Indecomposable Coverings with Concave Polygons

被引：27
|
作者：
Palvolgyi, Domotor [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, EPFL SB IMB DCG, Stn 8, CH-1015 Lausanne, Switzerland
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2010年 / 44卷 / 03期
关键词：
Multiple coverings; Sensor networks; PLANE;
D O I：
10.1007/s00454-009-9194-y
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold covering of some point set by the translates of this polygon that cannot be decomposed into two coverings. Moreover, we give a complete classification of open polygons with this property. We also construct for any polytope (having dimension at least three) and for any k, a k-fold covering of the space by its translates that cannot be decomposed into two coverings.
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页码：577 / 588
页数：12
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