Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms最新文献_第4页

Graph Classes with Few Minimal Separators. I. Finite Forbidden Induced Subgraphs 具有很少最小分隔符的图类。有限禁止诱导子图

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch119

Peter Gartland, D. Lokshtanov

引用次数: 1

The Power of Clairvoyance for Multi-Level Aggregation and Set Cover with Delay 具有延迟的多级聚合和集合覆盖的透视能力

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch59

Ngoc Mai Le, S. Umboh, Ningyuan Xie

引用次数: 5

Simple, deterministic, fast (but weak) approximations to edit distance and Dyck edit distance 简单，确定，快速(但弱)逼近编辑距离和Dyck编辑距离

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch188

M. Koucký, M. Saks

引用次数: 1

A Nearly-Tight Analysis of Multipass Pairing Heaps 多通道配对堆的近紧密分析

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch23

Corwin Sinnamon, R. Tarjan

引用次数: 1

Zigzagging through acyclic orientations of chordal graphs and hypergraphs 弦图和超图的无环取向之字形

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch117

J. Cardinal, H. P. Hoang, Arturo I. Merino, Torsten Mütze

{"title":"Zigzagging through acyclic orientations of chordal graphs and hypergraphs","authors":"J. Cardinal, H. P. Hoang, Arturo I. Merino, Torsten Mütze","doi":"10.1137/1.9781611977554.ch117","DOIUrl":"https://doi.org/10.1137/1.9781611977554.ch117","url":null,"abstract":"In 1993, Savage, Squire, and West described an inductive construction for generating every acyclic orientation of a chordal graph exactly once, flipping one arc at a time. We provide two generalizations of this result. Firstly, we describe Gray codes for acyclic orientations of hypergraphs that satisfy a simple ordering condition, which generalizes the notion of perfect elimination order of graphs. This unifies the Savage-Squire-West construction with a recent algorithm for generating elimination trees of chordal graphs (SODA 2022). Secondly, we consider quotients of lattices of acyclic orientations of chordal graphs, and we provide a Gray code for them, addressing a question raised by Pilaud (FPSAC 2022). This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group (SODA 2020). Our algorithms are derived from the Hartung-Hoang-M¨utze-Williams combinatorial generation framework, and they yield simple algorithms for computing Hamilton paths and cycles on large classes of polytopes, including chordal nestohedra and quotientopes. In particular, we derive an efficient implementation of the Savage-Squire-West construction. Along the way, we give an overview of old and recent results about the polyhedral and order-theoretic aspects of acyclic orientations of graphs and hypergraphs.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"28 1","pages":"3029-3042"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82002250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Low-degree Extension in Time O(n log n) over all Finite Fields 椭圆曲线快速傅里叶变换(ECFFT)第1部分:O(n log n)在所有有限域上的低次扩展

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-01 DOI: 10.1137/1.9781611977554.ch30

Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, D. Levit

引用次数: 4

Excluding Single-Crossing Matching Minors in Bipartite Graphs 二部图中排除单交匹配小调

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-12-19 DOI: 10.48550/arXiv.2212.09348

Archontia C. Giannopoulou, D. Thilikos, S. Wiederrecht

{"title":"Excluding Single-Crossing Matching Minors in Bipartite Graphs","authors":"Archontia C. Giannopoulou, D. Thilikos, S. Wiederrecht","doi":"10.48550/arXiv.2212.09348","DOIUrl":"https://doi.org/10.48550/arXiv.2212.09348","url":null,"abstract":"noindent By a seminal result of Valiant, computing the permanent of $(0,1)$-matrices is, in general, $#mathsf{P}$-hard. In 1913 P'olya asked for which $(0,1)$-matrices $A$ it is possible to change some signs such that the permanent of $A$ equals the determinant of the resulting matrix. In 1975, Little showed these matrices to be exactly the biadjacency matrices of bipartite graphs excluding $K_{3,3}$ as a {matching minor}. This was turned into a polynomial time algorithm by McCuaig, Robertson, Seymour, and Thomas in 1999. However, the relation between the exclusion of some matching minor in a bipartite graph and the tractability of the permanent extends beyond $K_{3,3}.$ Recently it was shown that the exclusion of any planar bipartite graph as a matching minor yields a class of bipartite graphs on which the {permanent} of the corresponding $(0,1)$-matrices can be computed efficiently. In this paper we unify the two results above into a single, more general result in the style of the celebrated structure theorem for single-crossing-minor-free graphs. We identify a class of bipartite graphs strictly generalising planar bipartite graphs and $K_{3,3}$ which includes infinitely many non-Pfaffian graphs. The exclusion of any member of this class as a matching minor yields a structure that allows for the efficient evaluation of the permanent. Moreover, we show that the evaluation of the permanent remains $#mathsf{P}$-hard on bipartite graphs which exclude $K_{5,5}$ as a matching minor. This establishes a first computational lower bound for the problem of counting perfect matchings on matching minor closed classes.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"17 1","pages":"2111-2121"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85603387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Online Min-Max Paging 在线最小最大分页

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-12-06 DOI: 10.48550/arXiv.2212.03016

