{"title":"Optimal Offline ORAM with Perfect Security via Simple Oblivious Priority Queues","authors":"Thore Thießen, Jan Vahrenhold","doi":"arxiv-2409.12021","DOIUrl":"https://doi.org/arxiv-2409.12021","url":null,"abstract":"Oblivious RAM (ORAM) is a well-researched primitive to hide the memory access\u0000pattern of a RAM computation; it has a variety of applications in trusted\u0000computing, outsourced storage, and multiparty computation. In this paper, we\u0000study the so-called offline ORAM in which the sequence of memory access\u0000locations to be hidden is known in advance. Apart from their theoretical\u0000significance, offline ORAMs can be used to construct efficient oblivious\u0000algorithms. We obtain the first optimal offline ORAM with perfect security from oblivious\u0000priority queues via time-forward processing. For this, we present a simple\u0000construction of an oblivious priority queue with perfect security. Our\u0000construction achieves an asymptotically optimal (amortized) runtime of\u0000$Theta(log N)$ per operation for a capacity of $N$ elements and is of\u0000independent interest. Building on our construction, we additionally present efficient\u0000external-memory instantiations of our oblivious, perfectly-secure construction:\u0000For the cache-aware setting, we match the optimal I/O complexity of\u0000$Theta(frac{1}{B} log frac{N}{M})$ per operation (amortized), and for the\u0000cache-oblivious setting we achieve a near-optimal I/O complexity of\u0000$O(frac{1}{B} log frac{N}{M} loglog_M N)$ per operation (amortized).","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263328","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":"Lempel-Ziv (LZ77) Factorization in Sublinear Time","authors":"Dominik Kempa, Tomasz Kociumaka","doi":"arxiv-2409.12146","DOIUrl":"https://doi.org/arxiv-2409.12146","url":null,"abstract":"Lempel-Ziv (LZ77) factorization is a fundamental problem in string\u0000processing: Greedily partition a given string $T$ from left to right into\u0000blocks (called phrases) so that each phrase is either the leftmost occurrence\u0000of a letter or the longest prefix of the unprocessed suffix that has another\u0000occurrence earlier in $T$. Due to numerous applications, LZ77 factorization is\u0000one of the most studied problems on strings. In the 47 years since its\u0000inception, several algorithms were developed for different models of\u0000computation, including parallel, GPU, external-memory, and quantum. Remarkably,\u0000however, the complexity of the most basic variant is still not settled: All\u0000existing algorithms in the RAM model run in $Omega(n)$ time, which is a\u0000$Theta(log n)$ factor away from the lower bound of $Omega(n/log n)$\u0000(following from the necessity to read the input, which takes $Theta(n/log n)$\u0000space for $Tin{0,1}^{n}$). We present the first $o(n)$-time algorithm for LZ77 factorization, breaking\u0000the linear-time barrier present for nearly 50 years. For $Tin{0,1}^{n}$, our\u0000algorithm runs in $mathcal{O}(n/sqrt{log n})=o(n)$ time and uses the optimal\u0000$mathcal{O}(n/log n)$ working space. Our algorithm generalizes to\u0000$Sigma=[0..sigma)$, where $sigma=n^{mathcal{O}(1)}$. The runtime and\u0000working space then become $mathcal{O}((nlogsigma)/sqrt{log n})$ and\u0000$mathcal{O}(n/log_{sigma} n)$. To obtain our algorithm, we prove a more\u0000general result: For any constant $epsilonin(0,1)$ and $Tin[0..sigma)^{n}$,\u0000in $mathcal{O}((nlogsigma)/sqrt{log n})$ time and using\u0000$mathcal{O}(n/log_{sigma}n)$ space, we can construct an\u0000$mathcal{O}(n/log_{sigma}n)$-size index that, given any $P=T[j..j+ell)$\u0000(represented as $(j,ell)$), computes the leftmost occurrence of $P$ in $T$ in\u0000$mathcal{O}(log^{epsilon}n)$ time. In other words, we solve the\u0000indexing/online variant of the LZ77 problem.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263104","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}
Hadley Black, Euiwoong Lee, Arya Mazumdar, Barna Saha
