TY - GEN
T1 - Balanced k-colorings
AU - Biedl, Therese C.
AU - Čenek, Eowyn
AU - Chan, Timothy M.
AU - Demaine, Erik D.
AU - Demaine, Martin L.
AU - Fleischer, Rudolf
AU - Wang, Ming Wei
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
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U2 - 10.1007/3-540-44612-5_16
DO - 10.1007/3-540-44612-5_16
M3 - Conference contribution
AN - SCOPUS:84959204758
SN - 3540679014
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 202
EP - 211
BT - Mathematical Foundations of Computer Science 2000 - 25th International Symposium, MFCS 2000 , Proceedings
A2 - Rovan, Branislav
A2 - Nielsen, Mogens
PB - Springer
T2 - 25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000
Y2 - 28 August 2000 through 1 September 2000
ER -