Abstract
The clustering problem with relational constraints can be formulated as an optimal graph partitioning problem. The complexity of this latter problem depends on the graphs and on the objective function. In particular the problem of maximizing the split of a connected partition is solvable in polynomial time on complete graphs (DELATTRE and HANSEN 80) and trees (HANSEN et al. 93), and is NP-hard on grid graphs (HANSEN et al. 93, GAREY and JOHNSON 77). In this paper an algorithm that solves in O(N 2 log N) time the Maximum Split problem on a grid graph with two rows and N columns (a ladder graph) is presented. Ladder structures naturally arise whenever there are two parallel ways connected by several “bridges” or “connectors” (for instance, river banks, assembly lines, processes).
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© 2002 Springer-Verlag Berlin Heidelberg
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Lari, I. (2002). Connected Maximum Split Clustering of Ladder Graphs. In: Gaul, W., Ritter, G. (eds) Classification, Automation, and New Media. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55991-4_11
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DOI: https://doi.org/10.1007/978-3-642-55991-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43233-3
Online ISBN: 978-3-642-55991-4
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