Paper by Erik D. Demaine

Therese C. Biedl, Eowyn Čenek, Timothy M. Chan, Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer, and Ming-Wei Wang, “Balanced k-Colorings”, Technical Report CS-2000-08, Department of Computer Science, University of Waterloo, March 2000.

While discrepancy theory is normally only studied in the context of 2-colorings, we explore the problem of k-coloring, for k ≥ 2, a set of vertices to minimize imbalance among a family of subsets of vertices. The imbalance is the maximum, over all subsets in the family, of the largest difference between the size of any two color classes in that subset. The discrepancy is the minimum possible imbalance. We show that the discrepancy is always at most 4d − 3, where d (the “dimension”) is the maximum number of subsets containing a common vertex. For 2-colorings, the bound on the discrepancy is at most max {2d − 3, 2}. Finally, we prove that several restricted versions of computing the discrepancy are NP-complete.

The paper is 11 pages.

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Related papers:
BalancedColoringDM (Balanced k-Colorings)
MFCS2000 (Balanced k-Colorings)

See also other papers by Erik Demaine.
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Last updated May 16, 2024 by Erik Demaine.