Ashish Chiplunkar, Monika Henzinger, Sagar Sudhir Kale, Maximilian Vötsch

{"title":"Online Min-Max Paging","authors":"Ashish Chiplunkar, Monika Henzinger, Sagar Sudhir Kale, Maximilian Vötsch","doi":"10.48550/arXiv.2212.03016","DOIUrl":"https://doi.org/10.48550/arXiv.2212.03016","url":null,"abstract":"Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called textit{min-max} paging, where the objective is to minimize the maximum number of faults on any page. While the classical paging problem, whose objective is to minimize the total number of faults, admits $k$-competitive deterministic and $O(log k)$-competitive randomized algorithms, we show that min-max paging does not admit a $c(k)$-competitive algorithm for any function $c$. Specifically, we prove that the randomized competitive ratio of min-max paging is $Omega(log(n))$ and its deterministic competitive ratio is $Omega(klog(n)/log(k))$, where $n$ is the total number of pages ever requested. We design a fractional algorithm for paging with a more general objective -- minimize the value of an $n$-variate differentiable convex function applied to the vector of the number of faults on each page. This gives an $O(log(n)log(k))$-competitive fractional algorithm for min-max paging. We show how to round such a fractional algorithm with at most a $k$ factor loss in the competitive ratio, resulting in a deterministic $O(klog(n)log(k))$-competitive algorithm for min-max paging. This matches our lower bound modulo a $mathrm{poly}(log(k))$ factor. We also give a randomized rounding algorithm that results in a $O(log^2 n log k)$-competitive algorithm.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"11 1","pages":"1545-1565"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82199560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Quantum Speed-ups for String Synchronizing Sets, Longest Common Substring, and k-mismatch Matching 串同步集、最长公共子串和k-错配匹配的量子加速

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-29 DOI: 10.48550/arXiv.2211.15945

Ce Jin, Jakob Nogler

{"title":"Quantum Speed-ups for String Synchronizing Sets, Longest Common Substring, and k-mismatch Matching","authors":"Ce Jin, Jakob Nogler","doi":"10.48550/arXiv.2211.15945","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15945","url":null,"abstract":"Longest Common Substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decisional version of this problem, LCS with threshold $d$, asks whether two length-$n$ input strings have a common substring of length $d$. The two extreme cases, $d=1$ and $d=n$, correspond respectively to Element Distinctness and Unstructured Search, two fundamental problems in quantum query complexity. However, the intermediate case $1ll dll n$ was not fully understood. We show that the complexity of LCS with threshold $d$ smoothly interpolates between the two extreme cases up to $n^{o(1)}$ factors: LCS with threshold $d$ has a quantum algorithm in $n^{2/3+o(1)}/d^{1/6}$ query complexity and time complexity, and requires at least $Omega(n^{2/3}/d^{1/6})$ quantum query complexity. Our result improves upon previous upper bounds $tilde O(min {n/d^{1/2}, n^{2/3}})$ (Le Gall and Seddighin ITCS 2022, Akmal and Jin SODA 2022), and answers an open question of Akmal and Jin. Our main technical contribution is a quantum speed-up of the powerful String Synchronizing Set technique introduced by Kempa and Kociumaka (STOC 2019). It consistently samples $n/tau^{1-o(1)}$ synchronizing positions in the string depending on their length-$Theta(tau)$ contexts, and each synchronizing position can be reported by a quantum algorithm in $tilde O(tau^{1/2+o(1)})$ time. As another application of our quantum string synchronizing set, we study the $k$-mismatch Matching problem, which asks if the pattern has an occurrence in the text with at most $k$ Hamming mismatches. Using a structural result of Charalampopoulos, Kociumaka, and Wellnitz (FOCS 2020), we obtain a quantum algorithm for $k$-mismatch matching with $k^{3/4} n^{1/2+o(1)}$ query complexity and $tilde O(kn^{1/2})$ time complexity.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"51 1","pages":"5090-5121"},"PeriodicalIF":0.0,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74677549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Toeplitz Low-Rank Approximation with Sublinear Query Complexity 具有亚线性查询复杂度的Toeplitz低秩逼近

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-21 DOI: 10.48550/arXiv.2211.11328

Michael Kapralov, Hannah Lawrence, M. Makarov, Cameron Musco, K. Sheth

{"title":"Toeplitz Low-Rank Approximation with Sublinear Query Complexity","authors":"Michael Kapralov, Hannah Lawrence, M. Makarov, Cameron Musco, K. Sheth","doi":"10.48550/arXiv.2211.11328","DOIUrl":"https://doi.org/10.48550/arXiv.2211.11328","url":null,"abstract":"We present a sublinear query algorithm for outputting a near-optimal low-rank approximation to any positive semidefinite Toeplitz matrix $T in mathbb{R}^{d times d}$. In particular, for any integer rank $k leq d$ and $epsilon,delta>0$, our algorithm makes $tilde{O} left (k^2 cdot log(1/delta) cdot text{poly}(1/epsilon) right )$ queries to the entries of $T$ and outputs a rank $tilde{O} left (k cdot log(1/delta)/epsilonright )$ matrix $tilde{T} in mathbb{R}^{d times d}$ such that $| T - tilde{T}|_F leq (1+epsilon) cdot |T-T_k|_F + delta |T|_F$. Here, $|cdot|_F$ is the Frobenius norm and $T_k$ is the optimal rank-$k$ approximation to $T$, given by projection onto its top $k$ eigenvectors. $tilde{O}(cdot)$ hides $text{polylog}(d) $ factors. Our algorithm is emph{structure-preserving}, in that the approximation $tilde{T}$ is also Toeplitz. A key technical contribution is a proof that any positive semidefinite Toeplitz matrix in fact has a near-optimal low-rank approximation which is itself Toeplitz. Surprisingly, this basic existence result was not previously known. Building on this result, along with the well-established off-grid Fourier structure of Toeplitz matrices [Cybenko'82], we show that Toeplitz $tilde{T}$ with near optimal error can be recovered with a small number of random queries via a leverage-score-based off-grid sparse Fourier sampling scheme.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"77 1","pages":"4127-4158"},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86230444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3