Polylogarithmic factor
Weba polylogarithmic factor better than cubic [1], we cannot obtain preprocessing time better than n3/2 and query time better than √ n simultaneously by purely combinatorial techniques with current knowledge, except for polylogarithmic-factor speedups. In view of the above hardness result, it is therefore worthwhile to pursue more modest WebWe develop new approximation algorithms for classical graph and set problems in the RAM model under space constraints. As one of our main results, we devise an algorithm for that runs in time , uses bits of space, an…
Polylogarithmic factor
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Webthe similarity graph) and ~cis a polylogarithmic factor in ndepending on p q. Although valuable in establishing su cient conditions for data to be clusterable, these results are not immediately applicable to data sets seen in many applications, particularly those arising from the analysis of social networks. For example, statistical analysis of ... WebIn mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n, () + () + + () +.The notation log k n is often used as a shorthand for (log n) k, analogous to sin 2 θ …
WebNov 21, 2008 · The algorithm is based on a new pivoting strategy, which is stable in practice. The new algorithm is optimal (up to polylogarithmic factors) in the amount of … WebApr 13, 2024 · A new estimator for network unreliability in very reliable graphs is obtained by defining an appropriate importance sampling subroutine on a dual spanning tree packing of the graph and an interleaving of sparsification and contraction can be used to obtain a better parametrization of the recursive contraction algorithm that yields a faster running time …
Webwhere the Θ ˜ $$ \tilde{\Theta} $$-notation suppresses polylogarithmic factors, that is, extra factors of form (log n) O (1) $$ {\left(\log n\right)}^{O(1)} $$. Furthermore, in the extra polylogarithmic factors are only needed when 1 − o (1) ≤ 4 n p 2 / log n ≤ 2 + o (1) $$ 1-o(1)\le 4n{p}^2/\log n\le 2+o(1) $$.
Webdemonstrating that our result is optimal up to polylogarithmic factors (see Section 6 for details). Theorem 8. Let AND-ORd,ndenote the d-level AND-OR tree onnvariables. Then deg(AND-ORg d,n) = Ω n1/2/log(d−2)/2 n for any constant d>0. Proof Idea. To introduce our proof technique, we first describe the metho d used in [15] to construct an
WebJan 1, 1998 · We consider noninteractive zero-knowledge proofs in the shared random string model proposed by Blum et al. [5]. Until recently there was a sizable polynomial gap … port city castings corporationWebup to a logarithmic factor (or constant factor when t = Ω(n)). We also obtain an explicit protocol that uses O(t2 ·log2 n) random bits, matching our lower bound up to a polylogarithmic factor. We extend these results from XOR to general symmetric Boolean functions and to addition over a finite Abelian group, showing how to amortize the ... irish rover songsWebk-median and k-means, [17] give constant factor approximation algorithms that use O(k3 log6 w) space and per point update time of O(poly(k;logw)).1 Their bound is polylogarithmic in w, but cubic in k, making it impractical unless k˝w.2 In this paper we improve their bounds and give a simpler algorithm with only linear dependency of k. port city blue portlandWebDec 3, 2024 · We show that with high probability G p contains a complete minor of order $\tilde{\Omega}(\sqrt{k})$ , where the ~ hides a polylogarithmic factor. Furthermore, in the case where the order of G is also bounded above by a constant multiple of k, we show that this polylogarithmic term can be removed, giving a tight bound. port city car wash port wentworth gaWebThe polylogarithmic factor can be avoided by instead using a binary gcd. Share. Improve this answer. Follow edited Aug 8, 2024 at 20:51. answered Oct 20, 2010 at 18:20. Craig Gidney … port city cafe portsmouth ohioWebDec 29, 2024 · In the special case of a spherical constraint, which arises in generalized eigenvector problems, we establish a nonasymptotic finite-sample bound of $\sqrt{1/T}$, … port city cafe biloxi ms menuWebJan 27, 2024 · Nonconvex optimization with great demand of fast solvers is ubiquitous in modern machine learning. This paper studies two simple accelerated gradient methods, … port city carrier