Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms最新文献

A Polynomial Time Algorithm for Finding a Minimum 4-Partition of a Submodular Function 求子模函数最小4分的多项式时间算法

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-12-06 DOI: 10.1137/1.9781611977554.ch64

Tsuyoshi Hirayama, Yuhao Liu, K. Makino, Ke Shi, Chao Xu

引用次数: 1

Player-optimal Stable Regret for Bandit Learning in Matching Markets 匹配市场中盗贼学习的玩家最优稳定遗憾

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-07-20 DOI: 10.1137/1.9781611977554.ch55

Fang-yuan Kong, Shuai Li

{"title":"Player-optimal Stable Regret for Bandit Learning in Matching Markets","authors":"Fang-yuan Kong, Shuai Li","doi":"10.1137/1.9781611977554.ch55","DOIUrl":"https://doi.org/10.1137/1.9781611977554.ch55","url":null,"abstract":"The problem of matching markets has been studied for a long time in the literature due to its wide range of applications. Finding a stable matching is a common equilibrium objective in this problem. Since market participants are usually uncertain of their preferences, a rich line of recent works study the online setting where one-side participants (players) learn their unknown preferences from iterative interactions with the other side (arms). Most previous works in this line are only able to derive theoretical guarantees for player-pessimal stable regret, which is defined compared with the players' least-preferred stable matching. However, under the pessimal stable matching, players only obtain the least reward among all stable matchings. To maximize players' profits, player-optimal stable matching would be the most desirable. Though citet{basu21beyond} successfully bring an upper bound for player-optimal stable regret, their result can be exponentially large if players' preference gap is small. Whether a polynomial guarantee for this regret exists is a significant but still open problem. In this work, we provide a new algorithm named explore-then-Gale-Shapley (ETGS) and show that the optimal stable regret of each player can be upper bounded by $O(Klog T/Delta^2)$ where $K$ is the number of arms, $T$ is the horizon and $Delta$ is the players' minimum preference gap among the first $N+1$-ranked arms. This result significantly improves previous works which either have a weaker player-pessimal stable matching objective or apply only to markets with special assumptions. When the preferences of participants satisfy some special conditions, our regret upper bound also matches the previously derived lower bound.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"16 1","pages":"1512-1522"},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84219989","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

Optimal Square Detection Over General Alphabets 通用字母的最优平方检测

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-03-13 DOI: 10.1137/1.9781611977554.ch189

J. Ellert, Paweł Gawrychowski, Garance Gourdel

{"title":"Optimal Square Detection Over General Alphabets","authors":"J. Ellert, Paweł Gawrychowski, Garance Gourdel","doi":"10.1137/1.9781611977554.ch189","DOIUrl":"https://doi.org/10.1137/1.9781611977554.ch189","url":null,"abstract":"Squares (fragments of the form $xx$, for some string $x$) are arguably the most natural type of repetition in strings. The basic algorithmic question concerning squares is to check if a given string of length $n$ is square-free, that is, does not contain a fragment of such form. Main and Lorentz [J. Algorithms 1984] designed an $mathcal{O}(nlog n)$ time algorithm for this problem, and proved a matching lower bound assuming the so-called general alphabet, meaning that the algorithm is only allowed to check if two characters are equal. However, their lower bound also assumes that there are $Omega(n)$ distinct symbols in the string. As an open question, they asked if there is a faster algorithm if one restricts the size of the alphabet. Crochemore [Theor. Comput. Sci. 1986] designed a linear-time algorithm for constant-size alphabets, and combined with more recent results his approach in fact implies such an algorithm for linearly-sortable alphabets. Very recently, Ellert and Fischer [ICALP 2021] significantly relaxed this assumption by designing a linear-time algorithm for general ordered alphabets, that is, assuming a linear order on the characters that permits constant time order comparisons. However, the open question of Main and Lorentz from 1984 remained unresolved for general (unordered) alphabets. In this paper, we show that testing square-freeness of a length-$n$ string over general alphabet of size $sigma$ can be done with $mathcal{O}(nlog sigma)$ comparisons, and cannot be done with $o(nlog sigma)$ comparisons. We complement this result with an $mathcal{O}(nlog sigma)$ time algorithm in the Word RAM model. Finally, we extend the algorithm to reporting all the runs (maximal repetitions) in the same complexity.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"110 1","pages":"5220-5242"},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81611563","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

Fully Dynamic Exact Edge Connectivity in Sublinear Time 在亚线性时间内的完全动态精确边连通性

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-02-12 DOI: 10.1137/1.9781611977554.ch3

Gramoz Goranci, M. Henzinger, Danupon Nanongkai, Thatchaphol Saranurak, M. Thorup, Christian Wulff-Nilsen

引用次数: 1

Maximal k-Edge-Connected Subgraphs in Weighted Graphs via Local Random Contraction 基于局部随机收缩的加权图中最大k边连通子图

