Bruno Nietlispach
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
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This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavaré (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. App…
For bin packing, the input consists of $n$ items with sizes $s_1,...,s_n \in [0,1]$ which have to be assigned to a minimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed techniques from discrepancy theory to find a solution using at most $OPT + O(\log OPT \cdot \log \log OPT)$ bins. In this paper, we present an approximation algorithm that has an additive gap of only $O(\log OPT)$ bins, which matches certain combinatorial lower bounds. Any further improvement would have to use more algebraic structure. Our improvement is based on …
Asymptotic structure. II. Path-width and additive quasi-isometry
该研究证明了与有界路径宽度图拟等距的图，可通过给目标图边赋非负整数长度，使原拟等距映射成为仅带加性常数误差的加性拟等距，完善了渐近结构中路径宽度与拟等距的关联理论。
Additive quasi-isometries and cacti
本文证明不含胖θ曲线的测地度量空间与仙人掌图存在加法拟等距，并由此推出所有拟等距于仙人掌图的空间亦然。
We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the bound on a previous result of the authors. Density conditions on subsets of the natural numbers that imply the existence of approximate powers of arithmetic progressions are developed and explored.
The investigation of the pair correlation statistics of sequences was initially motivated by questions concerning quasi-energy-spectra of quantum systems. However, the subject has been developed far beyond its roots in mathematical physics, and many challenging number-theoretic questions on the distribution of the pair correlations of certain sequences are still open. We give a short introduction into the subject, recall some known results and open problems, and in particular explain the recently established connection between the distribution of pair correlations of sequences on the torus and…
In the late 1990s, Kim and Vu pioneered an inductive method for showing concentration of certain random variables X. Shortly afterwards, Janson and Ruci{ń}ski developed an alternative inductive approach, which often gives comparable results for the upper tail Pr(X \ge (1+\eps) E[X]). In some cases, both methods yield upper tail estimates which are best possible up to a logarithmic factor in the exponent, but closing this narrow gap has remained a technical challenge. In this paper we present a BK-inequality based combinatorial sparsification idea that can recover this missing logarithmic term …
$K_{2,3}$-induced minor-free graphs admit quasi-isometry with additive distortion to graphs of tree-width at most two
本文提出了一种在亚二次时间内计算普遍可签名图直径的算法，通过证明$K_{2,3}$-诱导极小图可加误差地准等距于树宽至多为二的图。
Quasi-isometries between graphs with variable edge lengths
本文研究可变边长图之间的拟等距映射，并否定了 Nguyen、Scott 和 Seymour 关于通过调整目标图边长和加性畸变常数即可消除乘性畸变因子的猜想。
Additive Quasi-isometry via rooted graph partitions and layering partition
本文证明：若两图强等距路径复杂度有界且存在良好根化的有界划分，则存在树宽不超过目标的图，使源图与其有加性拟等距，并解决开放问题。
We study s(k,n), the maximum size of A+A where A is a k-subset of [n]. A few known functions from additive number theory can be expressed via s(k,n). For example, our estimates of s(k,n) imply new bounds on the maximum size of quasi-Sidon sets, a problem posed by Erdos and Freud [J. Number Th.38 (1991) 196-205]. Also, applications to so-called edge-magic labellings of graphs are given.
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