Polylogarithmic time

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August undefined, 2024

WebIn mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n , The notation logkn is often used as a shorthand for (log n)k, analogous to sin2θ for (sin θ)2 . In computer science, polylogarithmic functions occur as the order of time or memory used … WebJun 22, 2024 · We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated 2 O(√logn)-time algorithm of Panconesi and Srinivasan [STOC’92] and settles a central and long-standing question in distributed graph algorithms.It also leads to the first polylogarithmic-time deterministic …

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WebJun 26, 2024 · An algorithm is said to take logarithmic time if T(n) = O(log n).. An algorithm is said to run in polylogarithmic time if T(n) = O((log … WebDynamic graph connectivity in polylogarithmic worst case time (PDF, slides) Fully Dynamic 2-Edge Connectivity Algorithm in Polylogarithmic Time per Operation ; Lists of connectivity problems; Maintaining Dynamic Sequences under Equality Tests in Polylogarithmic Time . Distances and point-sets: china rain of worms

Zero-Knowledge IOPs with Linear-Time Prover and Polylogarithmic …

WebIn particular, for any m polynomial in n, an explicit global obstruction set S n,m can be constructed in time polynomial in n and, more strongly, in polylogarithmic time (in n) using polynomial number of processors. The proof of the strong flip theorem depends critically on the characterization by symmetries of the permanent as per the property ... In computational complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors. In other words, a problem with input size n is in NC if there exist constants c and k such that it can be solved in time O(log n) using O(n ) parallel processors. Stephen Cook coined the name "Nick's class" after Nick Pippenger, who had done extensive research on circuits with polyl… 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 … china rains worms

Polylogarithmic-Time Deterministic Network Decomposition and ...

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WebJul 25, 2024 · We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated $2^{O(\\sqrt{\\log n})}$-time … WebSep 5, 2024 · We propose a harmonic mutation operator for perturbative algorithm configurators that provably tunes single-parameter algorithms in polylogarithmic time for unimodal and approximately unimodal (i.e., non-smooth, rugged with an underlying gradient towards the optimum) parameter spaces. china rain shower head suppliersWebJun 9, 2024 · On the other hand, nondeterministic polylogarithmic time complexity classes, defined in terms of alternating random-access Turing machines and related families of circuits, have received some attention [5, 18]. Recently, a theorem analogous to Fagin’s famous theorem , was proven for nondeterministic polylogarithmic time . grammar for writing book pdf

"WebNov 8, 2024 · This work gives a deterministic fully-dynamic algorithm for general graphs, running in amortized O(log3 n) time per edge insertion or deletion, that maintains a bit indicating whether or not the graph is presently planar. Given a dynamic graph subject to insertions and deletions of edges, a natural question is whether the graph presently … " - Polylogarithmic time

Polylogarithmic time

Webically in polylogarithmic time in (general) graphs? (2) Is the constant factor in the dynamic algorithms small such that an efficient implementation is possible? New Results. This paper gives a positive answer to both questions. It presents a new technique for de-signing dynamic algorithms with polylogarithmic time WebDec 9, 2024 · For example, improving query complexity to be polylogarithmic would yield the first linear-time argument with polylogarithmic communication complexity. We conclude here by noting that the above approach has the additional benefit of being plausibly post-quantum, as the underlying linear-time hash function candidate is based on a lattice …

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WebAug 1, 2024 · Every polylogarithmic time property can be expressed in index logic. Suppose we are given a class C of ordered σ-structures which can be decided by a deterministic polylogarithmic time direct-access Turing machine M = (Q, Σ, δ, q 0, F, σ) that has m tapes Webically in polylogarithmic time in (general) graphs? (2) Is the constant factor in the dynamic algorithms small such that an efficient implementation is possible? New Results. This …

WebApr 23, 1999 · It is important at this time to find alternative foundations to the design of se- cure cryptography. We introduce a new model of generalized interactive proofs as a step in this di- rection. WebJul 25, 2024 · A simple polylogarithmic-time deterministic distributed algorithm for network decomposition that improves on a celebrated 2 O(√logn)-time algorithm and settles a …

WebOct 1, 2011 · In this article, we answer this question in the affirmative, and devise a deterministic algorithm that employs Δ 1+ o (1) colors, and runs in polylogarithmic time. Specifically, the running time of our algorithm is O ( f ( Δ )log Δ log n ), for an arbitrarily slow-growing function f ( Δ) = ω (1). We can also produce an O ( Δ 1+ η ... WebMay 25, 2024 · 1.1 Our Results. Our main result is an interactive oracle proof (IOP) [8, 44] that simultaneously achieves zero knowledge, linear-time proving, and polylogarithmic …

WebAug 21, 2024 · Furthermore, this efficient representation can be computed by evaluating 𝑓 on 𝑂 (log 𝑁) points defined over extensions of degree 𝑂 (log 𝑁) over 𝔽_𝑞. In particular, if 𝑓 is represented by the equation 𝐻 (𝑥) = 0 of its kernel 𝐾, then using Vélu’s formula the efficient representation can be computed in time 𝑂 ...

WebGraph Algorithms with Polylogarithmic Time 503. connectivity, bipartiteness, 1 1 e-approximate minimum spanning trees, and cycle-equivalence problem. The resulting … grammar for title of bookWebAug 1, 2024 · Every polylogarithmic time property can be expressed in index logic. Suppose we are given a class C of ordered σ-structures which can be decided by a deterministic … china raiser international logistics trackingWebApr 23, 1999 · It is important at this time to find alternative foundations to the design of se- cure cryptography. We introduce a new model of generalized interactive proofs as a step … grammar for writing bookWebbeautiful O(logn)-time randomized algorithms of Luby [Lub86] and Alon, Babai, and Itai [ABI86]. There is an abundanceof similar open questions about obtaining polylogarithmic-time determin-istic algorithms for other graph problems that admit polylogarithmic-time randomized algorithms; china rain water purifierWebUnder this assumption, we introduce a novel data structure for computing (1+ε)-approximate DP solutions in near-linear time and space in the static setting, and with polylogarithmic update times when the DP entries change dynamically. grammar for writing grade 10 pdfWebAn algorithm is said to have polynomial time complexity if its worst-case running time T worst(n) T worst ( n) for an input of size n n is upper bounded by a polynomial p(n) p ( n) for large enough n≥ n0 n ≥ n 0 . For example, if an algorithm's worst-case running time is T worst(n) ∈ O(2n4+5n3+6) T worst ( n) ∈ O ( 2 n 4 + 5 n 3 + 6 ... china rainy seasonWebA notable exception are zero-knowledge arguments with a linear-time prover and a polylogarithmic-time veriﬁer. This goal is presently achieved as a consequence of the … china rainwater tank treatment factories