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  • 1
    Electronic Resource
    Electronic Resource
    Maximum planar subgraphs and nice embeddings: Practical layout tools (1996)
    Springer
    Algorithmica 16 (1996), S. 33-59 
    Details
    ISSN: 1432-0541
    Keywords: Maximum planar subgraph ; Planar subgraph polytope ; Facets ; Branch and cut
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In automatic graph drawing a given graph has to be laid out in the plane, usually according to a number of topological and aesthetic constraints. Nice drawings for sparse nonplanar graphs can be achieved by determining a maximum planar subgraph and augmenting an embedding of this graph. This approach appears to be of limited value in practice, because the maximum planar subgraph problem is NP-hard. We attack the maximum planar subgraph problem with a branch-and-cut technique which gives us quite good, and in many cases provably optimum, solutions for sparse graphs and very dense graphs. In the theoretical part of the paper, the polytope of all planar subgraphs of a graphG is defined and studied. All subgraphs of a graphG, which are subdivisions ofK 5 orK 3,3, turn out to define facets of this polytope. For cliques contained inG, the Euler inequalities turn out to be facet-defining for the planar subgraph polytope. Moreover, we introduce the subdivision inequalities,V 2k inequalities, and the flower inequalities, all of which are facet-defining for the polytope. Furthermore, the composition of inequalities by 2-sums is investigated. We also present computational experience with a branch-and-cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision ofK 5 orK 3,3. These structures give us inequalities which are used as cutting planes. Finally, we try to convince the reader that the computation of maximum planar subgraphs is indeed a practical tool for finding nice embeddings by applying this method to graphs taken from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02086607
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  • 2
    Electronic Resource
    Electronic Resource
    Dynamische In-vivo- Anpreßdruckmessung zur Qualitätskontrolle der Kompressionsstrümpfe (1997)
    Springer
    Der Hautarzt 48 (1997), S. 471-476 
    Details
    ISSN: 1432-1173
    Keywords: Schlüsselwörter Kompressionstherapie ; Dynamische Anpreßdruckmessung ; Mikrodruckmeßsonde ; Compliance ; Key words Compression therapy ; Dynamic pressure measurement ; Piezometric microprobe ; Compliance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Summary The well-documented positive effect of compression stocking therapy on the venous macro- and microhemodynamics of the legs can only be attained if the stockings fit well. In order to determine the effective pressure exerted by compression stockings, we usually deleted in US journals. One can get this out of journal and author’s address have developed a new measuring method based on piezoresistant microprobes and a microprocessor unit. With our 2-mm-thick, 5-mm diameter probe, the pressure between the compression stocking and skin can be measured at any location desired. A temporal resolution of 50 Hz makes it possible to carry out dynamic measurements while the patient is walking or performing exercises on tiptoes. Here we present 4 typical cases out of a total of over 80 which we have evaluated. We have decided empirically that the pressure exerted by a class-2 compression stocking on the skin at the height of the ankles (b-position) should not exceed 70 mm Hg while resting and a peak of 110 mm Hg while exercising on tiptoes. At the middle of the calf (c-position) these values should not exceed 60 mm Hg at rest and 80 mm Hg on tiptoes. The pressure should decrease from the distal to proximal direction in order to produce a drainage gradient. We have found empirically that a pressure gradient of 30–40% from the b to the c measurement is favorable. Too high a proximal pressure or too high a pressure on a part of the lower leg causes pain and swelling. Too low a pressure, on the other hand, does not produce the desired vascular effect and alleviation of symptoms. Although dynamic pressure measurements take about 20–30 minutes per leg, they markedly improve patient compliance with compression therapy.
    Notes: Zusammenfassung Die gut dokumentierte günstige Wirkung der Kompressionstherapie mit Kompressionsstrümpfen auf die venöse Makro- und Mikrohaemodynamik der Beine läßt sich nur mit gut angepaßten Strümpfen erreichen. Um den effektiven Anpreßdruck zu bestimmen, wurde an der Universitäts-Hautklinik Tübingen eine neue Meßmethode, basierend auf piezoresistiven Mikromeßsonden und einer Mikroprozessoreinheit, entwickelt. Der Anpreßdruck zwischen Kompressionsstrumpf und Haut kann mit den 2 mm dicken und 5 mm im Durchmesser großen Sonden an beliebigen Hautarealen gemessen werden. Die zeitliche Auflösung von 50 Hz erlaubt dynamische Messungen beim Gehen oder bei Zehenspitzenständen. Es werden hier 4 typische Fallbeispiele aus bisher über 80 Messungen dargestellt. Empirisch wurde ermittelt, daß der Anpreßdruck eines Strumpfes mit Kompressionsklasse 2 auf die Haut auf Knöchelhöhe (b-Maß) 70 mmHg in Ruhe und 110 mmHg Spitzendruck bei Zehenspitzenständen bzw. 60 mmHg in Ruhe und 80 mmHg bei Zehenständen in Wadenmitte (c-Maß) nicht überschreiten sollte. Der Anpreßdruck soll von distal nach proximal abfallen, um entstauend zu wirken. Empirisch wurden Druckdifferenzen von 30–40% vom b- zum d-Maß als günstig ermittelt. Zu hohe proximale Drucke bzw. zu hohe Drucke an einem Unterschenkelsegment verursachen Schmerzen und Schwellung. Zu niedrige Drucke führen nicht zur Entstauung und gewünschten Beschwerdelinderung. Die Compliance der Patienten hinsichtlich der Kompressionstherapie läßt sich durch eine dynamische Anpreßdruckmessung, die allerdings etwa 20–30 min Zeit pro Bein in Anspruch nimmt, deutlich verbessern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001050050612
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    Paper (German National Licenses)
    Fulltext
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