Online computation of normalized substring complexity

Additional Titles: The normalized substring complexity $δ$ of a string is defined as $\max_k \{c[k]/k\}$, where $c[k]$ is the number of \textit{distinct} substrings of length $k$. This simply defined measure has recently attracted attention due to its established relationship to popular string compression algorithms. We consider the problem of computing $δ$ online, when the string is provided from a stream. We present two algorithms solving the problem: one working in $O(\log n)$ amortized time per character, and the other in $O(\log^3 n)$ worst-case time per character. To our knowledge, this is the first polylog-time online solution to this problem.

Συγγραφείς: Kucherov, Gregory, Nekrich, Yakov

Όροι ευρετηρίου: Data Structures and Algorithms, F.2.2, text

Σύνδεσμος: http://arxiv.org/abs/2510.16454

Faster Algorithms for Global Minimum Vertex-Cut in Directed Graphs

Additional Titles: We study the directed global minimum vertex-cut problem: given a directed vertex-weighted graph $G$, compute a vertex-cut $(L,S,R)$ in $G$ of minimum value, which is defined to be the total weight of all vertices in $S$. The problem, together with its edge-based variant, is one of the most basic in graph theory and algorithms, and has been studied extensively. The fastest currently known algorithm for directed global minimum vertex-cut (Henzinger, Rao and Gabow, FOCS 1996 and J. Algorithms 2000) has running time $\tilde{O}(mn)$, where $m$ and $n$ denote the number of edges and vertices in the input graph, respectively. A long line of work over the past decades led to faster algorithms for other main versions of the problem, including the undirected edge-based setting (Karger, STOC 1996 and J. ACM 2000), directed edge-based setting (Cen et al., FOCS 2021), and undirected vertex-based setting (Chuzhoy and Trabelsi, STOC 2025). However, for the vertex-based version in directed graphs, the 29 year-old $\tilde{O}(mn)$-time algorithm of Henzinger, Rao and Gabow remains the state of the art to this day, in all edge-density regimes. In this paper we break the $Θ(mn)$ running time barrier for the first time, by providing a randomized algorithm for directed global minimum vertex-cut, with running time $O\left(mn^{0.976}\cdot\operatorname{polylog} W\right)$ where $W$ is the ratio of largest to smallest vertex weight. Additionally, we provide a randomized $O\left(\min\left\{m^{1+o(1)}\cdot k,n^{2+o(1)}\right\}\right)$-time algorithm for the unweighted version of directed global minimum vertex-cut, where $k$ is the value of the optimal solution. The best previous algorithm for the problem achieved running time $\tilde O\left(\min\left\{k^2 \cdot m, mn^{11/12+o(1)}, n^{2+o(1)}\right\}\right)$ (Forster et al., SODA 2020, Li et al., STOC 2021).

