Nicht aus der Schweiz? Besuchen Sie lehmanns.de
Pedigree Polytopes - Tirukkattuppalli Subramanyam Arthanari

Pedigree Polytopes (eBook)

New Insights on Computational Complexity of Combinatorial Optimisation Problems
eBook Download: PDF
2023 | 2023
XXV, 221 Seiten
Springer Nature Singapore (Verlag)
978-981-19-9952-9 (ISBN)
Systemvoraussetzungen
160,49 inkl. MwSt
(CHF 156,80)
Der eBook-Verkauf erfolgt durch die Lehmanns Media GmbH (Berlin) zum Preis in Euro inkl. MwSt.
  • Download sofort lieferbar
  • Zahlungsarten anzeigen

This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.

This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question.

This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in these proofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.



Tiru Arthanari is serving the Department of Information Systems and Operations Management, University of Auckland, Auckland, New Zealand, contributing to the research environment. Tiru was awarded the International Anassilaos Award, Renato Calapso Prize for mathematics, at Reggio Calabria, Italy, in 2014. He received the 'Lifetime Achievement Award' from the Operations Research Society of India (ORSI) for outstanding contributions towards the promotion of operations research in India. Tiru was Head of the Indian Statistical Institute, Bangalore Centre, before moving to New Zealand. He has international recognition for his research showing most statistical problems are essentially constrained optimization problems, from his Wiley classic book, 'Mathematical programming in statistics' (with Y Dodge).

Tiru is Fellow and Life Member of the Indian Society for Probability and Statistics and Fellow and Life Member of the Operations Research Society of India. Tiru Arthanari is Adjunct Professor at C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science (AIMSCS, Hyderabad, India). He was elected as a corresponding member to the Accademia Peloritana Dei Pericolanti, established in 1729 in Sicily. He received the best paper award in 2016 for his paper published in JAIS. Tiru received the Research Excellence Award 2017 from the Business school. Tiru has published research articles in Discrete Mathematics, Discrete Applied Mathematics, Annals of Operations Research, European Journal of Operations Research, Discrete Optimization, Journal of the Association for Information Systems, International Journal of Production Economics, Journal of Cleaner Production, Journal of Operations & Production Management, Applied Economics, and Quality Engineering, among others.


This book defines and studies a combinatorial object called the pedigree and develops the theory for optimising a linear function over the convex hull of pedigrees (the Pedigree polytope). A strongly polynomial algorithm implementing the framework given in the book for checking membership in the pedigree polytope is a major contribution.This book challenges the popularly held belief in computer science that a problem included in the NP-complete class may not have a polynomial algorithm to solve. By showing STSP has a polynomial algorithm, this book settles the P vs NP question.This book has illustrative examples, figures, and easily accessible proofs for showing this unexpected result. This book introduces novel constructions and ideas previously not used in the literature. Another interesting feature of this book is it uses basic max-flow and linear multicommodity flow algorithms and concepts in theseproofs establishing efficient membership checking for the pedigree polytope. Chapters 3-7 can be adopted to give a course on Efficient Combinatorial Optimization. This book is the culmination of the author's research that started in 1982 through a presentation on a new formulation of STSP at the XIth International Symposium on Mathematical Programming at Bonn.
Erscheint lt. Verlag 27.3.2023
Zusatzinfo XXV, 221 p. 83 illus., 50 illus. in color.
Sprache englisch
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
Wirtschaft Betriebswirtschaft / Management Planung / Organisation
Schlagworte Combinatorial Optimisation • combinatorial optimization • Computational Complexity • efficient algorithm • Good algorithm • Maximal flow problem • np-completeness • NP vs P • Pedigree Polytopes • polyhedral combinatorics • Polynomial Solvability • Polynomial Time Algorithms • Symmetric Traveling Salesman Problem
ISBN-10 981-19-9952-X / 981199952X
ISBN-13 978-981-19-9952-9 / 9789811999529
Haben Sie eine Frage zum Produkt?
PDFPDF (Wasserzeichen)
Größe: 4,7 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasser­zeichen und ist damit für Sie persona­lisiert. Bei einer missbräuch­lichen Weiter­gabe des eBooks an Dritte ist eine Rück­ver­folgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seiten­layout eignet sich die PDF besonders für Fach­bücher mit Spalten, Tabellen und Abbild­ungen. Eine PDF kann auf fast allen Geräten ange­zeigt werden, ist aber für kleine Displays (Smart­phone, eReader) nur einge­schränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Mehr entdecken
aus dem Bereich
Discover tactics to decrease churn and expand revenue

von Jeff Mar; Peter Armaly

eBook Download (2024)
Packt Publishing (Verlag)
CHF 24,60