Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms最新文献_第5页

Bidder Subset Selection Problem in Auction Design 拍卖设计中投标人子集选择问题

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-20 DOI: 10.48550/arXiv.2211.10969

Xiaohui Bei, N. Gravin, P. Lu, Zhihao Gavin Tang

{"title":"Bidder Subset Selection Problem in Auction Design","authors":"Xiaohui Bei, N. Gravin, P. Lu, Zhihao Gavin Tang","doi":"10.48550/arXiv.2211.10969","DOIUrl":"https://doi.org/10.48550/arXiv.2211.10969","url":null,"abstract":"Motivated by practical concerns in the online advertising industry, we study a bidder subset selection problem in single-item auctions. In this problem, a large pool of candidate bidders have independent values sampled from known prior distributions. The seller needs to pick a subset of bidders and run a given auction format on the selected subset to maximize her expected revenue. We propose two frameworks for the subset restrictions: (i) capacity constraint on the set of selected bidders; and (ii) incurred costs for the bidders invited to the auction. For the second-price auction with anonymous reserve (SPA-AR), we give constant approximation polynomial time algorithms in both frameworks (in the latter framework under mild assumptions about the market). Our results are in stark contrast to the previous work of Mehta, Nadav, Psomas, Rubinstein [NeurIPS 2020], who showed hardness of approximation for the SPA without a reserve price. We also give complimentary approximation results for other well-studied auction formats such as anonymous posted pricing and sequential posted pricing. On a technical level, we find that the revenue of SPA-AR as a set function $f(S)$ of its bidders $S$ is fractionally-subadditive but not submodular. Our bidder selection problem with invitation costs is a natural question about (approximately) answering a demand oracle for $f(cdot)$ under a given vector of costs, a common computational assumption in the literature on combinatorial auctions.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"28 1","pages":"3788-3801"},"PeriodicalIF":0.0,"publicationDate":"2022-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90432126","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

Optimal Algorithms for Linear Algebra in the Current Matrix Multiplication Time 当前矩阵乘法时代线性代数的最优算法

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-18 DOI: 10.48550/arXiv.2211.09964

Nadiia Chepurko, K. Clarkson, Praneeth Kacham, David P. Woodruff

{"title":"Optimal Algorithms for Linear Algebra in the Current Matrix Multiplication Time","authors":"Nadiia Chepurko, K. Clarkson, Praneeth Kacham, David P. Woodruff","doi":"10.48550/arXiv.2211.09964","DOIUrl":"https://doi.org/10.48550/arXiv.2211.09964","url":null,"abstract":"We study fundamental problems in linear algebra, such as finding a maximal linearly independent subset of rows or columns (a basis), solving linear regression, or computing a subspace embedding. For these problems, we consider input matrices $mathbf{A}inmathbb{R}^{ntimes d}$ with $n>d$. The input can be read in $text{nnz}(mathbf{A})$ time, which denotes the number of nonzero entries of $mathbf{A}$. In this paper, we show that beyond the time required to read the input matrix, these fundamental linear algebra problems can be solved in $d^{omega}$ time, i.e., where $omega approx 2.37$ is the current matrix-multiplication exponent. To do so, we introduce a constant-factor subspace embedding with the optimal $m=mathcal{O}(d)$ number of rows, and which can be applied in time $mathcal{O}left(frac{text{nnz}(mathbf{A})}{alpha}right) + d^{2 + alpha}text{poly}(log d)$ for any trade-off parameter $alpha>0$, tightening a recent result by Chepurko et. al. [SODA 2022] that achieves an $exp(text{poly}(loglog n))$ distortion with $m=dcdottext{poly}(loglog d)$ rows in $mathcal{O}left(frac{text{nnz}(mathbf{A})}{alpha}+d^{2+alpha+o(1)}right)$ time. Our subspace embedding uses a recently shown property of stacked Subsampled Randomized Hadamard Transforms (SRHT), which actually increase the input dimension, to\"spread\"the mass of an input vector among a large number of coordinates, followed by random sampling. To control the effects of random sampling, we use fast semidefinite programming to reweight the rows. We then use our constant-factor subspace embedding to give the first optimal runtime algorithms for finding a maximal linearly independent subset of columns, regression, and leverage score sampling. To do so, we also introduce a novel subroutine that iteratively grows a set of independent rows, which may be of independent interest.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"8 1","pages":"4026-4049"},"PeriodicalIF":0.0,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82132367","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: 9

Improved Approximations for Unrelated Machine Scheduling 非相关机器调度的改进逼近

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-18 DOI: 10.48550/arXiv.2211.10398