{"title":"Clustering with Non-adaptive Subset Queries","authors":"Hadley Black, Euiwoong Lee, Arya Mazumdar, Barna Saha","doi":"arxiv-2409.10908","DOIUrl":"https://doi.org/arxiv-2409.10908","url":null,"abstract":"Recovering the underlying clustering of a set $U$ of $n$ points by asking\u0000pair-wise same-cluster queries has garnered significant interest in the last\u0000decade. Given a query $S subset U$, $|S|=2$, the oracle returns yes if the\u0000points are in the same cluster and no otherwise. For adaptive algorithms with\u0000pair-wise queries, the number of required queries is known to be $Theta(nk)$,\u0000where $k$ is the number of clusters. However, non-adaptive schemes require\u0000$Omega(n^2)$ queries, which matches the trivial $O(n^2)$ upper bound attained\u0000by querying every pair of points. To break the quadratic barrier for non-adaptive queries, we study a\u0000generalization of this problem to subset queries for $|S|>2$, where the oracle\u0000returns the number of clusters intersecting $S$. Allowing for subset queries of\u0000unbounded size, $O(n)$ queries is possible with an adaptive scheme\u0000(Chakrabarty-Liao, 2024). However, the realm of non-adaptive algorithms is\u0000completely unknown. In this paper, we give the first non-adaptive algorithms for clustering with\u0000subset queries. Our main result is a non-adaptive algorithm making $O(n log k\u0000cdot (log k + loglog n)^2)$ queries, which improves to $O(n log log n)$\u0000when $k$ is a constant. We also consider algorithms with a restricted query\u0000size of at most $s$. In this setting we prove that $Omega(max(n^2/s^2,n))$\u0000queries are necessary and obtain algorithms making $tilde{O}(n^2k/s^2)$\u0000queries for any $s leq sqrt{n}$ and $tilde{O}(n^2/s)$ queries for any $s\u0000leq n$. We also consider the natural special case when the clusters are\u0000balanced, obtaining non-adaptive algorithms which make $O(n log k) +\u0000tilde{O}(k)$ and $O(nlog^2 k)$ queries. Finally, allowing two rounds of\u0000adaptivity, we give an algorithm making $O(n log k)$ queries in the general\u0000case and $O(n log log k)$ queries when the clusters are balanced.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263331","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":"Tight Bounds for Classical Open Addressing","authors":"Michael A. Bender, William Kuszmaul, Renfei Zhou","doi":"arxiv-2409.11280","DOIUrl":"https://doi.org/arxiv-2409.11280","url":null,"abstract":"We introduce a classical open-addressed hash table, called rainbow hashing,\u0000that supports a load factor of up to $1 - varepsilon$, while also supporting\u0000$O(1)$ expected-time queries, and $O(log log varepsilon^{-1})$ expected-time\u0000insertions and deletions. We further prove that this tradeoff curve is optimal:\u0000any classical open-addressed hash table that supports load factor $1 -\u0000varepsilon$ must incur $Omega(log log varepsilon^{-1})$ expected time per\u0000operation. Finally, we extend rainbow hashing to the setting where the hash table is\u0000dynamically resized over time. Surprisingly, the addition of dynamic resizing\u0000does not come at any time cost -- even while maintaining a load factor of $ge\u00001 - varepsilon$ at all times, we can support $O(1)$ queries and $O(log log\u0000varepsilon^{-1})$ updates. Prior to our work, achieving any time bounds of the form\u0000$o(varepsilon^{-1})$ for all of insertions, deletions, and queries\u0000simultaneously remained an open question.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269555","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":"Selective algorithm processing of subset sum distributions","authors":"Nick Dawes","doi":"arxiv-2409.11076","DOIUrl":"https://doi.org/arxiv-2409.11076","url":null,"abstract":"The efficiency of exact subset sum problem algorithms which compute\u0000individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number\u0000of subset sums computed. $e$ is related to these algorithms' computational\u0000complexity. This system maps the sums into $kn$ bins to select its most\u0000efficient algorithm for each bin for each input value. These algorithms include\u0000additive, subtractive and repeated value dynamic programming. Cases which would\u0000otherwise be processed inefficiently (eg: all even values) are handled by\u0000modular arithmetic and by dynamically partioning the input values. The system's\u0000experimentally validated efficiency corresponds to O(max($T$, $n^2$)) with\u0000space complexity O(max($T$, $n$)), for $k=2$.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263330","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}
Paul Dütting, Thomas Kesselheim, Brendan Lucier, Rebecca Reiffenhäuser, Sahil Singla
