NDLI: The maximum cut problem on blow-ups of multiprojective spaces

Content Provider	Springer Nature Link
Author	Junca, Mauricio Velasco, Mauricio
Copyright Year	2013
Abstract	The maximum cut problem for a quintic del Pezzo surface Bl$_{4}$(ℙ$^{2}$) asks: Among all partitions of the 10 exceptional curves into two disjoint sets, what is the largest possible number of pairwise intersections? In this article we show that the answer is 12. More generally, we obtain bounds for the maximum cut problem for the minuscule varieties X $_{ a,b,c }$:=Bl$_{ b+c }$((ℙ$^{ c−1}$)$^{ a−1}$) studied by Mukai and Castravet-Tevelev and show that these bounds are asymptotically sharp for infinite families and exact in some cases. The key to our results is the fact that certain natural embeddings of the classes of (−1)-divisors on these varieties are optimal for the semidefinite relaxation of the maximum cut problem on graphs proposed by Goemans and Williamson. These results are a new optimality property of Weyl orbits of root systems of type A,D and E. Motivated by our results on the varieties X $_{ a,b,c }$ we show that the Goemans–Williamson maxcut stochastic approximation algorithm has provably optimal asymptotic performance in symmetric strongly regular graphs of bounded spectra, in marked contrast with its worst-case behavior.
Starting Page	797
Ending Page	827
Page Count	31
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	38
Issue Number	4
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2013-02-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Maximum cut problem Blow-ups of multiprojective space Goemans–Williamson algorithm Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Designs in Grassmannian Spaces and Lattices

Ambient Spaces of Dimensional Dual Arcs

Discrete Polymatroids

Semimodular Lattices and Semibuildings

Orthogonal Matroids

Planar Groups

Genomic tableaux

Symplectic Matroids

Andrei Zelevinsky

The maximum cut problem on blow-ups of multiprojective spaces

Similar Documents

Designs in Grassmannian Spaces and Lattices

Ambient Spaces of Dimensional Dual Arcs

Discrete Polymatroids

Semimodular Lattices and Semibuildings

Orthogonal Matroids

Planar Groups

Genomic tableaux

Symplectic Matroids

Andrei Zelevinsky

The maximum cut problem on blow-ups of multiprojective spaces