Συγγραφείς: Chuzhoy, Julia, Mosenzon, Ron, Trabelsi, Ohad

Όροι ευρετηρίου: Data Structures and Algorithms, F.2.2, text

Σύνδεσμος: http://arxiv.org/abs/2512.24355

Sublinear Time Low-Rank Approximation of Hankel Matrices

Additional Titles: Hankel matrices are an important class of highly-structured matrices, arising across computational mathematics, engineering, and theoretical computer science. It is well-known that positive semidefinite (PSD) Hankel matrices are always approximately low-rank. In particular, a celebrated result of Beckermann and Townsend shows that, for any PSD Hankel matrix $H \in \mathbb{R}^{n \times n}$ and any $ε> 0$, letting $H_k$ be the best rank-$k$ approximation of $H$, $\|H-H_k\|_F \leq ε\|H\|_F$ for $k = O(\log n \log(1/ε))$. As such, PSD Hankel matrices are natural targets for low-rank approximation algorithms. We give the first such algorithm that runs in \emph{sublinear time}. In particular, we show how to compute, in $\polylog(n, 1/ε)$ time, a factored representation of a rank-$O(\log n \log(1/ε))$ Hankel matrix $\widehat{H}$ matching the error guarantee of Beckermann and Townsend up to constant factors. We further show that our algorithm is \emph{robust} -- given input $H+E$ where $E \in \mathbb{R}^{n \times n}$ is an arbitrary non-Hankel noise matrix, we obtain error $\|H - \widehat{H}\|_F \leq O(\|E\|_F) + ε\|H\|_F$. Towards this algorithmic result, our first contribution is a \emph{structure-preserving} existence result - we show that there exists a rank-$k$ \emph{Hankel} approximation to $H$ matching the error bound of Beckermann and Townsend. Our result can be interpreted as a finite-dimensional analog of the widely applicable AAK theorem, which shows that the optimal low-rank approximation of an infinite Hankel operator is itself Hankel. Armed with our existence result, and leveraging the well-known Vandermonde structure of Hankel matrices, we achieve our sublinear time algorithm using a sampling-based approach that relies on universal ridge leverage score bounds for Vandermonde matrices.

Συγγραφείς: Kapralov, Michael, Musco, Cameron, Sheth, Kshiteej

Όροι ευρετηρίου: Data Structures and Algorithms, Numerical Analysis, text

Σύνδεσμος: http://arxiv.org/abs/2511.21418

$O(\log n)$-Approximation Algorithms for Bipartiteness Ratio

Additional Titles: We propose an $O(\log n)$-approximation algorithm for the bipartiteness ratio of undirected graphs introduced by Trevisan (SIAM Journal on Computing, vol. 41, no. 6, 2012), where $n$ is the number of vertices. Our approach extends the cut-matching game framework for sparsest cut to the bipartiteness ratio, and requires only $\mathop{\mathrm{polylog}} n$ many single-commodity undirected maximum flow computations. Therefore, with the current fastest undirected max-flow algorithms, it runs in almost linear time. Along the way, we introduce the concept of well-linkedness for skew-symmetric graphs and prove a novel characterization of bipartiteness ratio in terms of well-linkedness in an auxiliary skew-symmetric graph, which may be of independent interest. As an application, we devise an $\tilde{O}(mn)$-time algorithm for the minimum uncut problem: given a graph whose optimal cut leaves an $η$ fraction of edges uncut, we find a cut that leaves only an $O(\log n \log(1/η)) \cdot η$ fraction of edges uncut, where $m$ is the number of edges. Finally, we propose a directed analogue of the bipartiteness ratio, and we give a polynomial-time algorithm that achieves an $O(\log n)$ approximation for this measure via a directed Leighton--Rao-style embedding. We also propose an algorithm for the minimum directed uncut problem with a guarantee similar to that for the minimum uncut problem.

Συγγραφείς: Soma, Tasuku, Ye, Mingquan, Yoshida, Yuichi

Όροι ευρετηρίου: Data Structures and Algorithms, text

Σύνδεσμος: http://arxiv.org/abs/2507.12847

Generalized Flow in Nearly-linear Time on Moderately Dense Graphs

Additional Titles: In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $γ_e >0$ governing whether the flow is increased or decreased as it crosses edge $e$. We provide a randomized $\tilde{O}( (m + n^{1.5}) \cdot \mathrm{polylog}(\frac{W}δ))$ time algorithm for solving the generalized maximum flow and generalized minimum cost flow problems in this setting where $δ$ is the target accuracy and $W$ is the maximum of all costs, capacities, and loss factors and their inverses. This improves upon the previous state-of-the-art $\tilde{O}(m \sqrt{n} \cdot \log^2(\frac{W}δ) )$ time algorithm, obtained by combining the algorithm of [Daitch-Spielman, 2008] with techniques from [Lee-Sidford, 2014]. To obtain this result we provide new dynamic data structures and spectral results regarding the matrices associated to generalized flows and apply them through the interior point method framework of [Brand-Lee-Liu-Saranurak-Sidford-Song-Wang, 2021].

