Journal of the ACM (JACM)最新文献

{"title":"Near-optimal Linear Decision Trees for k-SUM and Related Problems","authors":"D. Kane, Shachar Lovett, S. Moran","doi":"10.1145/3285953","DOIUrl":"https://doi.org/10.1145/3285953","url":null,"abstract":"We construct near-optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant k, we construct linear decision trees that solve the k-SUM problem on n elements using O(n log2 n) linear queries. Moreover, the queries we use are comparison queries, which compare the sums of two k-subsets; when viewed as linear queries, comparison queries are 2k-sparse and have only { −1,0,1} coefficients. We give similar constructions for sorting sumsets A+B and for solving the SUBSET-SUM problem, both with optimal number of queries, up to poly-logarithmic terms. Our constructions are based on the notion of “inference dimension,” recently introduced by the authors in the context of active classification with comparison queries. This can be viewed as another contribution to the fruitful link between machine learning and discrete geometry, which goes back to the discovery of the VC dimension.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88078524","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":"Parallel Bayesian Search with No Coordination","authors":"P. Fraigniaud, Amos Korman, Yoav Rodeh","doi":"10.1145/3304111","DOIUrl":"https://doi.org/10.1145/3304111","url":null,"abstract":"Coordinating the actions of agents (e.g., volunteers analyzing radio signals in SETI@home) yields efficient search algorithms. However, such an efficiency is often at the cost of implementing complex coordination mechanisms which may be expensive in terms of communication and/or computation overheads. Instead, non-coordinating algorithms, in which each agent operates independently from the others, are typically very simple, and easy to implement. They are also inherently robust to slight misbehaviors, or even crashes of agents. In this article, we investigate the “price of non-coordinating,” in terms of search performance, and we show that this price is actually quite small. Specifically, we consider a parallel version of a classical Bayesian search problem, where set of k≥1 searchers are looking for a treasure placed in one of the boxes indexed by positive integers, according to some distribution p. Each searcher can open a random box at each step, and the objective is to find the treasure in a minimum number of steps. We show that there is a very simple non-coordinating algorithm which has expected running time at most 4(1−1/k+1)2 OPT+10, where OPT is the expected running time of the best fully coordinated algorithm. Our algorithm does not even use the precise description of the distribution p, but only the relative likelihood of the boxes. We prove that, under this restriction, our algorithm has the best possible competitive ratio with respect to OPT. For the case where a complete description of the distribution p is given to the search algorithm, we describe an optimal non-coordinating algorithm for Bayesian search. This latter algorithm can be twice as fast as our former algorithm in practical scenarios such as uniform distributions. All these results provide a complete characterization of non-coordinating Bayesian search. The take-away message is that, for their simplicity and robustness, non-coordinating algorithms are viable alternatives to complex coordinating mechanisms subject to significant overheads. Most of these results apply as well to linear search, in which the indices of the boxes reflect their relative importance, and where important boxes must be visited first.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80461338","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":"Approximate Counting, the Lovász Local Lemma, and Inference in Graphical Models","authors":"Ankur Moitra","doi":"10.1145/3268930","DOIUrl":"https://doi.org/10.1145/3268930","url":null,"abstract":"In this article, we introduce a new approach to approximate counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula Φ when the width is logarithmic in the maximum degree. This closes an exponential gap between the known upper and lower bounds. Moreover, our algorithm extends straightforwardly to approximate sampling, which shows that under Lovász Local Lemma-like conditions it is not only possible to find a satisfying assignment, it is also possible to generate one approximately uniformly at random from the set of all satisfying assignments. Our approach is a significant departure from earlier techniques in approximate counting, and is based on a framework to bootstrap an oracle for computing marginal probabilities on individual variables. Finally, we give an application of our results to show that it is algorithmically possible to sample from the posterior distribution in an interesting class of graphical models.