betrieblichen Praxis und im internationalen Vergleich von Instrumenten des Beschaeftigungstransfers Ergaenzender Bericht der Begleitforschung zu den Zuschuessen zu Sozialplanmassnahmen nach Paragraphen 254ff. SGB III

Seit dem 1. Januar 1998 kann die Bundesanstalt fuer Arbeit Wiedereingliederungsmassnahmen foerdern, die in einem Sozialplan fuer vor dem Verlust ihres Arbeitsplatzes stehende Arbeitnehmer vorgesehen sind. Von September 1998 bis August 2000 hat das Institut Arbeit und Technik im Auftrag des IAB eine Begleitforschung zur Implementation der Massnahmen durchgefuehrt. Hauptzweck der Veroeffentlichung ist es, die Fallstudien, aus denen im Endbericht Schlussfolgerungen gezogen werden, dem interessierten Leser in ausfuehrlicherer Form zugaenglich zu machen. Ausserdem wird ein Blick sowohl ueber die Landesgrenzen als auch ueber die Grenzen des Begleitforschungsauftrages geworfen. Um die Diskussion darueber zu befruchten, wie man berufliche Uebergaenge bei strukturellem Wandel des Beschaeftigungssystems noch wirksamer unterstuetzen koennte, werden Erfahrungen mit den oesterreichischen 'Arbeitsstiftungen' sowie mit den franzoesischen Transfervereinbarungen (conventions de conversion) vorgestellt. Im Anschluss daran werden im Schlusskapitel Anregungen zur Weiterentwicklung der proaktiven Arbeitsfoerderung in Deutschland gegeben. (IAB2)Available from IAB-43215 BL 457,0 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman