04650nam 22008535 450 991029976350332120251116134445.03-319-13915-010.1007/978-3-319-13915-9(CKB)3710000000404012(SSID)ssj0001501644(PQKBManifestationID)11830245(PQKBTitleCode)TC0001501644(PQKBWorkID)11446476(PQKB)11448319(DE-He213)978-3-319-13915-9(MiAaPQ)EBC6312315(MiAaPQ)EBC5590871(Au-PeEL)EBL5590871(OCoLC)908105002(PPN)185490271(EXLCZ)99371000000040401220150413d2015 u| 0engurnn#008mamaatxtccrOptimal Interconnection Trees in the Plane Theory, Algorithms and Applications /by Marcus Brazil, Martin Zachariasen1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (XVII, 344 p. 150 illus., 135 illus. in color.)Algorithms and Combinatorics,0937-5511 ;29Bibliographic Level Mode of Issuance: Monograph3-319-13914-2 Preface:- 1 Euclidean and Minkowski Steiner Trees -- 2 Fixed Orientation Steiner Trees -- 3 Rectilinear Steiner Trees -- 4 Steiner Trees with Other Costs and Constraints -- 5 Steiner Trees in Graphs and Hypergraphs -- A Appendix.This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.  Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees.  The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.Algorithms and Combinatorics,0937-5511 ;29Combinatorial analysisComputer science—MathematicsGeometryMathematical optimizationAlgorithmsApplied mathematicsEngineering mathematicsCombinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Discrete Mathematics in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17028Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26008Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Mathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Combinatorial analysis.Computer science—Mathematics.Geometry.Mathematical optimization.Algorithms.Applied mathematics.Engineering mathematics.Combinatorics.Discrete Mathematics in Computer Science.Geometry.Optimization.Algorithms.Mathematical and Computational Engineering.511.52Brazil Marcusauthttp://id.loc.gov/vocabulary/relators/aut755549Zachariasen Martinauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299763503321Optimal Interconnection Trees in the Plane2523315UNINA