Pub Date : 1900-01-01DOI: 10.1051/RO/1997310100451
K. Jansen, Petra Scheffler, G. Woeginger
Given a graph G = (V, E), we consider the problem of finding a set of D pairwise disjoint cliques in the graph with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness of this problem for undirected path graphs. Moreover, we investigate a closely related scheduling problem. Given D times units, we look for a sequence of workers w 1 ,...,w K and a partition J 1 ,..., J k of the job set such that J i can be executed by w i within D time units. The goal is to find a sequence with minimum total wage of the workers.
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Pub Date : 1900-01-01DOI: 10.1285/I15900932V11P119
P. Dierolf
The aim of this article is to show that a few reasonable assumptions lead to a complete theory describing linear transfer systems.
这篇文章的目的是表明，一些合理的假设导致一个完整的理论描述线性传递系统。
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Pub Date : 1900-01-01DOI: 10.1007/978-3-642-57014-8_15
N. Lehdili, C. O. A. Salem
{"title":"Proximal Methods: Decomposition and Selection","authors":"N. Lehdili, C. O. A. Salem","doi":"10.1007/978-3-642-57014-8_15","DOIUrl":"https://doi.org/10.1007/978-3-642-57014-8_15","url":null,"abstract":"","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"21 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114038781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-642-79958-7_44
C. Meinel
{"title":"Die Entwicklung der Informatik braucht Theorie und Praxis. Ein Fallbeispiel aus dem CAD-Schaltkreisentwurf","authors":"C. Meinel","doi":"10.1007/978-3-642-79958-7_44","DOIUrl":"https://doi.org/10.1007/978-3-642-79958-7_44","url":null,"abstract":"","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125513244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-94-011-0924-6_17
P. Gritzmann, V. Klee
{"title":"On the Complexity of some Basic Problems in Computational Convexity: II. Volume and mixed volumes","authors":"P. Gritzmann, V. Klee","doi":"10.1007/978-94-011-0924-6_17","DOIUrl":"https://doi.org/10.1007/978-94-011-0924-6_17","url":null,"abstract":"","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131374165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1090/S0002-9947-97-01741-8
R. Gardner, P. Gritzmann
We study the determination of finite subsets of the integer lattice En, n > 2, by X-rays. In this context, an X-ray of a set in a direction u gives the number of points in the set on each line parallel to u. For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory and convexity, we prove that there are four prescribed lattice directions such that convex subsets of En (i.e., finite subsets F with F = En n conv F) are determined, among all such sets, by their X-rays in these directions. We also show that three X-rays do not suffice for this purpose. This answers a question of Larry Shepp, and yields a stability result related to Hammer's X-ray problem. We further show that any set of seven prescribed mutually nonparallel lattice directions in 22 have the property that convex subsets of 22 are determined, among all such sets, by their X-rays in these directions. We also consider the use of orthogonal projections in the interactive technique of successive determination, in which the information from previous projections can be used in deciding the direction for the next projection. We obtain results for finite subsets of the integer lattice and also for arbitrary finite subsets of Euclidean space which are the best possible with respect to the numbers of projections used.
研究了用x射线确定整数格En, n > 2的有限子集。在这种情况下，集合在u方向上的x射线给出了集合中平行于u的每条线上的点的个数。由于实际原因，只允许在晶格方向上的x射线，即平行于晶格中非零向量的方向。结合代数数论和凸性的方法，证明了有四个规定的格方向，使得En的凸子集(即F = enn conv F的有限子集F)在所有这样的集合中，由它们在这些方向上的x射线决定。我们还表明，三张x光片不足以达到这个目的。这回答了Larry Shepp的一个问题，并得出了与Hammer的x射线问题相关的稳定性结果。我们进一步证明了22中七个规定的相互不平行晶格方向的任何集合具有22的凸子集在所有这些集合中由它们在这些方向上的x射线决定的性质。我们还考虑在连续确定的交互技术中使用正交投影，其中从先前的投影信息可以用于确定下一个投影的方向。对于整数格的有限子集和欧几里德空间的任意有限子集，我们得到了关于所使用的投影数的最佳可能的结果。
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Pub Date : 1900-01-01DOI: 10.1080/15326349908807522
Richard Rödler
Our aim is a stochastic model for the average income of a given annuity fund. Therefore we consider a special kind of stochastic process {X n : n ∈ IN} satisfying a condition of the form: E(X n+1 |F n ) = α n X n + β n [P] for all n ∈ IN. (0.1) In equation (0.1) X n+1 denotes the income of the annuity fund at time n+ 1 (future) and F n is the information about the money market up to time n (present). We wish to find conditions under which such a stochastic process is P-almost surely convergent and to determine whether or not there is a limiting income from our annuity fund. The question of L 1 -convergence is also considered.
我们的目标是建立一个给定年金基金平均收入的随机模型。因此，我们考虑一类特殊的随机过程{X n: n∈IN}满足E(X n+1 |F n) = α n X n+ β n [P]对于所有n∈IN。(0.1)式(0.1)中，X n+1表示n+1时刻(未来)的年金基金收益，F n表示截至n时刻(现在)的货币市场信息。我们希望找到这样一个随机过程p -几乎肯定收敛的条件，并确定我们的年金基金是否存在限制收益。本文还考虑了L - 1收敛性问题。
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