Information Technology Convergence and Services最新文献

{"title":"Local Access to Random Walks","authors":"Amartya Shankha Biswas, Edward Pyne, R. Rubinfeld","doi":"10.4230/LIPIcs.ITCS.2022.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.24","url":null,"abstract":"For a graph G on n vertices, naively sampling the position of a random walk of at time t requires work Ω(t). We desire local access algorithms supporting positionG(t) queries, which return the position of a random walk from some fixed start vertex s at time t, where the joint distribution of returned positions is 1/ poly(n) close to those of a uniformly random walk in l1 distance. We first give an algorithm for local access to random walks on a given undirected d-regular graph with Õ( 1 1−λ √ n) runtime per query, where λ is the second-largest eigenvalue of the random walk matrix of the graph in absolute value. Since random d-regular graphs G(n, d) are expanders with high probability, this gives an Õ( √ n) algorithm for a graph drawn from G(n, d) whp, which improves on the naive method for small numbers of queries. We then prove that no algorithm with subconstant error given probe access to an input d-regular graph can have runtime better than Ω( √ n/ log(n)) per query in expectation when the input graph is drawn from G(n, d), obtaining a nearly matching lower bound. We further show an Ω(n1/4) runtime per query lower bound even with an oblivious adversary (i.e. when the query sequence is fixed in advance). We then show that for families of graphs with additional group theoretic structure, dramatically better results can be achieved. We give local access to walks on small-degree abelian Cayley graphs, including cycles and hypercubes, with runtime polylog(n) per query. This also allows for efficient local access to walks on polylog degree expanders. We show that our techniques apply to graphs with high degree by extending or results to graphs constructed using the tensor product (giving fast local access to walks on degree n graphs for any ε ∈ (0, 1]) and Cartesian product. 2012 ACM Subject Classification Theory of computation → Streaming, sublinear and near linear time algorithms","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"526 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132352910","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}

{"title":"Symmetric Sparse Boolean Matrix Factorization and Applications","authors":"Sitan Chen, Zhao Song, Runzhou Tao, Ruizhe Zhang","doi":"10.4230/LIPIcs.ITCS.2022.46","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.46","url":null,"abstract":"In this work, we study a variant of nonnegative matrix factorization where we wish to find a symmetric factorization of a given input matrix into a sparse, Boolean matrix. Formally speaking, given $mathbf{M}inmathbb{Z}^{mtimes m}$, we want to find $mathbf{W}in{0,1}^{mtimes r}$ such that $| mathbf{M} - mathbf{W}mathbf{W}^top |_0$ is minimized among all $mathbf{W}$ for which each row is $k$-sparse. This question turns out to be closely related to a number of questions like recovering a hypergraph from its line graph, as well as reconstruction attacks for private neural network training. As this problem is hard in the worst-case, we study a natural average-case variant that arises in the context of these reconstruction attacks: $mathbf{M} = mathbf{W}mathbf{W}^{top}$ for $mathbf{W}$ a random Boolean matrix with $k$-sparse rows, and the goal is to recover $mathbf{W}$ up to column permutation. Equivalently, this can be thought of as recovering a uniformly random $k$-uniform hypergraph from its line graph. Our main result is a polynomial-time algorithm for this problem based on bootstrapping higher-order information about $mathbf{W}$ and then decomposing an appropriate tensor. The key ingredient in our analysis, which may be of independent interest, is to show that such a matrix $mathbf{W}$ has full column rank with high probability as soon as $m = widetilde{Omega}(r)$, which we do using tools from Littlewood-Offord theory and estimates for binary Krawtchouk polynomials.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122419835","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}

{"title":"Garland's Technique for Posets and High Dimensional Grassmannian Expanders","authors":"T. Kaufman, Ran J. Tessler","doi":"10.4230/LIPIcs.ITCS.2023.78","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2023.78","url":null,"abstract":"Local to global machinery plays an important role in the study of simplicial complexes, since the seminal work of Garland [G] to our days. In this work we develop a local to global machinery for general posets. We show that the high dimensional expansion notions and many recent expansion results have a generalization to posets. Examples are fast convergence of high dimensional random walks generalizing [KO,AL], an equivalence with a global random walk definition, generalizing [DDFH] and a trickling down theorem, generalizing [O]. In particular, we show that some posets, such as the Grassmannian poset, exhibit qualitatively stronger trickling down effect than simplicial complexes. Using these methods, and the novel idea of Posetification, to Ramanujan complexes [LSV1,LSV2], we construct a constant degree expanding Grassmannian poset, and analyze its expansion. This it the first construction of such object, whose existence was conjectured in [DDFH].","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"269 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116247308","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}