{"title":"Online Combinatorial Allocations and Auctions with Few Samples","authors":"Paul Dütting, Thomas Kesselheim, Brendan Lucier, Rebecca Reiffenhäuser, Sahil Singla","doi":"arxiv-2409.11091","DOIUrl":"https://doi.org/arxiv-2409.11091","url":null,"abstract":"In online combinatorial allocations/auctions, n bidders sequentially arrive,\u0000each with a combinatorial valuation (such as submodular/XOS) over subsets of m\u0000indivisible items. The aim is to immediately allocate a subset of the remaining\u0000items to maximize the total welfare, defined as the sum of bidder valuations. A\u0000long line of work has studied this problem when the bidder valuations come from\u0000known independent distributions. In particular, for submodular/XOS valuations,\u0000we know 2-competitive algorithms/mechanisms that set a fixed price for each\u0000item and the arriving bidders take their favorite subset of the remaining items\u0000given these prices. However, these algorithms traditionally presume the\u0000availability of the underlying distributions as part of the input to the\u0000algorithm. Contrary to this assumption, practical scenarios often require the\u0000learning of distributions, a task complicated by limited sample availability.\u0000This paper investigates the feasibility of achieving O(1)-competitive\u0000algorithms under the realistic constraint of having access to only a limited\u0000number of samples from the underlying bidder distributions. Our first main contribution shows that a mere single sample from each bidder\u0000distribution is sufficient to yield an O(1)-competitive algorithm for\u0000submodular/XOS valuations. This result leverages a novel extension of the\u0000secretary-style analysis, employing the sample to have the algorithm compete\u0000against itself. Although online, this first approach does not provide an online\u0000truthful mechanism. Our second main contribution shows that a polynomial number\u0000of samples suffices to yield a $(2+epsilon)$-competitive online truthful\u0000mechanism for submodular/XOS valuations and any constant $epsilon>0$. This\u0000result is based on a generalization of the median-based algorithm for the\u0000single-item prophet inequality problem to combinatorial settings with multiple\u0000items.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269932","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":"Learning-Augmented Frequency Estimation in Sliding Windows","authors":"Rana Shahout, Ibrahim Sabek, Michael Mitzenmacher","doi":"arxiv-2409.11516","DOIUrl":"https://doi.org/arxiv-2409.11516","url":null,"abstract":"We show how to utilize machine learning approaches to improve sliding window\u0000algorithms for approximate frequency estimation problems, under the\u0000``algorithms with predictions'' framework. In this dynamic environment,\u0000previous learning-augmented algorithms are less effective, since properties in\u0000sliding window resolution can differ significantly from the properties of the\u0000entire stream. Our focus is on the benefits of predicting and filtering out\u0000items with large next arrival times -- that is, there is a large gap until\u0000their next appearance -- from the stream, which we show improves the\u0000memory-accuracy tradeoffs significantly. We provide theorems that provide\u0000insight into how and by how much our technique can improve the sliding window\u0000algorithm, as well as experimental results using real-world data sets. Our work\u0000demonstrates that predictors can be useful in the challenging sliding window\u0000setting.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269554","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}
Daniel Funke, Demian Hespe, Peter Sanders, Sabine Storandt, Carina Truschel
{"title":"Pareto Sums of Pareto Sets: Lower Bounds and Algorithms","authors":"Daniel Funke, Demian Hespe, Peter Sanders, Sabine Storandt, Carina Truschel","doi":"arxiv-2409.10232","DOIUrl":"https://doi.org/arxiv-2409.10232","url":null,"abstract":"In bi-criteria optimization problems, the goal is typically to compute the\u0000set of Pareto-optimal solutions. Many algorithms for these types of problems\u0000rely on efficient merging or combining of partial solutions and filtering of\u0000dominated solutions in the resulting sets. In this article, we consider the\u0000task of computing the Pareto sum of two given Pareto sets $A, B$ of size $n$.