Polylogarithmic factor
WebWe give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and … WebJun 11, 2016 · This improves over the best previously known bound of ~O(n/k) [Klauck et al., SODA 2015], and is optimal (up to a polylogarithmic factor) in view of an existing lower bound of ~Ω(n/k2). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms.
Polylogarithmic factor
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WebRESEARCH ISSN 0249-6399 ISRN INRIA/RR--8261--FR+ENG REPORT N° 8261 March 2013 Project-Team Vegas Separating linear forms for bivariate systems Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier Webup 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 ...
WebDec 23, 2013 · Moreover, our method matches up to polylogarithmic factors a theoretical limit established by Nesterov and Nemirovski in 1994 regarding the use of a "universal … WebHence, we achieve the same time bound as matching but increase the space by an (n) factor. We can improve the time by polylogarithmic factors using faster algorithms for matching [3, 4,6,7,23 ...
WebJan 27, 2024 · Nonconvex optimization with great demand of fast solvers is ubiquitous in modern machine learning. This paper studies two simple accelerated gradient methods, … 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 …
WebText indexing is a classical algorithmic problem that has been studied for over four decades: given a text T, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in T in time proportional to the query’s length. The earliest optimal-time solution to the problem, the suffix tree, dates back to …
WebAbstract. A new parallel algorithm for the maximal independent set problem is constructed. It runs in O ( log 4 n) time when implemented on a linear number of EREW-processors. This is the first deterministic algorithm for the maximal independent set problem (MIS) whose running time is polylogarithmic and whose processor-time product is optimal ... cinebench r23 world rankingWebWe analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, -norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number of arithmetic operations, they match the current time complexity of multiplying two -by- matrices (up to polylogarithmic factors). … diabetic nephropathy lab findingsWebFor the case where the diameter and maximum degree are small, we give an alternative strategy in which we first discover the latencies and then use an algorithm for known latencies based on a weighted spanner construction. (Our algorithms are within polylogarithmic factors of being tight both for known and unknown latencies.) cinebench r23 windows armWebdemonstrating 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 cinebench r23 reviewsWebthe 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 ... diabetic nephropathy laboratory findingsWebsu ciently large polylogarithmic factor ClogC(n). These factors are made precise later in the paper. Our algorithmic part is a reduction of the general case to the setting of Theorem 3.3. This is achieved by repeatedly removing almost divisors (i.e., nding an almost divisor dand replacing Xby X(d)=d). Theorem 3.4. (Algorithmic Part, Informal) diabetic nephropathy medical treatmentWebMay 21, 2024 · The energy of a Mead memory architecture and a mesh network memory architecture are analyzed and it is shown that a processor architecture using these memory elements can reach the decoding energy lower bounds to within a polylogarithmic factor. Similar scaling rules are derived for polar list decoders and belief propagation decoders. cinebench r23 スコアが低い