{"title":"Buying Data Over Time: Approximately Optimal Strategies for Dynamic Data-Driven Decisions","authors":"Nicole Immorlica, Ian A. Kash, Brendan Lucier","doi":"10.4230/LIPIcs.ITCS.2021.77","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.77","url":null,"abstract":"We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before choosing an action each round, the agent can purchase noisy samples about the state of the world. The agent has a budget to spend on these samples, and has flexibility in deciding how to spread that budget across rounds. We investigate the problem of choosing a sampling algorithm that optimizes total expected payoff. For example: is it better to buy samples steadily over time, or to buy samples in batches? We solve for the optimal policy, and show that it is a natural instantiation of the latter. Under a more general model that includes per-round fixed costs, we prove that a variation on this batching policy is a 2-approximation. 2012 ACM Subject Classification Theory of computation → Design and analysis of algorithms; Theory of computation → Markov decision processes","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129408155","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}

{"title":"Approximately Strategyproof Tournament Rules in the Probabilistic Setting","authors":"Kimberly Ding, S. Weinberg","doi":"10.4230/LIPIcs.ITCS.2021.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.14","url":null,"abstract":"We consider the manipulability of tournament rules which map the results of ( n 2 ) pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than 1/3, and this is the best possible among any Condorcet-consistent tournament rule (which selects an undefeated team whenever one exists) [14, 15]. These lower bounds require the manipulators to know precisely the outcome of all future matches. We take a beyond worst-case view and instead consider tournaments which are “close to uniform”: the outcome of all matches are independent, and no team is believed to win any match with probability exceeding 1/2 + ε. We show that Randomized Single Elimination Bracket [14] and a new tournament rule we term Randomized Death Match have the property that no pair of teams can manipulate the outcome of their match to improve their probability of winning by more than ε/3 + 2ε2/3, for all ε, and this is the best possible among any Condorcet-consistent tournament rule. Our main technical contribution is a recursive framework to analyze the manipulability of certain forms of tournament rules. In addition to our main results, this view helps streamline previous analysis of Randomized Single Elimination Bracket, and may be of independent interest. 2012 ACM Subject Classification Theory of computation → Algorithmic game theory","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122199288","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}

{"title":"Algorithms and Hardness for Multidimensional Range Updates and Queries","authors":"Joshua Lau, Angus Ritossa","doi":"10.4230/LIPIcs.ITCS.2021.37","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.37","url":null,"abstract":"Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class of data structure problems over integer arrays in one or more dimensions. These problems allow range updates (such as filling all cells in a range with a constant) and queries (such as finding the sum or maximum of values in a range). In this work, we consider these operations along with updates that replace each cell in a range with the minimum, maximum, or sum of its existing value, and a constant. In one dimension, it is known that segment trees can be leveraged to facilitate any $n$ of these operations in $tilde{O}(n)$ time overall. Other than a few specific cases, until now, higher dimensional variants have been largely unexplored. We show that no truly subquadratic time algorithm can support certain pairs of these updates simultaneously without falsifying several popular conjectures. On the positive side, we show that truly subquadratic algorithms can be obtained for variants induced by other subsets. We provide two approaches to designing such algorithms that can be generalised to online and higher dimensional settings. First, we give almost-tight $tilde{O}(n^{3/2})$ time algorithms for single-update variants where the update operation distributes over the query operation. Second, for other variants, we provide a general framework for reducing to instances with a special geometry. Using this, we show that $O(m^{3/2-epsilon})$ time algorithms for counting paths and walks of length 2 and 3 between vertex pairs in sparse graphs imply truly subquadratic data structures for certain variants; to this end, we give an $tilde{O}(m^{(4omega-1)/(2omega+1)}) = O(m^{1.478})$ time algorithm for counting simple 3-paths between vertex pairs.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126457719","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}

