Information Technology Convergence and Services最新文献

{"title":"Low-bandwidth recovery of linear functions of Reed-Solomon-encoded data","authors":"N. Shutty, Mary Wootters","doi":"10.4230/LIPIcs.ITCS.2022.117","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.117","url":null,"abstract":"We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions $F:mathbb{F}^k to mathbb{F}$ of some data $x in mathbb{F}^k$, given access to an encoding $c in mathbb{F}^n$ of $x$ under an error correcting code. In our model -- relevant in distributed storage, distributed computation and secret sharing -- each symbol of $c$ is held by a different party, and we aim to minimize the total amount of information downloaded from each party in order to compute $F(x)$. Special cases of this problem have arisen in several domains, and we believe that it is fruitful to study this problem in generality. Our main result is a low-bandwidth scheme to compute linear functions for Reed-Solomon codes, even in the presence of erasures. More precisely, let $epsilon>0$ and let $mathcal{C}: mathbb{F}^k to mathbb{F}^n$ be a full-length Reed-Solomon code of rate $1 - epsilon$ over a field $mathbb{F}$ with constant characteristic. For any $gamma in [0, epsilon)$, our scheme can compute any linear function $F(x)$ given access to any $(1 - gamma)$-fraction of the symbols of $mathcal{C}(x)$, with download bandwidth $O(n/(epsilon - gamma))$ bits. In contrast, the naive scheme that involves reconstructing the data $x$ and then computing $F(x)$ uses $Theta(n log n)$ bits. Our scheme has applications in distributed storage, coded computation, and homomorphic secret sharing.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126380109","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":"Lower Bounds for Symmetric Circuits for the Determinant","authors":"A. Dawar, G. Wilsenach","doi":"10.4230/LIPIcs.ITCS.2022.52","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.52","url":null,"abstract":"Dawar and Wilsenach (ICALP 2020) introduce the model of symmetric arithmetic circuits and show an exponential separation between the sizes of symmetric circuits for computing the determinant and the permanent. The symmetry restriction is that the circuits which take a matrix input are unchanged by a permutation applied simultaneously to the rows and columns of the matrix. Under such restrictions we have polynomial-size circuits for computing the determinant but no subexponential size circuits for the permanent. Here, we consider a more stringent symmetry requirement, namely that the circuits are unchanged by arbitrary even permutations applied separately to rows and columns, and prove an exponential lower bound even for circuits computing the determinant. The result requires substantial new machinery. We develop a general framework for proving lower bounds for symmetric circuits with restricted symmetries, based on a new support theorem and new two-player restricted bijection games. These are applied to the determinant problem with a novel construction of matrices that are bi-adjacency matrices of graphs based on the CFI construction. Our general framework opens the way to exploring a variety of symmetry restrictions and studying trade-offs between symmetry and other resources used by arithmetic circuits.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117161594","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":"Correlation Detection in Trees for Planted Graph Alignment","authors":"Luca Ganassali, L. Massoulié, M. Lelarge","doi":"10.4230/LIPIcs.ITCS.2022.74","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.74","url":null,"abstract":"Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or feasible. We propose MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign to succeed in polynomial time at partial alignment whenever tree detection is feasible. As a result our analysis of tree detection reveals new ranges of parameters for which partial alignment of sparse random graphs is feasible in polynomial time. We then conjecture that graph alignment is not feasible in polynomial time when the associated tree detection problem is impossible. If true, this conjecture together with our sufficient conditions on tree detection impossibility would imply the existence of a hard phase for graph alignment, i.e. a parameter range where alignment cannot be done in polynomial time even though it is known to be feasible in non-polynomial time.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115211409","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":"An Efficient Semi-Streaming PTAS for Tournament Feedback ArcSet with Few Passes","authors":"Anubhav Baweja, Justin Jia, David P. Woodruff","doi":"10.4230/LIPIcs.ITCS.2022.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.16","url":null,"abstract":"We present the first semi-streaming PTAS for the minimum feedback arc set problem on directed tournaments in a small number of passes. Namely, we obtain a $(1 + varepsilon)$-approximation in polynomial time $O left( text{poly}(n) 2^{text{poly}(1/varepsilon)} right)$, with $p$ passes in $n^{1+1/p} cdot text{poly}left(frac{log n}{varepsilon}right)$ space. The only previous algorithm with this pass/space trade-off gave a $3$-approximation (SODA, 2020), and other polynomial-time algorithms which achieved a $(1+varepsilon)$-approximation did so with quadratic memory or with a linear number of passes. We also present a new time/space trade-off for $1$-pass algorithms that solve the tournament feedback arc set problem. This problem has several applications in machine learning such as creating linear classifiers and doing Bayesian inference. We also provide several additional algorithms and lower bounds for related streaming problems on directed graphs, which is a mostly unexplored territory.