Συγγραφείς: Jiang, Shunhua, Kapralov, Michael, Li, Lawrence, Sidford, Aaron

Όροι ευρετηρίου: Data Structures and Algorithms, text

Σύνδεσμος: http://arxiv.org/abs/2510.17740

Subquadratic Algorithms and Hardness for Attention with Any Temperature

Additional Titles: Despite the popularity of the Transformer architecture, the standard algorithm for computing Attention suffers from quadratic time complexity in context length $n$. Alman and Song [NeurIPS 2023] showed that when the head dimension $d = Θ(\log n)$, subquadratic Attention is possible if and only if the inputs have small entries bounded by $B = o(\sqrt{\log n})$ in absolute values, under the Strong Exponential Time Hypothesis ($\mathsf{SETH}$). Equivalently, subquadratic Attention is possible if and only if the softmax is applied with high temperature for $d=Θ(\log n)$. Running times of these algorithms depend exponentially on $B$ and thus they do not lead to even a polynomial-time algorithm outside the specific range of $B$. This naturally leads to the question: when can Attention be computed efficiently without strong assumptions on temperature? Are there fast attention algorithms that scale polylogarithmically with entry size $B$? In this work, we resolve this question and characterize when fast Attention for arbitrary temperatures is possible. First, for all constant $d = O(1)$, we give the first subquadratic $\tilde{O}(n^{2 - 1/d} \cdot \mathrm{polylog}(B))$ time algorithm for Attention with large $B$. Our result holds even for matrices with large head dimension if they have low rank. In this regime, we also give a similar running time for Attention gradient computation, and therefore for the full LLM training process. Furthermore, we show that any substantial improvement on our algorithm is unlikely. In particular, we show that even when $d = 2^{Θ(\log^* n)}$, Attention requires $n^{2 - o(1)}$ time under $\mathsf{SETH}$. Finally, in the regime where $d = \mathrm{poly}(n)$, we show that the standard algorithm is optimal under popular fine-grained complexity assumptions.

Συγγραφείς: Gupta, Shreya, Huang, Boyang, Saha, Barna, Xu, Yinzhan, Ye, Christopher

Όροι ευρετηρίου: Machine Learning, Computational Complexity, F.2.1, text

Σύνδεσμος: http://arxiv.org/abs/2505.14840

Overflow-Safe Polylog-Time Parallel Minimum-Weight Perfect Matching Decoder: Toward Experimental Demonstration

Συγγραφείς: Mikami, Ryo, Yamasaki, Hayata

Θεματικοί όροι: Quantum Physics

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2603.03776

Longest common extensions with wildcards: trade-off and applications

Additional Titles: We study the Longest Common Extension (LCE) problem in a string containing wildcards. Wildcards (also called 'don't cares' or 'holes') are special characters that match any other character in the alphabet, similar to the character '?' in Unix commands or '.' in regular expression engines. We consider the problem parametrized by G, the number of maximal contiguous groups of wildcards in the input string. Our main contribution is a simple data structure for this problem that can be built in O(n (G/t) log n) time, occupies O(nG/t) space, and answers queries in O(t) time, for any t ∈ [1 .. G]. Up to the O(log n) factor, this interpolates smoothly between the data structure of Crochemore et al. [JDA 2015], which has O(nG) preprocessing time and space, and O(1) query time, and a simple solution based on the 'kangaroo jumping' technique [Landau and Vishkin, STOC 1986], which has O(n) preprocessing time and space, and O(G) query time. By establishing a connection between this problem and Boolean matrix multiplication, we show that our solution is optimal up to subpolynomial factors when G = Ω(n) under a widely believed hypothesis. In addition, we develop a new simple, deterministic and combinatorial algorithm for sparse Boolean matrix multiplication. Finally, we show that our data structure can be used to obtain efficient algorithms for approximate pattern matching and structural analysis of strings with wildcards. First, we consider the problem of pattern matching with k errors (i.e., edit operations) in the setting where both the pattern and the text may contain wildcards. The 'kangaroo jumping' technique can be adapted to yield an algorithm for this problem with runtime O(n(k+G)), where G is the total number of maximal contiguous groups of wildcards in the text and the pattern and n is the length of the text. By combining 'kangaroo jumping' with a tailor-made data structure for LCE queries, Akutsu [IPL 1995] devised an O(n√{km} polylog m)-time algorithm. We improve on bo

Συγγραφείς: Bathie, G., Charalampopoulos, Panagiotis, Starikovskaya, T.

