Engineering DFS-Based Graph Algorithms

Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for the efficient implementation of DFS-based graph algorithms and exemplify them on three algorithms for computing strongly connected components. The techniques lead to speed-ups by a factor of two to three compared to the implementations provided by LEDA and BOOST. We have obtained similar speed-ups for biconnected components algorithms. We also compare the graph data types of LEDA and BOOST

Dynamic fractional cascading

The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In the present paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key in n lists takes time O(log N+nloglogN) and an insertion or deletion takes time O(loglogN). Here N is the total size of all lists. If only insertions or deletions have to be supported the O(loglogN) factor reduces to O(1). As an application we show that queries, insertions and deletions into segment trees or range trees can be supported in t ime O(lognloglogn), when n is the number of segments (points)

A lower bound for the complexity of the union-split-find problem

We prove a Theta(loglog n) (i.e. matching upper and lower) bound on the complexity of the Union-Split-Find problem, a variant of the Union-Find problem. Our lower bound holds for all pointer machine algorithms and does not require the separation assumption used in the lower bound arguments of Tarjan [T79] and Blum [B86]. We complement this with a Theta(log n) bound for the Split-Find problem under the separation assumption. This shows that the separation assumption can imply an exponential loss in efficiency

An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm

We describe an implementation of the Hopcroft and Tarjan planarity test and embedding algorithm. The program tests the planarity of the input graph and either constructs a combinatorial embedding (if the graph is planar) or exhibits a Kuratowski subgraph (if the graph is non-planar)

Existenz isoperimetrischer Gebiete in einer Klasse von unbeschränkten Mengen unter besonderer Berücksichtigung des Paraboloids

Mein Ausgangspunkt war die isoperimetrische Eigenschaft der Kugel im Rn sowie Verallgemeinerungen dieser Eigenschaft auf andere Gebiete, speziell das Ergebnis von Benjamini und Cao für Flächen auf dem Rand des Paraboloids. Das Ziel war eine Verallgemeinerung ihres Resultats auf das ganze Paraboloid. Verschiedene Beispiele gaben erste Hinweise, in welchen Fällen überhaupt Lösungen des isoperimetrischen Problems zu erwarten sind. Nach einer Einführung des Begriffs geometrisch asymptotisch flach und dem der Volumenvergleichsbedingung konnte ich die Existenz einer Lösung des isoperimetrischen Problems in einer großen Klasse von Mengen beweisen, darunter auch für das Paraboloid. Die Regularitätstheorie konnte dann im Fall des Paraboloids gut weiterentwickelt werden, indem mit Hilfe einer isoperimetrischen Ungleichung die Beschränktheit gezeigt werden konnte. Was immer noch fehlt, ist die konkrete Form der isoperimetrischen Gebiete. Hier kann man eventuell eine Rotationssymmetrie vermuten. Dazu muss man aber die spezielle Geometrie des Paraboloids ausnutzen, da für allgemeine rotationssymmetrische Mengen eine isoperimetrische Menge nicht rotationssymmetrisch sein muss. In der Tat ist die Frage nach der konkreten Gestalt bei vielen Mengen noch ungeklärt.My starting point was the isoperimetric property of the sphere in Rn and some abstractions on other sets, especially the results of Benjamini and Cao on the boundary of a paraboloid. The aim was to extend their result on the full paraboloid. Starting with some examples I tried to get the right properties for existence of isoperimetric domains. Two properties turned out to be very useful: geometric asymptotic flatness and a volume comparison condition. They are enough to prove the existence of solutions. Both conditions are fulfilled by the paraboloid. There's still a big open problem: the concrete shape of isoperimetric domains. In some way it seems to be okay to conjecture rotational symmetry, but there are counter-examples, if we have just existence of the solutions and rotational symmetry of the set

Associations of Suicide Rates With Socioeconomic Status and Social Isolation: Findings From Longitudinal Register and Census Data

Suicide represents a major challenge to public mental health. In order to provide empirical evidence for prevention strategies, we hypothesized current levels of low socioeconomic status (SES) and high social isolation (SI) to be linked to increased suicide rates in N = 390 administrative districts since SES and SI are associated with mental illness. Effects of SES on suicide rates were further expected to be especially pronounced in districts with individuals showing high SI levels as SI reduces the reception of social support and moderates the impact of low SES on poor mental health. We linked German Microcensus data to register data on all 149,033 German suicides between 1997 and 2010 and estimated Prentice and Sheppard’s model for aggregate data to test the hypotheses, accounting for spatial effect correlations. The findings reveal increases in district suicide rates by 1.20% (p < 0.035) for 1% increases of district unemployment, suicide rate decreases of -0.39% (p < 0.028) for 1% increases in incomes, increases of 1.65% (p < 0.033) in suicides for 1% increases in one-person-households and increases in suicide rates of 0.54% (p < 0.036) for 1% decreases in single persons' incomes as well as suicide rate increases of 3.52% (p < 0.000) for 1% increases in CASMIN scores of individuals who moved throughout the year preceding suicide. The results represent appropriate starting points for the development of suicide prevention strategies. For the definition of more precise measures, future work should focus on the causal mechanisms resulting in suicidality incorporating individual level data

