The Steiner Problem in a Space with a Minkowski Metrics and its Application to Printed Circuit Design

Cezary Stępień

Abstract

The Steiner Problem is one of problems related to tracing connections on a printed circuit board. In the work, an approach basing on Minkowski metrics idea is shown. This metrics makes possible to shorten the length of paths through tracing them not only in two mutually perpendicular directions, but also in the other given ones. There is described the way, how one can pass from the conception of a unity cost in a given direction to the Minkowski metrics. Next, there is presented the Steiner Problem with an assumption that the unity sphere is only convex and symmetrical. In last part, algorithms of finding Steiner points for certain classes of Minkowski spaces, particularly useful to designing PC-board, are presented.
Diploma typeDoctor of Philosophy
Author Cezary Stępień (FEIT / IN)
Cezary Stępień,,
- The Institute of Computer Science
Title in EnglishThe Steiner Problem in a Space with a Minkowski Metrics and its Application to Printed Circuit Design
Languagepl polski
Certifying UnitFaculty of Electonics (FEIT)
Start date25-09-1979
Defense Date31-05-1983
End date21-06-1983
Supervisor Jan Zabrodzki (FEIT / IN)
Jan Zabrodzki,,
- The Institute of Computer Science

Internal reviewers Wiesław Traczyk (FEIT / AK)
Wiesław Traczyk,,
- The Institute of Control and Computation Engineering
External reviewers Jacek Bańkowski
Jacek Bańkowski,,
-
Pages140
Keywords in EnglishSteiner Problem, Minkowski metrics, Designing printed circuit boards
Abstract in EnglishThe Steiner Problem is one of problems related to tracing connections on a printed circuit board. In the work, an approach basing on Minkowski metrics idea is shown. This metrics makes possible to shorten the length of paths through tracing them not only in two mutually perpendicular directions, but also in the other given ones. There is described the way, how one can pass from the conception of a unity cost in a given direction to the Minkowski metrics. Next, there is presented the Steiner Problem with an assumption that the unity sphere is only convex and symmetrical. In last part, algorithms of finding Steiner points for certain classes of Minkowski spaces, particularly useful to designing PC-board, are presented.
KBN classificationInformatyka

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