Polylogarithmic time

Author: spuw

August undefined, 2024

Webthat distance in polylogarithmic ((log N)”(lte)) time. 1 Introduction 1.1 Very long mathematical proofs An interesting foundational problem is posed by some mathematical … 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 …

Checking computations in polylogarithmic time Proceedings of …

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 … first republic bank public

Polylogarithmic function - Wikipedia

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: 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 … 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 first republic bank promo

Fast Perturbative Algorithm Configurators Parallel Problem …

Polylogarithmic-time deterministic network decomposition and ...

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… 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 ... first republic bank redwood cityWebNov 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 … first republic bank promotions

"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 deletions with approximation ratio strictly better than $2$. Specifically, we obtain a $1+\\frac{1}{\\sqrt{2}}+ε\\approx 1.707+ε$ approximation in bipartite graphs and a … " - Polylogarithmic time

Polylogarithmic time

Tight dynamic problem lower bounds from generalized BMM and …

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 8, 2024 · We present an IOP that simultaneously achieves the properties of zero knowledge, linear-time proving, and polylogarithmic-time verification. We construct a zero …

Did you know?

WebJun 22, 2024 · Jacob Holm and Eva Rotenberg. 2024. Fully-dynamic Planarity Testing in Polylogarithmic Time. arXiv: 1911.03449 Google Scholar; Jacob Holm and Eva … 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 ...

WebChecking computations in polylogarithmic time. Computing methodologies. Symbolic and algebraic manipulation. Symbolic and algebraic algorithms. Theorem proving algorithms. … Webbeautiful 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;

WebGraph Algorithms with Polylogarithmic Time 503. connectivity, bipartiteness, 1 1 e-approximate minimum spanning trees, and cycle-equivalence problem. The resulting … 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 …

WebJun 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 .

WebA 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 … first republic bank rankingWebJul 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 … first republic bank quarterly reportWebJul 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 … first republic bank refinanceWebJun 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 … first republic bank relationship managerWebJan 1, 1991 · Checking Computations in Polylogarithmic Time. January 1991; ... .We show that every nondeterministic computational task S(x; y), defined as a polynomial time … first republic bank refinancing interest rateWebSep 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. first republic bank rescue californiaWebthat distance in polylogarithmic ((log N)”(lte)) time. 1 Introduction 1.1 Very long mathematical proofs An interesting foundational problem is posed by some mathematical proofs which are too large to be checked by a single human. The proof of the Four Color Theorem [AHK], consid-ered controversial at the time, started with a Lemma first republic bank rescue online