We study the problem of discrepancy of finite point sets in the unit square with respect to convex polygons, when the directions of the edges are fixed, when the number of edges is bounded, as well as when no such restrictions are imposed. In all three cases, we obtain estimates for the supremum norm that are very close to best possible. © 2007 Elsevier Inc. All rights reserved.
Chen, W., Travaglini, G. (2007). Discrepancy with respect to convex poygons. JOURNAL OF COMPLEXITY, 23(4-6), 662-672 [10.1016/j.jco.2007.03.006].
Discrepancy with respect to convex poygons
TRAVAGLINI, GIANCARLO
2007
Abstract
We study the problem of discrepancy of finite point sets in the unit square with respect to convex polygons, when the directions of the edges are fixed, when the number of edges is bounded, as well as when no such restrictions are imposed. In all three cases, we obtain estimates for the supremum norm that are very close to best possible. © 2007 Elsevier Inc. All rights reserved.
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