Max-min weight balanced connected partition

For a connected graph and a positive integral vertex weight function , a max-min weight balanced connected -partition of , denoted as , is a partition of into disjoint vertex subsets such that each (the subgraph of induced by ) is connected, and is maximum. Such a problem has a lot of applications i...

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Bibliographic Details
Published in:Journal of global optimization Vol. 57; no. 4; pp. 1263 - 1275
Main Authors: Wang, Lele, Zhang, Zhao, Wu, Di, Wu, Weili, Fan, Lidan
Format: Journal Article
Language:English
Published: Boston Springer US 01.12.2013
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Approximation
Balancing
Computer Science
Graphs
Image processing
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
FPTAS
Balanced connected partition
Pseudo-polynomial time algorithm
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:For a connected graph and a positive integral vertex weight function , a max-min weight balanced connected -partition of , denoted as , is a partition of into disjoint vertex subsets such that each (the subgraph of induced by ) is connected, and 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 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 . A step-stone for the analysis of the FPTAS depends on a lower bound for the optimal value of 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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-0028-8