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123753319","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":"Making Auctions Robust to Aftermarkets","authors":"Moshe Babaioff, Nicole Immorlica, Yingkai Li, Brendan Lucier","doi":"10.4230/LIPIcs.ITCS.2023.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2023.9","url":null,"abstract":"A prevalent assumption in auction theory is that the auctioneer has full control over the market and that the allocation she dictates is final. In practice, however, agents might be able to resell acquired items in an aftermarket. A prominent example is the market for carbon emission allowances. These allowances are commonly allocated by the government using uniform-price auctions, and firms can typically trade these allowances among themselves in an aftermarket that may not be fully under the auctioneer's control. While the uniform-price auction is approximately efficient in isolation, we show that speculation and resale in aftermarkets might result in a significant welfare loss. Motivated by this issue, we consider three approaches, each ensuring high equilibrium welfare in the combined market. The first approach is to adopt smooth auctions such as discriminatory auctions. This approach is robust to correlated valuations and to participants acquiring information about others' types. However, discriminatory auctions have several downsides, notably that of charging bidders different prices for identical items, resulting in fairness concerns that make the format unpopular. Two other approaches we suggest are either using posted-pricing mechanisms, or using uniform-price auctions with anonymous reserves. We show that when using balanced prices, both these approaches ensure high equilibrium welfare in the combined market. The latter also inherits many of the benefits from uniform-price auctions such as price discovery, and can be introduced with a minor modification to auctions currently in use to sell carbon emission allowances.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133629606","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":"Smaller ACC0 Circuits for Symmetric Functions","authors":"Brynmor Chapman, Ryan Williams","doi":"10.4230/LIPIcs.ITCS.2022.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.38","url":null,"abstract":"What is the power of constant-depth circuits with $MOD_m$ gates, that can count modulo $m$? Can they efficiently compute MAJORITY and other symmetric functions? When $m$ is a constant prime power, the answer is well understood: Razborov and Smolensky proved in the 1980s that MAJORITY and $MOD_m$ require super-polynomial-size $MOD_q$ circuits, where $q$ is any prime power not dividing $m$. However, relatively little is known about the power of $MOD_m$ circuits for non-prime-power $m$. For example, it is still open whether every problem in $EXP$ can be computed by depth-$3$ circuits of polynomial size and only $MOD_6$ gates. We shed some light on the difficulty of proving lower bounds for $MOD_m$ circuits, by giving new upper bounds. We construct $MOD_m$ circuits computing symmetric functions with non-prime power $m$, with size-depth tradeoffs that beat the longstanding lower bounds for $AC^0[m]$ circuits for prime power $m$. Our size-depth tradeoff circuits have essentially optimal dependence on $m$ and $d$ in the exponent, under a natural circuit complexity hypothesis. For example, we show for every $varepsilon>0$ that every symmetric function can be computed with depth-3 $MOD_m$ circuits of $exp(O(n^{varepsilon}))$ size, for a constant $m$ depending only on $varepsilon>0$. That is, depth-$3$ $CC^0$ circuits can compute any symmetric function in emph{subexponential} size. This demonstrates a significant difference in the power of depth-$3$ $CC^0$ circuits, compared to other models: for certain symmetric functions, depth-$3$ $AC^0$ circuits require $2^{Omega(sqrt{n})}$ size [H{aa}stad 1986], and depth-$3$ $AC^0[p^k]$ circuits (for fixed prime power $p^k$) require $2^{Omega(n^{1/6})}$ size [Smolensky 1987]. Even for depth-two $MOD_p circ MOD_m$ circuits, $2^{Omega(n)}$ lower bounds were known [Barrington Straubing Th'erien 1990].","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123964278","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":"Balanced Allocations with Incomplete Information: The Power of Two Queries","authors":"Dimitrios Los, Thomas Sauerwald","doi":"10.4230/LIPIcs.ITCS.2022.103","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.103","url":null,"abstract":"We consider the allocation of m balls into n bins with incomplete information. In the classical Two-Choice process a ball first queries the load of two randomly chosen bins and is then placed in the least loaded bin. In our setting, each ball also samples two random bins but can only estimate a bin’s load by sending binary queries of the form “Is the load at least the median?” or “Is the load at least 100?”