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-02-05 DOI: 10.48550/arXiv.2302.02290

Chaitanya Nalam, Thatchaphol Saranurak

{"title":"Maximal k-Edge-Connected Subgraphs in Weighted Graphs via Local Random Contraction","authors":"Chaitanya Nalam, Thatchaphol Saranurak","doi":"10.48550/arXiv.2302.02290","DOIUrl":"https://doi.org/10.48550/arXiv.2302.02290","url":null,"abstract":"The emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward recursive-mincut algorithm with $Omega(mn)$ time has remained the fastest algorithm until now. All previous progress gives a speed-up only when the graph is unweighted, and $k$ is small enough (e.g.~Henzinger~et~al.~(ICALP'15), Chechik~et~al.~(SODA'17), and Forster~et~al.~(SODA'20)). We give the first algorithm that breaks through the long-standing $tilde{O}(mn)$-time barrier in emph{weighted undirected} graphs. More specifically, we show a maximal $k$-edge-connected subgraphs algorithm that takes only $tilde{O}(mcdotmin{m^{3/4},n^{4/5}})$ time. As an immediate application, we can $(1+epsilon)$-approximate the emph{strength} of all edges in undirected graphs in the same running time. Our key technique is the first local cut algorithm with emph{exact} cut-value guarantees whose running time depends only on the output size. All previous local cut algorithms either have running time depending on the cut value of the output, which can be arbitrarily slow in weighted graphs or have approximate cut guarantees.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"11 1","pages":"183-211"},"PeriodicalIF":0.0,"publicationDate":"2023-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90168105","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

Balanced Allocations with Heterogeneous Bins: The Power of Memory 异构箱的均衡分配:内存的力量

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-24 DOI: 10.1137/1.9781611977554.ch169

Dimitrios Los, Thomas Sauerwald, John Sylvester

{"title":"Balanced Allocations with Heterogeneous Bins: The Power of Memory","authors":"Dimitrios Los, Thomas Sauerwald, John Sylvester","doi":"10.1137/1.9781611977554.ch169","DOIUrl":"https://doi.org/10.1137/1.9781611977554.ch169","url":null,"abstract":"We consider the allocation of $m$ balls (jobs) into $n$ bins (servers). In the standard Two-Choice process, at each step $t=1,2,ldots,m$ we first sample two bins uniformly at random and place a ball in the least loaded bin. It is well-known that for any $m geq n$, this results in a gap (difference between the maximum and average load) of $log_2 log n + Theta(1)$ (with high probability). In this work, we consider the Memory process [Mitzenmacher, Prabhakar and Shah 2002] where instead of two choices, we only sample one bin per step but we have access to a cache which can store the location of one bin. Mitzenmacher, Prabhakar and Shah showed that in the lightly loaded case ($m = n$), the Memory process achieves a gap of $mathcal{O}(log log n)$. Extending the setting of Mitzenmacher et al. in two ways, we first allow the number of balls $m$ to be arbitrary, which includes the challenging heavily loaded case where $m geq n$. Secondly, we follow the heterogeneous bins model of Wieder [Wieder 2007], where the sampling distribution of bins can be biased up to some arbitrary multiplicative constant. Somewhat surprisingly, we prove that even in this setting, the Memory process still achieves an $mathcal{O}(log log n)$ gap bound. This is in stark contrast with the Two-Choice (or any $d$-Choice with $d=mathcal{O}(1)$) process, where it is known that the gap diverges as $m rightarrow infty$ [Wieder 2007]. Further, we show that for any sampling distribution independent of $m$ (but possibly dependent on $n$) the Memory process has a gap that can be bounded independently of $m$. Finally, we prove a tight gap bound of $mathcal{O}(log n)$ for Memory in another relaxed setting with heterogeneous (weighted) balls and a cache which can only be maintained for two steps.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"45 1","pages":"4448-4477"},"PeriodicalIF":0.0,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83649691","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

Approximating Knapsack and Partition via Dense Subset Sums 用密集子集和逼近背包和分区

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-23 DOI: 10.1137/1.9781611977554.ch113

Mingyang Deng, Ce Jin, Xiao Mao

{"title":"Approximating Knapsack and Partition via Dense Subset Sums","authors":"Mingyang Deng, Ce Jin, Xiao Mao","doi":"10.1137/1.9781611977554.ch113","DOIUrl":"https://doi.org/10.1137/1.9781611977554.ch113","url":null,"abstract":"Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. - Knapsack can be $(1 - varepsilon)$-approximated in $tilde O(n + (1/varepsilon) ^ {2.2} )$ time, improving the previous $tilde O(n + (1/varepsilon) ^ {2.25} )$ by Jin (ICALP'19). There is a known conditional lower bound of $(n+varepsilon)^{2-o(1)}$ based on $(min,+)$-convolution hypothesis. - Partition can be $(1 - varepsilon)$-approximated in $tilde O(n + (1/varepsilon) ^ {1.25} )$ time, improving the previous $tilde O(n + (1/varepsilon) ^ {1.5} )$ by Bringmann and Nakos (SODA'21). There is a known conditional lower bound of $(1/varepsilon)^{1-o(1)}$ based on Strong Exponential Time Hypothesis. Both of our new algorithms apply the additive combinatorial results on dense subset sums by Galil and Margalit (SICOMP'91), Bringmann and Wellnitz (SODA'21). Such techniques have not been explored in the context of Knapsack prior to our work. In addition, we design several new methods to speed up the divide-and-conquer steps which naturally arise in solving additive problems.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"72 1","pages":"2961-2979"},"PeriodicalIF":0.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86909724","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: 10

