SDP-based bounds for graph partition via extended ADMM

Angelika Wiegele () and Shudian Zhao ()
Additional contact information
Angelika Wiegele: Alpen-Adria-Universität Klagenfurt
Shudian Zhao: Alpen-Adria-Universität Klagenfurt

Computational Optimization and Applications, 2022, vol. 82, issue 1, No 10, 291 pages

Abstract: Abstract We study two NP-complete graph partition problems, k-equipartition problems and graph partition problems with knapsack constraints (GPKC). We introduce tight SDP relaxations with nonnegativity constraints to get lower bounds, the SDP relaxations are solved by an extended alternating direction method of multipliers (ADMM). In this way, we obtain high quality lower bounds for k-equipartition on large instances up to $$n =1000$$ n = 1000 vertices within as few as 5 min and for GPKC problems up to $$n=500$$ n = 500 vertices within as little as 1 h. On the other hand, interior point methods fail to solve instances from $$n=300$$ n = 300 due to memory requirements. We also design heuristics to generate upper bounds from the SDP solutions, giving us tighter upper bounds than other methods proposed in the literature with low computational expense.

Keywords: Graph partitioning; Semidefinite programming; ADMM; Combinatorial optimization (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00355-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00355-1

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00355-1

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().