\u0000The Pareto sum $C$ contains all non-dominated points of the Minkowski sum $M =\u0000{a+b|a in A, bin B}$. Since the Minkowski sum has a size of $n^2$, but the\u0000Pareto sum $C$ can be much smaller, the goal is to compute $C$ without having\u0000to compute and store all of $M$. We present several new algorithms for\u0000efficient Pareto sum computation, including an output-sensitive successive\u0000algorithm with a running time of $O(n log n + nk)$ and a space consumption of\u0000$O(n+k)$ for $k=|C|$. If the elements of $C$ are streamed, the space\u0000consumption reduces to $O(n)$. For output sizes $k geq 2n$, we prove a\u0000conditional lower bound for Pareto sum computation, which excludes running\u0000times in $O(n^{2-delta})$ for $delta > 0$ unless the (min,+)-convolution\u0000hardness conjecture fails. The successive algorithm matches this lower bound\u0000for $k in Theta(n)$. However, for $k in Theta(n^2)$, the successive\u0000algorithm exhibits a cubic running time. But we also present an algorithm with\u0000an output-sensitive space consumption and a running time of $O(n^2 log n)$,\u0000which matches the lower bound up to a logarithmic factor even for large $k$.\u0000Furthermore, we describe suitable engineering techniques to improve the\u0000practical running times of our algorithms. Finally, we provide an extensive\u0000comparative experimental study on generated and real-world data. As a showcase\u0000application, we consider preprocessing-based bi-criteria route planning in road\u0000networks.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263332","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}
Jingbang Chen, Mehrdad Ghadiri, Hoai-An Nguyen, Richard Peng, Junzhao Yang
{"title":"Entrywise Approximate Laplacian Solving","authors":"Jingbang Chen, Mehrdad Ghadiri, Hoai-An Nguyen, Richard Peng, Junzhao Yang","doi":"arxiv-2409.10022","DOIUrl":"https://doi.org/arxiv-2409.10022","url":null,"abstract":"We study the escape probability problem in random walks over graphs. Given\u0000vertices, $s,t,$ and $p$, the problem asks for the probability that a random\u0000walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be\u0000exponentially small even for unweighted undirected graphs with polynomial\u0000mixing time. Therefore current approaches, which are mostly based on\u0000fixed-point arithmetic, require $n$ bits of precision in the worst case. We\u0000present algorithms and analyses for weighted directed graphs under\u0000floating-point arithmetic and improve the previous best running times in terms\u0000of the number of bit operations. We believe our techniques and analysis could\u0000have a broader impact on the computation of random walks on graphs both in\u0000theory and in practice.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269558","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":"Multi-Slot Tag Assignment Problem in Billboard Advertisement","authors":"Dildar Ali, Suman Banerjee, Yamuna Prasad","doi":"arxiv-2409.09623","DOIUrl":"https://doi.org/arxiv-2409.09623","url":null,"abstract":"Nowadays, billboard advertising has emerged as an effective advertising\u0000technique due to higher returns on investment. Given a set of selected slots\u0000and tags, how to effectively assign the tags to the slots remains an important\u0000question. In this paper, we study the problem of assigning tags to the slots\u0000such that the number of tags for which influence demand of each zone is\u0000satisfied gets maximized. Formally, we call this problem the Multi-Slot Tag\u0000Assignment Problem. The input to the problem is a geographical region\u0000partitioned into several zones, a set of selected tags and slots, a trajectory,\u0000a billboard database, and the influence demand for every tag for each zone. The\u0000task here is to find out the assignment of tags to the slots, such the number\u0000of tags for which the zonal influence demand is satisfied is maximized. We show\u0000that the problem is NP-hard, and we propose an efficient approximation\u0000algorithm to solve this problem. A time and space complexity analysis of the\u0000proposed methodology has been done. The proposed methodology has been\u0000implemented with real-life datasets, and a number of experiments have been\u0000carried out to show the effectiveness and efficiency of the proposed approach.\u0000The obtained results have been compared with the baseline methods, and we\u0000observe that the proposed approach leads to a number of tags whose zonal\u0000influence demand is satisfied.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263333","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}
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