很少的序列对就足够了：表示所有矩形位置
Few Sequence Pairs Suffice: Representing All Rectangle Placements
摘要：
我们认为，一般的非重叠放置的矩形的空间关系（西，南，东，北）对矩形的表示。如果一组表示包含$n$矩形的每一个布局的表示，我们称它为完备的。证明了关于表示完备集的最小基数的$\mathcal{O}(\frac{n!}{n^6} \cdot (\frac{11+5 \sqrt 5}{2})^n)$的一个新的上界和$Ω(\frac{n!}{n^4} \cdot (4 + 2 \sqrt2)^n)$的一个新的下界.这些结果的证明中的一个关键概念是避免模式的排列。新的上界直接改进了著名的序列对表示，它的大小为$(n!)^2$，只考虑一组有限的序列对。这意味着理论上更快的算法VLSI布局问题。
英文摘要：
We consider representations of general non-overlapping placements of rectangles by spatial relations (west, south, east, north) of pairs of rectangles. We call a set of representations complete if it contains a representation of every placement of $n$ rectangles. We prove a new upper bound of $\mathcal{O}(\frac{n!}{n^6} \cdot (\frac{11+5 \sqrt 5}{2})^n)$ and a new lower bound of $Ω(\frac{n!}{n^4} \cdot (4 + 2 \sqrt2)^n)$ on the minimum cardinality of complete sets of representations. A key concept in the proofs of these results are pattern-avoiding permutations. The new upper bound directly improves upon the well-known sequence pair representation, which has size $(n!)^2$, by only considering a restricted set of sequence pairs. It implies theoretically faster algorithms for VLSI placement problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