Existenz isoperimetrischer Gebiete in einer Klasse von unbeschränkten Mengen unter besonderer Berücksichtigung des Paraboloids

Mein Ausgangspunkt war die isoperimetrische Eigenschaft der Kugel im Rn sowie Verallgemeinerungen dieser Eigenschaft auf andere Gebiete, speziell das Ergebnis von Benjamini und Cao für Flächen auf dem Rand des Paraboloids. Das Ziel war eine Verallgemeinerung ihres Resultats auf das ganze Paraboloid. Verschiedene Beispiele gaben erste Hinweise, in welchen Fällen überhaupt Lösungen des isoperimetrischen Problems zu erwarten sind. Nach einer Einführung des Begriffs geometrisch asymptotisch flach und dem der Volumenvergleichsbedingung konnte ich die Existenz einer Lösung des isoperimetrischen Problems in einer großen Klasse von Mengen beweisen, darunter auch für das Paraboloid. Die Regularitätstheorie konnte dann im Fall des Paraboloids gut weiterentwickelt werden, indem mit Hilfe einer isoperimetrischen Ungleichung die Beschränktheit gezeigt werden konnte. Was immer noch fehlt, ist die konkrete Form der isoperimetrischen Gebiete. Hier kann man eventuell eine Rotationssymmetrie vermuten. Dazu muss man aber die spezielle Geometrie des Paraboloids ausnutzen, da für allgemeine rotationssymmetrische Mengen eine isoperimetrische Menge nicht rotationssymmetrisch sein muss. In der Tat ist die Frage nach der konkreten Gestalt bei vielen Mengen noch ungeklärt.My starting point was the isoperimetric property of the sphere in Rn and some abstractions on other sets, especially the results of Benjamini and Cao on the boundary of a paraboloid. The aim was to extend their result on the full paraboloid. Starting with some examples I tried to get the right properties for existence of isoperimetric domains. Two properties turned out to be very useful: geometric asymptotic flatness and a volume comparison condition. They are enough to prove the existence of solutions. Both conditions are fulfilled by the paraboloid. There\u27s still a big open problem: the concrete shape of isoperimetric domains. In some way it seems to be okay to conjecture rotational symmetry, but there are counter-examples, if we have just existence of the solutions and rotational symmetry of the set

LEDA-Manual Version 3.0

No abstract available

Historische Bausubstanz einfach erneuern

Die typischen historischen Holzgebäude in Oberwalliser Dörfern sollen nicht ungenutzt verfallen. Mit effizienteren Planungsprozessen, abgestimmten Musterlösungen und damit reduzierten Umbaukosten gelingt es der BFH gemeinsam mit engagierten regionalen und nationalen Wirtschaftspartnern, den Gebäuden neues Leben einzuhauchen

Associations of Suicide Rates With Socioeconomic Status and Social Isolation: Findings From Longitudinal Register and Census Data

Suicide represents a major challenge to public mental health. In order to provide empirical evidence for prevention strategies, we hypothesized current levels of low socioeconomic status (SES) and high social isolation (SI) to be linked to increased suicide rates in N = 390 administrative districts since SES and SI are associated with mental illness. Effects of SES on suicide rates were further expected to be especially pronounced in districts with individuals showing high SI levels as SI reduces the reception of social support and moderates the impact of low SES on poor mental health. We linked German Microcensus data to register data on all 149,033 German suicides between 1997 and 2010 and estimated Prentice and Sheppard’s model for aggregate data to test the hypotheses, accounting for spatial effect correlations. The findings reveal increases in district suicide rates by 1.20% (p < 0.035) for 1% increases of district unemployment, suicide rate decreases of -0.39% (p < 0.028) for 1% increases in incomes, increases of 1.65% (p < 0.033) in suicides for 1% increases in one-person-households and increases in suicide rates of 0.54% (p < 0.036) for 1% decreases in single persons' incomes as well as suicide rate increases of 3.52% (p < 0.000) for 1% increases in CASMIN scores of individuals who moved throughout the year preceding suicide. The results represent appropriate starting points for the development of suicide prevention strategies. For the definition of more precise measures, future work should focus on the causal mechanisms resulting in suicidality incorporating individual level data