. For the lightly loaded case m = O(n), Feldheim and Gurel-Gurevich (2021) showed that with one query it is possible to achieve a maximum load of O( √ log n/ log log n), and they also pose the question whether a maximum load of m/n + O( √ log n/ log log n) is possible for any m = Ω(n). In this work, we resolve this open problem by proving a lower bound of m/n + Ω( √ log n) for a fixed m = Θ(n √ log n), and a lower bound of m/n + Ω(log n/ log log n) for some m depending on the used strategy. We complement this negative result by proving a positive result for multiple queries. In particular, we show that with only two binary queries per chosen bin, there is an oblivious strategy which ensures a maximum load of m/n + O( √ log n) for any m ≥ 1. Further, for any number of k = O(log log n) binary queries, the upper bound on the maximum load improves to m/n + O(k(log n)1/k) for any m ≥ 1. This result for k queries has several interesting consequences: (i) it implies new bounds for the (1 + β)-process introduced by Peres, Talwar and Wieder (2015), (ii) it leads to new bounds for the graphical balanced allocation process on dense expander graphs, and (iii) it recovers and generalizes the bound of m/n + O(log log n) on the maximum load achieved by the Two-Choice process, including the heavily loaded case m = Ω(n) which was derived in previous works by Berenbrink et al. (2006) as well as Talwar and Wieder (2014). One novel aspect of our proofs is the use of multiple super-exponential potential functions, which might be of use in future work. 2012 ACM Subject Classification Mathematics of computing → Probability and statistics; Mathematics of computing → Discrete mathematics; Theory of computation → Randomness, geometry and discrete structures; Theory of computation → Design and analysis of algorithms","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134115155","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":"Noisy Boolean Hidden Matching with Applications","authors":"Michael Kapralov, Amulya Musipatla, Jakab Tardos, David P. Woodruff, Samson Zhou","doi":"10.4230/LIPIcs.ITCS.2022.91","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.91","url":null,"abstract":"The Boolean Hidden Matching (BHM) problem, introduced in a seminal paper of Gavinsky et. al. [STOC'07], has played an important role in the streaming lower bounds for graph problems such as triangle and subgraph counting, maximum matching, MAX-CUT, Schatten $p$-norm approximation, maximum acyclic subgraph, testing bipartiteness, $k$-connectivity, and cycle-freeness. The one-way communication complexity of the Boolean Hidden Matching problem on a universe of size $n$ is $Theta(sqrt{n})$, resulting in $Omega(sqrt{n})$ lower bounds for constant factor approximations to several of the aforementioned graph problems. The related (and, in fact, more general) Boolean Hidden Hypermatching (BHH) problem introduced by Verbin and Yu [SODA'11] provides an approach to proving higher lower bounds of $Omega(n^{1-1/t})$ for integer $tgeq 2$. Reductions based on Boolean Hidden Hypermatching generate distributions on graphs with connected components of diameter about $t$, and basically show that long range exploration is hard in the streaming model of computation with adversarial arrivals. In this paper we introduce a natural variant of the BHM problem, called noisy BHM (and its natural noisy BHH variant), that we use to obtain higher than $Omega(sqrt{n})$ lower bounds for approximating several of the aforementioned problems in graph streams when the input graphs consist only of components of diameter bounded by a fixed constant. We also use the noisy BHM problem to show that the problem of classifying whether an underlying graph is isomorphic to a complete binary tree in insertion-only streams requires $Omega(n)$ space, which seems challenging to show using BHM or BHH alone.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131283555","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":"Faster Sparse Matrix Inversion and Rank Computation in Finite Fields","authors":"Sílvia Casacuberta, Rasmus Kyng","doi":"10.4230/LIPIcs.ITCS.2022.33","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.33","url":null,"abstract":"We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected O (cid:0) n 2 . 2131 (cid:1) time for the current values of fast rectangular matrix multiplication. We achieve the same running time for the computation of the rank and nullspace of a sparse matrix over a finite field. This improvement relies on two key techniques. First, we adopt the decomposition of an arbitrary matrix into block Krylov and Hankel matrices from Eberly et al. (ISSAC 2007). Second, we show how to recover the explicit inverse of a block Hankel matrix using low displacement rank techniques for structured matrices and fast rectangular matrix multiplication algorithms. We generalize our inversion method to block structured matrices with other displacement operators and strengthen the best known upper bounds for explicit inversion of block Toeplitz-like and block Hankel-like matrices, as well as for explicit inversion of block Vandermonde-like matrices with structured blocks. As a further application, we improve the complexity of several algorithms in topological data analysis and in finite group theory.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131160417","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":"Indistinguishability Obfuscation of Null Quantum Circuits and Applications","authors":"James Bartusek, Giulio Malavolta","doi":"10.4230/LIPIcs.ITCS.2022.15","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.15","url":null,"abstract":"We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of ''dual-mode'' classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131969251","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}