http://www.dagstuhl.de/13082

17. – 22. Februar 2013, Dagstuhl Seminar 13082

Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices

Organisatoren

LeRoy B. Beasley (Utah State University, US)
Hartmut Klauck (Nanyang TU – Singapore, SG)
Troy Lee (National University of Singapore, SG)
Dirk Oliver Theis (University of Tartu, EE)

Auskunft zu diesem Dagstuhl Seminar erteilt

Dagstuhl Service Team

Dokumente

Dagstuhl Report, Volume 3, Issue 2 Dagstuhl Report
Motivationstext
Teilnehmerliste
Gemeinsame Dokumente
Dagstuhl's Impact: Dokumente verfügbar
Programm des Dagstuhl Seminars [pdf]

Summary

The nonnegative rank is a measure of the complexity of a matrix that has applications ranging from Communication Complexity to Combinatorial Optimization. At the time of the proposal of the seminar, known lower bounds for the nonnegative rank were either trivial (rank lower bound) or known not to work in many important cases (bounding the nondeterministic communication complexity of the support of the matrix).

Over the past couple of years in Combinatorial Optimization, there has been a surge of interest in lower bounds on the sizes of Linear Programming formulations. A number of new methods have been developed, for example characterizing nonnegative rank as a variant of randomized communication complexity. The link between communication complexity and nonnegative rank was also instrumental recently in proving exponential lower bounds on the sizes of extended formulations of the Traveling Salesman polytope, answering a longstanding open problem.

This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of tools and methods between these fields. The focus of the seminar was on discussions, open problems and talks surveying the basic tools and techniques from each area.

In the short time since the seminar, its participants have made progress on a number of open problems.

License
  Creative Commons BY 3.0 Unported license
  LeRoy B. Beasley, Hartmut Klauck, Troy Lee, and Dirk Oliver Theis

Related Dagstuhl Seminar

Classification

  • Data Structures / Algorithms / Complexity
  • Optimization / Scheduling

Keywords

  • Communication Compleixty
  • Linear & Combinatorial Optimization
  • Matrix Theory

Buchausstellung

Bücher der Teilnehmer 

Buchausstellung im Erdgeschoss der Bibliothek

(nur in der Veranstaltungswoche).

Dokumentation

In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.

 

Download Übersichtsflyer (PDF).

Publikationen

Es besteht weiterhin die Möglichkeit, eine umfassende Kollektion begutachteter Arbeiten in der Reihe Dagstuhl Follow-Ups zu publizieren.

Dagstuhl's Impact

Bitte informieren Sie uns, wenn eine Veröffentlichung ausgehend von
Ihrem Seminar entsteht. Derartige Veröffentlichungen werden von uns in der Rubrik Dagstuhl's Impact separat aufgelistet  und im Erdgeschoss der Bibliothek präsentiert.