Όροι ευρετηρίου: School of Computing and Mathematical Sciences, Article, PeerReviewed

Σύνδεσμος: https://eprints.bbk.ac.uk/id/eprint/54397/1/esa_final.pdf
https://eprints.bbk.ac.uk/id/eprint/54397/
https://doi.org/10.4230/LIPIcs.ESA.2024.19
https://eprints.bbk.ac.uk/id/eprint/54397
https://doi.org/10.4230/LIPIcs.ESA.2024.19
10.4230/LIPIcs.ESA.2024.19

A linear-processor polylog-time algorithm for shortest paths in planar graphs

Συγγραφείς: Klein, P.N., Subramanian, S.

Πηγή: Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Computer science foundations Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on. :259-270 1993

Relation: Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science

Elastic-degenerate string matching via fast matrix multiplication

Additional Titles: An elastic-degenerate (ED) string is a sequence of n sets of strings of total length N which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of length m in an ED text. The EDSM problem has recently received some attention in the combinatorial pattern matching community, and an O(nm1.5√logm+N)-time algorithm is known [Aoyama et al., CPM 2018]. The standard assumption in the prior work on this question is that N is substantially larger than both n and m, and thus we would like to have a linear dependency on the former. Under this assumption, the natural open problem is whether we can decrease the 1.5 exponent in the time complexity, similarly as in the related (but, to the best of our knowledge, not equivalent) word break problem [Backurs and Indyk, FOCS 2016]. Our starting point is a conditional lower bound for the EDSM problem. We use the popular combinatorial Boolean matrix multiplication (BMM) conjecture stating that there is no truly subcubic combinatorial algorithm for BMM [Abboud and Williams, FOCS 2014]. By designing an appropriate reduction, we show that a combinatorial algorithm solving the EDSM problem in O(nm1.5−ϵ+N) time, for any ϵ>0, refutes this conjecture. Our reduction should be understood as an indication that decreasing the exponent requires fast matrix multiplication. String periodicity and fast Fourier transform are two standard tools in string algorithms. Our main technical contribution is that we successfully combine these tools with fast matrix multiplication to design a noncombinatorial O~(nmω−1+N)-time algorithm for EDSM, where ω denotes the matrix multiplication exponent and the O~(⋅) notation suppresses polylog factors. To the best of our knowledge, we are the first to combine these tools. In particular, using the fact that ω<2.373 [Alman and Williams, SODA 2021; Le Gall, ISSAC 2014; Williams, STOC 2012], we obtain an O(nm1.373+N)-time algorithm for EDS

Συγγραφείς: Bernardini, G. (Giulia), Gawrychowski, P. (Paweł), Pisanti, N. (Nadia), Pissis, S. (Solon), Rosone, G. (Giovanna)

Πηγή: SIAM Journal on Computing vol. 51 no. 3, pp. 549-576

Όροι ευρετηρίου: string algorithms, pattern matching, elastic-degenerate string, matrix multiplication, fast Fourier transform, info:eu-repo/semantics/article

Σύνδεσμος: https://ir.cwi.nl/pub/32732
info:eu-repo/grantAgreement/EC/H2020/872539