Sungjin Im, Shi Li

引用次数: 4

Approaching the Soundness Barrier: A Near Optimal Analysis of the Cube versus Cube Test 接近音障:立方体对立方体测试的近最优分析

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-17 DOI: 10.48550/arXiv.2211.09341

Dor Minzer, Kai Zheng

引用次数: 0

The Exact Bipartite Matching Polytope Has Exponential Extension Complexity 精确二部匹配多边形具有指数扩展复杂度

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-16 DOI: 10.48550/arXiv.2211.09106

Xinrui Jia, O. Svensson, Weiqiang Yuan

引用次数: 1

Higher degree sum-of-squares relaxations robust against oblivious outliers 高阶平方和松弛对遗忘异常值具有鲁棒性

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-14 DOI: 10.48550/arXiv.2211.07327

Tommaso d'Orsi, Rajai Nasser, Gleb Novikov, David Steurer

{"title":"Higher degree sum-of-squares relaxations robust against oblivious outliers","authors":"Tommaso d'Orsi, Rajai Nasser, Gleb Novikov, David Steurer","doi":"10.48550/arXiv.2211.07327","DOIUrl":"https://doi.org/10.48550/arXiv.2211.07327","url":null,"abstract":"We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $alpha$ fraction of the entries. We introduce a family of algorithms that under mild assumptions recover the signal $X^*$ in all estimation problems for which there exists a sum-of-squares algorithm that succeeds in recovering the signal $X^*$ when the noise $N$ is Gaussian. This essentially shows that it is enough to design a sum-of-squares algorithm for an estimation problem with Gaussian noise in order to get the algorithm that works with the symmetric noise model. Our framework extends far beyond previous results on symmetric noise models and is even robust to adversarial perturbations. As concrete examples, we investigate two problems for which no efficient algorithms were known to work for heavy-tailed noise: tensor PCA and sparse PCA. For the former, our algorithm recovers the principal component in polynomial time when the signal-to-noise ratio is at least $tilde{O}(n^{p/4}/alpha)$, that matches (up to logarithmic factors) current best known algorithmic guarantees for Gaussian noise. For the latter, our algorithm runs in quasipolynomial time and matches the state-of-the-art guarantees for quasipolynomial time algorithms in the case of Gaussian noise. Using a reduction from the planted clique problem, we provide evidence that the quasipolynomial time is likely to be necessary for sparse PCA with symmetric noise. In our proofs we use bounds on the covering numbers of sets of pseudo-expectations, which we obtain by certifying in sum-of-squares upper bounds on the Gaussian complexities of sets of solutions. This approach for bounding the covering numbers of sets of pseudo-expectations may be interesting in its own right and may find other application in future works.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"32 1","pages":"3513-3550"},"PeriodicalIF":0.0,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77521388","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: 6

Fast Distributed Brooks' Theorem 快速分布布鲁克斯定理

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-14 DOI: 10.48550/arXiv.2211.07606

Manuela Fischer, Yannic Maus, Magn'us M. Halld'orsson

{"title":"Fast Distributed Brooks' Theorem","authors":"Manuela Fischer, Yannic Maus, Magn'us M. Halld'orsson","doi":"10.48550/arXiv.2211.07606","DOIUrl":"https://doi.org/10.48550/arXiv.2211.07606","url":null,"abstract":"We give a randomized $Delta$-coloring algorithm in the LOCAL model that runs in $text{poly} log log n$ rounds, where $n$ is the number of nodes of the input graph and $Delta$ is its maximum degree. This means that randomized $Delta$-coloring is a rare distributed coloring problem with an upper and lower bound in the same ballpark, $text{poly}loglog n$, given the known $Omega(log_Deltalog n)$ lower bound [Brandt et al., STOC '16]. Our main technical contribution is a constant time reduction to a constant number of $(text{deg}+1)$-list coloring instances, for $Delta = omega(log^4 n)$, resulting in a $text{poly} loglog n$-round CONGEST algorithm for such graphs. This reduction is of independent interest for other settings, including providing a new proof of Brooks' theorem for high degree graphs, and leading to a constant-round Congested Clique algorithm in such graphs. When $Delta=omega(log^{21} n)$, our algorithm even runs in $O(log^* n)$ rounds, showing that the base in the $Omega(log_Deltalog n)$ lower bound is unavoidable. Previously, the best LOCAL algorithm for all considered settings used a logarithmic number of rounds. Our result is the first CONGEST algorithm for $Delta$-coloring non-constant degree graphs.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"100 1","pages":"2567-2588"},"PeriodicalIF":0.0,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75861387","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: 6

