Polylogarithmic time

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August undefined, 2024

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 … 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

Evaluating isogenies in polylogarithmic time - IACR

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 … 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 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 hcl-12s-h

Short PCPs Veriﬁable in Polylogarithmic Time

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 … 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 … 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 … hcl-13

Dynamic Matching with Better-than-2 Approximation in Polylogarithmic …

Short PCPPs verifiable in polylogarithmic time with O(1) queries

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 ... 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: hcl-12s-1/2hWebDec 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 … gold coast youth crime

"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 ... " - Polylogarithmic time

Polylogarithmic time

Algorithms Free Full-Text Efficient Data Structures for Range ...

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 … 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 …

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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;

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 … WebJan 1, 1991 · Checking Computations in Polylogarithmic Time. January 1991; ... .We show that every nondeterministic computational task S(x; y), defined as a polynomial 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 ... WebJun 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 …

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.

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 … gold coast yoga centre palm beach qldWebAug 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) … gold coast youth justice centreWebGraph Algorithms with Polylogarithmic Time 503. connectivity, bipartiteness, 1 1 e-approximate minimum spanning trees, and cycle-equivalence problem. The resulting … gold coast yoga palm beachWebJul 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 … gold coast youth conferenceWebUnder 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. gold coast youth housingIn 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… hcl136WebOct 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 ... gold coast youth justice service centre