{"title":"Majorizing Measures for the Optimizer","authors":"Sander Borst, D. Dadush, Neil Olver, Makrand Sinha","doi":"10.4230/LIPIcs.ITCS.2021.73","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.73","url":null,"abstract":"The theory of majorizing measures, extensively developed by Fernique, Talagrand and many others, provides one of the most general frameworks for controlling the behavior of stochastic processes. In particular, it can be applied to derive quantitative bounds on the expected suprema and the degree of continuity of sample paths for many processes. One of the crowning achievements of the theory is Talagrand’s tight alternative characterization of the suprema of Gaussian processes in terms of majorizing measures. The proof of this theorem was difficult, and thus considerable effort was put into the task of developing both shorter and easier to understand proofs. A major reason for this difficulty was considered to be theory of majorizing measures itself, which had the reputation of being opaque and mysterious. As a consequence, most recent treatments of the theory (including by Talagrand himself) have eschewed the use of majorizing measures in favor of a purely combinatorial approach (the generic chaining) where objects based on sequences of partitions provide roughly matching upper and lower bounds on the desired expected supremum. In this paper, we return to majorizing measures as a primary object of study, and give a viewpoint that we think is natural and clarifying from an optimization perspective. As our main contribution, we give an algorithmic proof of the majorizing measures theorem based on two parts: We make the simple (but apparently new) observation that finding the best majorizing measure can be cast as a convex program. This also allows for efficiently computing the measure using off-the-shelf methods from convex optimization. We obtain tree-based upper and lower bound certificates by rounding, in a series of steps, the primal and dual solutions to this convex program. While duality has conceptually been part of the theory since its beginnings, as far as we are aware no explicit link to convex optimization has been previously made. 2012 ACM Subject Classification Mathematics of computing → Stochastic processes; Mathematics of computing → Convex optimization; Theory of computation → Randomness, geometry and discrete structures","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129676830","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}

{"title":"Sampling Arborescences in Parallel","authors":"Nima Anari, Nathan Hu, A. Saberi, Aaron Schild","doi":"10.4230/LIPIcs.ITCS.2021.83","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.83","url":null,"abstract":"We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the exact number of arborescences can be computed by a determinant [Tut48], and sampling can be reduced to counting [JVV86, JS96]. However, the classic reduction from sampling to counting seems to be inherently sequential. This raises the question of designing efficient parallel algorithms for sampling. We show that sampling arborescences can be done in RNC. \u0000For several well-studied combinatorial structures, counting can be reduced to the computation of a determinant, which is known to be in NC [Csa75]. These include arborescences, planar graph perfect matchings, Eulerian tours in digraphs, and determinantal point processes. However, not much is known about efficient parallel sampling of these structures. Our work is a step towards resolving this mystery.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127113448","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}

{"title":"Non-quasi-linear Agents in Quasi-linear Mechanisms","authors":"Moshe Babaioff, R. Cole, Jason D. Hartline, Nicole Immorlica, Brendan Lucier","doi":"10.4230/LIPIcs.ITCS.2021.84","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.84","url":null,"abstract":"Mechanisms with money are commonly designed under the assumption that agents are quasi-linear, meaning they have linear disutility for spending money. We study the implications when agents with non-linear (specifically, convex) disutility for payments participate in mechanisms designed for quasi-linear agents. We first show that any mechanism that is truthful for quasi-linear buyers has a simple best response function for buyers with non-linear disutility from payments, in which each bidder simply scales down her value for each potential outcome by a fixed factor, equal to her target return on investment (ROI). We call such a strategy ROI-optimal. We prove the existence of a Nash equilibrium in which agents use ROI-optimal strategies for a general class of allocation problems. Motivated by online marketplaces, we then focus on simultaneous second-price auctions for additive bidders and show that all ROI-optimal equilibria in this setting achieve constant-factor approximations to suitable welfare and revenue benchmarks.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130560614","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}

{"title":"Comparison Graphs: a Unified Method for Uniformity Testing","authors":"Uri Meir","doi":"10.4230/LIPIcs.ITCS.2021.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2021.17","url":null,"abstract":"Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far from it. The most studied problem in the field is arguably uniformity testing, where one needs to distinguish the case that $P$ is uniform over $[n]$ from the case that $P$ is $epsilon$-far from being uniform (in $ell_1$). In the classic model, it is known that $Thetaleft(sqrt{n}/epsilon^2right)$ samples are necessary and sufficient for this task. This problem was recently considered in various restricted models that pose, for example, communication or memory constraints. In more than one occasion, the known optimal solution boils down to counting collisions among the drawn samples (each two samples that have the same value add one to the count), an idea that dates back to the first uniformity tester, and was coined the name \"collision-based tester\". \u0000In this paper, we introduce the notion of comparison graphs and use it to formally define a generalized collision-based tester. Roughly speaking, the edges of the graph indicate the tester which pairs of samples should be compared (that is, the original tester is induced by a clique, where all pairs are being compared). We prove a structural theorem that gives a sufficient condition for a comparison graph to induce a good uniformity tester. As an application, we develop a generic method to test uniformity, and devise nearly-optimal uniformity testers under various computational constraints. We improve and simplify a few known results, and introduce a new constrained model in which the method also produces an efficient tester. \u0000The idea behind our method is to translate computational constraints of a certain model to ones on the comparison graph, which paves the way to finding a good graph.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134444871","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}