Elastic-degenerate string matching with 1 error

Additional Titles: An elastic-degenerate (ED) string is a sequence of n finite sets of strings of total length N, introduced to represent a set of related DNA sequences, also known as a pangenome. The ED string matching (EDSM) problem consists in reporting all occurrences of a pattern of length m in an ED text. The EDSM problem has recently received some attention by the combinatorial pattern matching community, culminating in an O~(nmω−1)+O(N)-time algorithm [Bernardini et al., SIAM J. Comput. 2022], where ω denotes the matrix multiplication exponent and the O~(⋅) notation suppresses polylog factors. In the k-EDSM problem, the approximate version of EDSM, we are asked to report all pattern occurrences with at most k errors. k-EDSM can be solved in O(k2mG+kN) time under edit distance, where G denotes the total number of strings in the ED text [Bernardini et al., Theor. Comput. Sci. 2020]. Unfortunately, G is only bounded by N, and so even for k=1, the existing algorithm runs in Ω(mN) time in the worst case. Here we make progress in this direction. We show that 1-EDSM can be solved in O((nm2+N)logm) or O(nm3+N) time under edit distance. For the decision version of the problem, we present a faster O(nm2logm−−−−−√+Nloglogm)-time algorithm. Our algorithms rely on non-trivial reductions from 1-EDSM to special instances of classic computational geometry problems (2d rectangle stabbing or range emptiness), which we show how to solve efficiently.

Συγγραφείς: Bernardini, G. (Giulia), Gabory, E.A.D. (Esteban), Pissis, S. (Solon), Stougie, L. (Leen), Sweering, M.J.M. (Michelle), Zuba, W.P. (Wiktor)

Όροι ευρετηρίου: String algorithms, Approximate string matching, Edit distance, Degenerate strings, Elastic-degenerate strings, info:eu-repo/semantics/conferenceObject

Σύνδεσμος: https://ir.cwi.nl/pub/32721
info:eu-repo/grantAgreement/NWO/NWO/OCENW.2019.015
info:eu-repo/grantAgreement/NWO/NWO/024.002.003
info:eu-repo/grantAgreement/EC/H2020/872539
info:eu-repo/grantAgreement/EC/H2020/956229

Real-weighted Diameter and Eccentricity of Minor-free and Bounded VC-dimension Graphs in Truly Subquadratic Time

Συγγραφείς: Zheng, Da Wei

Θεματικοί όροι: Data Structures and Algorithms

Σύνδεσμος πρόσβασης: https://arxiv.org/abs/2607.01926

Truly subcubic min-plus product for less structured matrices, with applications

Additional Titles: Copyright © 2020 by SIAM The All-Pairs Shortest Paths (APSP) problem is one of the most basic problems in computer science. The fastest known algorithms for APSP in n-node graphs run in n3−o(1) time, and it is a big open problem whether a truly subcubic, O(n3−ε) for ε > 0 time algorithm exists for APSP. The Min-Plus product of two n × n matrices is known to be equivalent to APSP, where the optimal running times of the two problems differ by at most a constant factor. A natural way to approach understanding the complexity of APSP is thus understanding what structure (if any) is needed to solve Min-Plus product in truly subcubic time. The goal of this paper is to get truly subcubic algorithms for Min-Plus product for less structured inputs than what was previously known, and to apply them to versions of APSP and other problems. The results are as follows: (1) Our main result is the first truly subcubic algorithm for the Min-Plus product of two n×n matrices A and B with polylog n bit integer entries, where B has a partitioning into nε × nε blocks (for any ε > 0) where each block is at most nδ-far (for δ < 3 − ω, where 2 ≤ ω < 2.373) in '∞ norm from a constant rank integer matrix. This result presents the most general case to date of Min-Plus product that is still solvable in truly subcubic time. (2) The first application of our main result is a truly subcubic algorithm for APSP in a new type of geometric graph. Chan'10 solved APSP in truly subcubic time in geometric graphs whose edges have weights that are a function of the identities of the edge's end-points. Our result extends Chan's result in the case of integer edge weights by allowing the weights to differ from a function of the end-point identities by at most nδ for small δ. (3) In a second application we consider a batch version of the range mode problem in which one is given a sequence of numbers a1, . . ., an and n intervals defining contiguous subsequences, and one is asked to compute the range mode of each s

