Abstract
Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers l i and ui, 1 ≤i ≤q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least l i and at most u i for each index i, 1 ≤i ≤q. The problem of finding such a “uniform” partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.
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References
Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree-decomposable graphs. J. Algorithms 12, 308–340 (1991)
Bodlaender, H.L.: Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees. J. Algorithms 11, 631–643 (1990)
Bozkaya, B., Erkut, E., Laporte, G.: A tabu search heuristic and adaptive memory procedure for political districting. European J. Operational Research 144, 12–26 (2003)
Gonzalez, R.C., Wintz, P.: Digital Image Processing. Addison-Wesley, Reading (1977)
Ito, T., Zhou, X., Nishizeki, T.: Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size. J. Discrete Algorithms 4, 142–154 (2006)
Lucertini, M., Perl, Y., Simeone, B.: Most uniform path partitioning and its use in image processing. Discrete Applied Mathematics 42, 227–256 (1993)
Takamizawa, K., Nishizeki, T., Saito, N.: Linear-time computability of combinatorial problems on series-parallel graphs. J. ACM 29, 623–641 (1982)
Tsichritzis, D.C., Bernstein, P.A.: Operating Systems. Academic Press, New York (1974)
Williams Jr., J.C.: Political redistricting: a review. Papers in Regional Science 74, 13–40 (1995)
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© 2006 Springer-Verlag Berlin Heidelberg
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Ito, T., Goto, K., Zhou, X., Nishizeki, T. (2006). Partitioning a Multi-weighted Graph to Connected Subgraphs of Almost Uniform Size. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_9
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DOI: https://doi.org/10.1007/11809678_9
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