{"title":"The Disjoint Cliques Problem","authors":"K. Jansen, Petra Scheffler, G. Woeginger","doi":"10.1051/RO/1997310100451","DOIUrl":"https://doi.org/10.1051/RO/1997310100451","url":null,"abstract":"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.","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"80 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":"133134388","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}
{"title":"The Structure Theorem for Linear Transfer Systems","authors":"P. Dierolf","doi":"10.1285/I15900932V11P119","DOIUrl":"https://doi.org/10.1285/I15900932V11P119","url":null,"abstract":"The aim of this article is to show that a few reasonable assumptions lead to a complete theory describing linear transfer systems.","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"40 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":"127656567","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}
{"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}
{"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}
{"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}
{"title":"Discrete Tomography: Determination of Finite Sets by X-Rays","authors":"R. Gardner, P. Gritzmann","doi":"10.1090/S0002-9947-97-01741-8","DOIUrl":"https://doi.org/10.1090/S0002-9947-97-01741-8","url":null,"abstract":"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.","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"95-13 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":"129882199","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}
{"title":"Convergence of Disturbed Martingales and a Stochastic Model for Annuity Funds","authors":"Richard Rödler","doi":"10.1080/15326349908807522","DOIUrl":"https://doi.org/10.1080/15326349908807522","url":null,"abstract":"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.","PeriodicalId":142744,"journal":{"name":"Universität Trier, Mathematik/Informatik, Forschungsbericht","volume":"65 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":"116169243","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}