An Improved Approximation for Maximum Weighted k-Set Packing 最大加权k集填充的一种改进逼近

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-18 DOI: 10.48550/arXiv.2301.07537

Theophile Thiery, J. Ward

{"title":"An Improved Approximation for Maximum Weighted k-Set Packing","authors":"Theophile Thiery, J. Ward","doi":"10.48550/arXiv.2301.07537","DOIUrl":"https://doi.org/10.48550/arXiv.2301.07537","url":null,"abstract":"We consider the weighted $k$-set packing problem, in which we are given a collection of weighted sets, each with at most $k$ elements and must return a collection of pairwise disjoint sets with maximum total weight. For $k = 3$, this problem generalizes the classical 3-dimensional matching problem listed as one of the Karp's original 21 NP-complete problems. We give an algorithm attaining an approximation factor of $1.786$ for weighted 3-set packing, improving on the recent best result of $2-frac{1}{63,700,992}$ due to Neuwohner. Our algorithm is based on the local search procedure of Berman that attempts to improve the sum of squared weights rather than the problem's objective. When using exchanges of size at most $k$, this algorithm attains an approximation factor of $frac{k+1}{2}$. Using exchanges of size $k^2(k-1) + k$, we provide a relatively simple analysis to obtain an approximation factor of 1.811 when $k = 3$. We then show that the tools we develop can be adapted to larger exchanges of size $2k^2(k-1) + k$ to give an approximation factor of 1.786. Although our primary focus is on the case $k = 3$, our approach in fact gives slightly stronger improvements on the factor $frac{k+1}{2}$ for all $k>3$. As in previous works, our guarantees hold also for the more general problem of finding a maximum weight independent set in a $(k+1)$-claw free graph.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"31 1","pages":"1138-1162"},"PeriodicalIF":0.0,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81996149","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

Non-Stochastic CDF Estimation Using Threshold Queries 使用阈值查询的非随机CDF估计

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-01-13 DOI: 10.48550/arXiv.2301.05682

Princewill Okoroafor, Vaishnavi Gupta, Robert D. Kleinberg, Eleanor Goh

{"title":"Non-Stochastic CDF Estimation Using Threshold Queries","authors":"Princewill Okoroafor, Vaishnavi Gupta, Robert D. Kleinberg, Eleanor Goh","doi":"10.48550/arXiv.2301.05682","DOIUrl":"https://doi.org/10.48550/arXiv.2301.05682","url":null,"abstract":"Estimating the empirical distribution of a scalar-valued data set is a basic and fundamental task. In this paper, we tackle the problem of estimating an empirical distribution in a setting with two challenging features. First, the algorithm does not directly observe the data; instead, it only asks a limited number of threshold queries about each sample. Second, the data are not assumed to be independent and identically distributed; instead, we allow for an arbitrary process generating the samples, including an adaptive adversary. These considerations are relevant, for example, when modeling a seller experimenting with posted prices to estimate the distribution of consumers' willingness to pay for a product: offering a price and observing a consumer's purchase decision is equivalent to asking a single threshold query about their value, and the distribution of consumers' values may be non-stationary over time, as early adopters may differ markedly from late adopters. Our main result quantifies, to within a constant factor, the sample complexity of estimating the empirical CDF of a sequence of elements of $[n]$, up to $varepsilon$ additive error, using one threshold query per sample. The complexity depends only logarithmically on $n$, and our result can be interpreted as extending the existing logarithmic-complexity results for noisy binary search to the more challenging setting where noise is non-stochastic. Along the way to designing our algorithm, we consider a more general model in which the algorithm is allowed to make a limited number of simultaneous threshold queries on each sample. We solve this problem using Blackwell's Approachability Theorem and the exponential weights method. As a side result of independent interest, we characterize the minimum number of simultaneous threshold queries required by deterministic CDF estimation algorithms.","PeriodicalId":92709,"journal":{"name":"Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms","volume":"24 1","pages":"3551-3572"},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83522318","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

Improved girth approximation in weighted undirected graphs 改进的加权无向图的周长近似

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.ch85

Avi Kadria, L. Roditty, Aaron Sidford, V. V. Williams, Uri Zwick

引用次数: 1