Polylogarithmic time

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August undefined, 2024

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 … 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 …

Fully-dynamic planarity testing in polylogarithmic time - Semantic …

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 … chuck wallace middle age spread

Subpath Queries on Compressed Graphs: A Survey

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 ... 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 … 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 … chuckwalla raceway calendar

Recognizing the Tractability in Big Data Computing

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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 . 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. destination wattensWeba 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. chuckwalla facts for kids

"WebChecking computations in polylogarithmic time. Computing methodologies. Symbolic and algebraic manipulation. Symbolic and algebraic algorithms. Theorem proving algorithms. … " - Polylogarithmic time

Polylogarithmic time

Dynamic Matching with Better-than-2 Approximation in …

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 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 ...

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

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 … 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 …

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 …

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 … chuckwalla raceway californiaWebNov 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 … destination wedding activitiesWebApr 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 … destination wedding attire bucks countyWebJun 10, 2024 · We also show that the Dynamic Subgraph Connectivity problem on undirected graphs with m edges has no combinatorial algorithms with poly(m) pre-processing time, O(m 2/3−є) update time and O(m 1−є) query time for є > 0, matching the upper bound given by Chan, Pătraşcu, and Roditty [SICOMP’11], and improving the … destination wedding bridesmaid dressesWebJul 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 … destination wedding assistir online legendadoWebJun 22, 2024 · Jacob Holm and Eva Rotenberg. 2024. Fully-dynamic Planarity Testing in Polylogarithmic Time. arXiv: 1911.03449 Google Scholar; Jacob Holm and Eva … destination wedding amelia islandWebAug 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 … destination wedding amalfi coast