Max-min weight balanced connected partition

Lele Wang, Zhao Zhang (), Di Wu, Weili Wu and Lidan Fan

Journal of Global Optimization, 2013, vol. 57, issue 4, 1263-1275

Abstract: For a connected graph $$G=(V,E)$$ and a positive integral vertex weight function $$w$$ , a max-min weight balanced connected $$k$$ -partition of $$G$$ , denoted as $$BCP_k$$ , is a partition of $$V$$ into $$k$$ disjoint vertex subsets $$(V_1,V_2,\ldots ,V_k)$$ such that each $$G[V_i]$$ (the subgraph of $$G$$ induced by $$V_i$$ ) is connected, and $$\min _{1\le i\le k}\{w(V_i)\}$$ is maximum. Such a problem has a lot of applications in image processing and clustering, and was proved to be NP-hard. In this paper, we study $$BCP_k$$ on a special class of graphs: trapezoid graphs whose maximum degree is bounded by a constant. A pseudo-polynomial time algorithm is given, based on which an FPTAS is obtained for $$k=2,3,4$$ . A step-stone for the analysis of the FPTAS depends on a lower bound for the optimal value of $$BCP_k$$ in terms of the total weight of the graph. In providing such a lower bound, a byproduct of this paper is that any 4-connected trapezoid graph on at least seven vertices has a 4-contractible edge, which may have a value in its own right. Copyright Springer Science+Business Media New York 2013

Keywords: Balanced connected partition; Pseudo-polynomial time algorithm; FPTAS (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10898-012-0028-8 (text/html)
Access to full text is restricted to subscribers.

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:jglopt:v:57:y:2013:i:4:p:1263-1275

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-012-0028-8

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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