منابع مشابه
A Lower Bound on Opaque Sets
We prove a lower bound of 2.00002 on the the total length of a set (of curves) that intersects every line that intersects the unit square. The best known lower bound has been 2, established by Jones in 1964.
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An opaque set (or a barrier) for U ⊆ R is a set B of finite-length curves such that any line intersecting U also intersects B. In this paper, we consider the lower bound for the shortest barrier when U is the unit equilateral triangle. The known best lower bound for triangles is the classic one by Jones [9], which exhibits that the length of the shortest barrier for any convex polygon is at lea...
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Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the length of a shortest path connecting p and q in G divided by their Euclidean distance |pq|. The maximum detour over all pairs of points is called the geometric dilation δ(G). EbbersBaumann, Grüne and Klein have shown that every finite point set is contained in a pla...
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Let LD(G) denote the minimum cardinality of a locating-dominating set for graph G. If T is a tree of order n with l leaf vertices and s support vertices, then a known lower bound of Blidia, Chellali, Maffray, Moncel and Semri [Australas. J. Combin. 39 (2007), 219–232] is LD(T ) ≥ (n+ 1 + l − s)/3 . In this paper, we show that LD(T ) ≥ (n+ 1 + 2(l − s))/3 and these bounds are sharp. We construct...
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This paper provides upper and lower bounds on the information rates achievable with a minimum mean square error (MMSE) Tomlinson-Harashima precoder (THP) assuming ideal interleaving. We also give an exact formula for zero-forcing (ZF) THP achievable information rates. At high SNR, the performance of the MMSE-THP and the ZF-THP identically suuer only the 2.55 bit or 1.53 dB \shaping" loss from c...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2019
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2019.01.002