Συγγραφείς: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, Williams, VV, Xu, Y

Πηγή: arXiv

Όροι ευρετηρίου: Article, http://purl.org/eprint/type/ConferencePaper

Σύνδεσμος: https://hdl.handle.net/1721.1/137947
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Computing and testing small connectivity in near-linear time and queries via fast local cut algorithms

Additional Titles: Consider the following “local” cut-detection problem in a directed graph: We are given a seed vertex x and need to remove at most k edges so that at most ν edges can be reached from x (a “local” cut) or output to indicate that no such cut exists. If we are given query access to the input graph, then this problem can in principle be solved without reading the whole graph and with query complexity depending on k and ν. In this paper we consider a slack variant of this problem where, when such a cut exists, we can output a cut with up to O(kν) edges reachable from x. We present a simple randomized algorithm spending O(k2ν) time and O(kν) queries for the above variant, improving in particular a previous time bound of O(kO(k)ν) by Chechik et al. [SODA'17]. We also extend our algorithm to handle an approximate variant. We demonstrate that these local algorithms are versatile primitives for designing substantially improved algorithms for classic graph problems by providing the following three applications. (Throughout, Õ(T) hides polylog(T).) 1. A randomized algorithm for the classic k-vertex connectivity problem that takes near-linear time when k = O(polylog(n)), namely Õ(m + nk3) time in undirected graphs. Prior to our work, the state of the art for this range of k were linear-time algorithms for k ≤ 3 [Tarjan FOCS'71; Hopcroft, Tarjan SICOMP'73] and a recent algorithm with Õ(m + n4/3k7/3) time [Nanongkai et al., STOC'19]. The story is the same for directed graphs where our Õ(mk2)-time algorithm is near-linear when k = O(polylog(n)). Our techniques also yield an improved approximation scheme. 2. Property testing algorithms for k-edge and -vertex connectivity with query complexities that are near-linear in k, exponentially improving the state-of-the-art. This resolves two open problems, one by Goldreich and Ron [STOC'97] and one by Orenstein and Ron [Theor. Comput. Sci.'11]. 3. A faster algorithm for computing the maximal kedge connected subgraphs, improving prior work of

Συγγραφείς: Forster, Sebastian, Na Nongkai, Danupon, Yang, Liu, Saranurak, Thatchaphol, Yingchareonthawornchai, Sorrachai

Όροι ευρετηρίου: Clustering algorithms, Directed graphs, Approximation scheme, Computing and testing, Connected subgraphs, K-vertex connectivity, Linear-time algorithms, Randomized Algorithms, Undirected graph, Vertex connectivity, Graph algorithms, Computer Sciences, Datavetenskap (datalogi), Conference paper, info:eu-repo/semantics/conferenceObject, text

Σύνδεσμος: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-274213
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, p. 2046-2065

The Polylog-Time Hierarchy Captured by Restricted Second-Order Logic

Συγγραφείς: Ferrarotti, F., Gonzalez, S., Schewe, K.-D., Turull-Torres, J.M.

Πηγή: 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) SYNASC Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2018 20th International Symposium on. :133-140 Sep, 2018

Relation: 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

Efficient matrix chain ordering in polylog time

Συγγραφείς: Bradford, P.G., Rawlins, G.J.E., Shannon, G.E.