Steiner Connectivity Augmentation and Splitting-off in Poly-logarithmic Maximum Flows 多对数最大流中的Steiner连通性增强与分离

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-10 DOI: 10.48550/arXiv.2211.05769

Ruoxu Cen, W. He, Jason Li, Debmalya Panigrahi

{"title":"Steiner Connectivity Augmentation and Splitting-off in Poly-logarithmic Maximum Flows","authors":"Ruoxu Cen, W. He, Jason Li, Debmalya Panigrahi","doi":"10.48550/arXiv.2211.05769","DOIUrl":"https://doi.org/10.48550/arXiv.2211.05769","url":null,"abstract":"We give an almost-linear time algorithm for the Steiner connectivity augmentation problem: given an undirected graph, find a smallest (or minimum weight) set of edges whose addition makes a given set of terminals $tau$-connected (for any given $tau>0$). The running time of our algorithm is dominated by polylogarithmic calls to any maximum flow subroutine; using the recent almost-linear time maximum flow algorithm (Chen et al., FOCS 2022), we get an almost-linear running time for our algorithm as well. This is tight up to the polylogarithmic factor even for just two terminals. Prior to our work, an almost-linear (in fact, near-linear) running time was known only for the special case of global connectivity augmentation, i.e., when all vertices are terminals (Cen et al., STOC 2022). We also extend our algorithm to the closely related Steiner splitting-off problem, where the edges incident on a vertex have to be {em split-off} while maintaining the (Steiner) connectivity of a given set of terminals. Prior to our work, a nearly-linear time algorithm was known only for the special case of global connectivity (Cen et al., STOC 2022). The only known generalization beyond global connectivity was to preserve all pairwise connectivities using a much slower algorithm that makes $n$ calls to an all-pairs maximum flow (or Gomory-Hu tree) subroutine (Lau and Yung, SICOMP 2013), as against polylog(n) calls to a (single-pair) maximum flow subroutine in this work.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"143 1","pages":"2449-2488"},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75854047","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: 2

Discrepancy Minimization via Regularization 通过正则化实现差异最小化

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-10 DOI: 10.48550/arXiv.2211.05509

L. Pesenti, Adrian Vladu

引用次数: 1

Finding Triangles and Other Small Subgraphs in Geometric Intersection Graphs 在几何相交图中寻找三角形和其他小子图

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2022-11-10 DOI: 10.48550/arXiv.2211.05345

Timothy M. Chan

{"title":"Finding Triangles and Other Small Subgraphs in Geometric Intersection Graphs","authors":"Timothy M. Chan","doi":"10.48550/arXiv.2211.05345","DOIUrl":"https://doi.org/10.48550/arXiv.2211.05345","url":null,"abstract":"We consider problems related to finding short cycles, small cliques, small independent sets, and small subgraphs in geometric intersection graphs. We obtain a plethora of new results. For example: * For the intersection graph of $n$ line segments in the plane, we give algorithms to find a 3-cycle in $O(n^{1.408})$ time, a size-3 independent set in $O(n^{1.652})$ time, a 4-clique in near-$O(n^{24/13})$ time, and a $k$-clique (or any $k$-vertex induced subgraph) in $O(n^{0.565k+O(1)})$ time for any constant $k$; we can also compute the girth in near-$O(n^{3/2})$ time. * For the intersection graph of $n$ axis-aligned boxes in a constant dimension $d$, we give algorithms to find a 3-cycle in $O(n^{1.408})$ time for any $d$, a 4-clique (or any 4-vertex induced subgraph) in $O(n^{1.715})$ time for any $d$, a size-4 independent set in near-$O(n^{3/2})$ time for any $d$, a size-5 independent set in near-$O(n^{4/3})$ time for $d=2$, and a $k$-clique (or any $k$-vertex induced subgraph) in $O(n^{0.429k+O(1)})$ time for any $d$ and any constant $k$. * For the intersection graph of $n$ fat objects in any constant dimension $d$, we give an algorithm to find any $k$-vertex (non-induced) subgraph in $O(nlog n)$ time for any constant $k$, generalizing a result by Kaplan, Klost, Mulzer, Roddity, Seiferth, and Sharir (1999) for 3-cycles in 2D disk graphs. A variety of techniques is used, including geometric range searching, biclique covers,\"high-low\"tricks, graph degeneracy and separators, and shifted quadtrees. We also prove a near-$Omega(n^{4/3})$ conditional lower bound for finding a size-4 independent set for boxes.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"146 1","pages":"1777-1805"},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80576452","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: 4