Polylogarithmic time

WebNov 23, 2024 · Polylogarithmic time is a special case of the sublinear time, and it is not sufficient for characterizing the tractability in big data computing. Similar to the \(\sqcap \) -tractability theory [ 9 ], Yang et al. placed a logarithmic-size restriction on the preprocessing result and relaxed the query execution time to PTIME and introduced the corresponding … 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…

algorithm - What is the meaning of O ( polylog (n) )? In …

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 … WebOct 30, 2024 · Let T[1,n] be a string of length n and T[i,j] be the substring of T starting at position i and ending at position j. A substring T[i,j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and information retrieval. Given string T as input, the … how do ap courses work https://cfandtg.com

Descriptive Complexity of Deterministic Polylogarithmic Time

WebJul 15, 2024 · We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and … Weba polylogarithmic time verifier making O(1/ ) queries into a theorem and proof, whose proof length is T(n) ·2(logT(n)) , again for verifying membership in L∈NTIME(T(n)). This PCP matches the query complexity and proof length of the system of [BGH+04a], which was proved only for NP and uses a polynomial-time verification procedure. WebAn 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 ... how do ap classes prepare you for college

Descriptive complexity of deterministic polylogarithmic …

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

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Polylogarithmic time

time complexity - standard sequential algorithm with polylog runtime …

WebNov 26, 2009 · Abuse of notation or not, polylog(n) does mean "some polynomial in log(n)", just as "poly(n)" can mean "some polynomial in n". So O(polylog(n)) means "O((log n) k) for … 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.

Polylogarithmic time

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An algorithm is said to run in polylogarithmic time if its time is for some constant k. Another way to write this is . For example, matrix chain ordering can be solved in polylogarithmic time on a parallel random-access machine, and a graph can be determined to be planar in a fully dynamic way in time per insert/delete operation. WebWe show that the asymptotic gain in the time complexity when using collision detection depends heavily on the task by investigating three prominent problems for wireless networks, ... It is an exponential improvement over prior work, if the diameter D is polylogarithmic in the number of nodes n, ie D ∈ O ...

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 … WebUnder 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.

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 … 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.

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

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 … how do apartment waitlists workWebthat distance in polylogarithmic ((log N)”(lte)) time. 1 Introduction 1.1 Very long mathematical proofs An interesting foundational problem is posed by some mathematical … how do apa headers workWebAug 1, 2009 · TLDR. This work shows that if the query complexity is relaxed to polynomial, then one can construct PCPs of linear length for circuit-SAT, and PCP of length O (tlog t) … how do apes learnhow do apartment building boilers workWebJul 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 … how do apartments calculate 3 times the rentWebJun 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 … how do apartment water heaters workWebDynamic 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: how do aphids travel