Πηγή: Proceedings of 8th International Parallel Processing Symposium Parallel Processing Symposium, 1994. Proceedings., Eighth International. :234-241 1994

Relation: Proceedings of 8th International Parallel Processing Symposium

Fine-grained complexity of k-OPT in bounded-degree graphs for solving TSP

Additional Titles: The Traveling Salesman Problem asks to find a minimum-weight Hamiltonian cycle in an edge-weighted complete graph. Local search is a widely-employed strategy for finding good solutions to TSP. A popular neighborhood operator for local search is k-opt, which turns a Hamiltonian cycle C into a new Hamiltonian cycle C' by replacing k edges. We analyze the problem of determining whether the weight of a given cycle can be decreased by a k-opt move. Earlier work has shown that (i) assuming the Exponential Time Hypothesis, there is no algorithm that can detect whether or not a given Hamiltonian cycle C in an n-vertex input can be improved by a k-opt move in time f(k)n o(k/ log k) for any function f, while (ii) it is possible to improve on the brute-force running time of O(n k) and save linear factors in the exponent. Modern TSP heuristics are very successful at identifying the most promising edges to be used in k-opt moves, and experiments show that very good global solutions can already be reached using only the top-O(1) most promising edges incident to each vertex. This leads to the following question: can improving k-opt moves be found efficiently in graphs of bounded degree? We answer this question in various regimes, presenting new algorithms and conditional lower bounds. We show that the aforementioned ETH lower bound also holds for graphs of maximum degree three, but that in bounded-degree graphs the best improving k-move can be found in time O(n (23/135+ϵk)k), where lim k→∞ ϵk= 0. This improves upon the best-known bounds for general graphs. Due to its practical importance, we devote special attention to the range of k in which improving k-moves in bounded-degree graphs can be found in quasi-linear time. For k ≤ 7, we give quasi-linear time algorithms for general weights. For k = 8 we obtain a quasi-linear time algorithm when the weights are bounded by O(polylog n). On the other hand, based on established fine-grained c

Συγγραφείς: Bonnet, Édouard, Iwata, Yoichi, Jansen, Bart M.P., Kowalik, Łukasz

Πηγή: Bender, Michael A., Svensson, Ola, Herman, Grzegorz (Ed.), 27th Annual European Symposium on Algorithms (ESA 2019), p.23:1-23:14. Dagstuhl: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. [ISBN 978-3-95977-124-5]

Όροι ευρετηρίου: Bounded degree, K-OPT, Traveling salesman problem, Conferentiebijdrage, Conference contribution

Σύνδεσμος: https://research.tue.nl/en/publications/ee3e46d8-46b1-4e96-8681-0249da4ad30f

Fast polylog-time reconfiguration of structurally fault-tolerant multiprocessors

Συγγραφείς: Dutt, S.

Πηγή: Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing Parallel and distributed processing Parallel and Distributed Processing, 1993. Proceedings of the Fifth IEEE Symposium on. :762-770 1993

Relation: Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing

Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms

Συγγραφείς: Forster, Sebastian, Nanongkai, Danupon, Saranurak, Thatchaphol, Yang, Liu, Yingchareonthawornchai, Sorrachai

Θεματικοί όροι: Computer Science - Data Structures and Algorithms

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1910.14344

Quasi-linear-time algorithm for a longest common circular factor.

Συγγραφείς: Alzamel, Mai¹ (AUTHOR) malzamel@ksu.edu.sa, Crochemore, Maxime^2,3 (AUTHOR) maxime.crochemore@kcl.ac.uk, Iliopoulos, Costas S.^1,2 (AUTHOR), Kociumaka, Tomasz⁴ (AUTHOR) tomasz.kociumaka@mpi-inf.mpg.de, Radoszewski, Jakub^1,5 (AUTHOR) jrad@mimuw.edu.pl, Rytter, Wojciech⁵ (AUTHOR) rytter@mimuw.edu.pl, Straszyński, Juliusz⁵ (AUTHOR) j.straszynski@mimuw.edu.pl, Waleń, Tomasz⁵ (AUTHOR) walen@mimuw.edu.pl, Zuba, Wiktor⁵ (AUTHOR) w.zuba@mimuw.edu.pl

Πηγή: Theoretical Computer Science. Jun2026, Vol. 1075, pN.PAG-N.PAG. 1p.

Θεματικοί όροι: *Algorithms, *Time complexity, *Computational complexity