Premium
Flow‐dependent networks: Existence and behavior at Steiner points
Author(s) -
Cox Christopher L.
Publication year - 1998
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199805)31:3<149::aid-net1>3.0.co;2-f
Subject(s) - flow (mathematics) , flow network , boundary (topology) , steiner tree problem , mathematics , computer science , function (biology) , combinatorics , mathematical optimization , topology (electrical circuits) , geometry , mathematical analysis , evolutionary biology , biology
Given boundary points, prescribed flows between each pair of boundary points, and a cost per unit length as a function of flow, we seek a cost‐minimizing network. Such flow‐dependent networks model, e.g., traffic networks with a given flow of traffic between pairs of cities or communication networks with a given number of channels between pairs of locations. We prove the existence of cost‐minimizing networks, study their junctions, and prove that edges can meet in fours as well as in threes. © 1998 John Wiley & Sons, Inc. Networks 31: 149–156, 1998