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75497840","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":"Capacity Upper Bounds for Deletion-type Channels","authors":"Mahdi Cheraghchi","doi":"10.1145/3281275","DOIUrl":"https://doi.org/10.1145/3281275","url":null,"abstract":"We develop a systematic approach, based on convex programming and real analysis for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information Theory, 2006). Our framework can be applied to obtain capacity upper bounds for any repetition distribution (the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions). Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. The corresponding univariate function is carefully designed according to the underlying distribution of repetitions, and the choices vary depending on the desired strength of the upper bounds as well as the desired simplicity of the function (e.g., being only efficiently computable versus having an explicit closed-form expression in terms of elementary, or common special, functions). Among our results, we show the following: (1) The capacity of the binary deletion channel with deletion probability d is at most (1 − d) φ for d ≥ 1/2 and, assuming that the capacity function is convex, is at most 1 − d log(4/φ) for d < 1/2, where φ = (1 + √5)/2 is the golden ratio. This is the first nontrivial capacity upper bound for any value of d outside the limiting case d → 0 that is fully explicit and proved without computer assistance. (2) We derive the first set of capacity upper bounds for the Poisson-repeat channel. Our results uncover further striking connections between this channel and the deletion channel and suggest, somewhat counter-intuitively, that the Poisson-repeat channel is actually analytically simpler than the deletion channel and may be of key importance to a complete understanding of the deletion channel. (3) We derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. In turn, we upper bound these functions in terms of explicit elementary and standard special functions, whose maximums can be found even more efficiently (and sometimes analytically, for example, for d = 1/2).","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87038042","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":"Polynomial Multiplication over Finite Fields in Time ( O(n log n )","authors":"David Harvey, J. van der Hoeven","doi":"10.1145/3505584","DOIUrl":"https://doi.org/10.1145/3505584","url":null,"abstract":"Assuming a widely believed hypothesis concerning the least prime in an arithmetic progression, we show that polynomials of degree less than ( n ) over a finite field ( mathbb {F}_q ) with ( q ) elements can be multiplied in time ( O (n log q log (n log q)) ) , uniformly in ( q ) . Under the same hypothesis, we show how to multiply two ( n ) -bit integers in time ( O (n log n) ) ; this algorithm is somewhat simpler than the unconditional algorithm from the companion paper [22]. Our results hold in the Turing machine model with a finite number of tapes.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72664951","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":"Exact Algorithms via Monotone Local Search","authors":"F. Fomin, Serge Gaspers, D. Lokshtanov, Saket Saurabh","doi":"10.1145/3284176","DOIUrl":"https://doi.org/10.1145/3284176","url":null,"abstract":"We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the family contains at least one set. A typical example of a subset problem is WEIGHTED d-SAT. Here, the input is a CNF-formula with clauses of size at most d, and an integer W. The universe is the set of variables and the variables have integer weights. The family contains all the subsets S of variables such that the total weight of the variables in S does not exceed W and setting the variables in S to 1 and the remaining variables to 0 satisfies the formula. Our approach is based on “monotone local search,” where the goal is to extend a partial solution to a solution by adding as few elements as possible. More formally, in the extension problem, we are also given as input a subset X of the universe and an integer k. The task is to determine whether one can add at most k elements to X to obtain a set in the (implicitly defined) family. Our main result is that a cknO(1) time algorithm for the extension problem immediately yields a randomized algorithm for finding a solution of any size with running time O((2−1/c)n). In many cases, the extension problem can be reduced to simply finding a solution of size at most k. Furthermore, efficient algorithms for finding small solutions have been extensively studied in the field of parameterized algorithms. Directly applying these algorithms, our theorem yields in one stroke significant improvements over the best known exponential-time algorithms for several well-studied problems, including d-HITTING SET, FEEDBACK VERTEX SET, NODE UNIQUE LABEL COVER, and WEIGHTED d-SAT. Our results demonstrate an interesting and very concrete connection between parameterized algorithms and exact exponential-time algorithms. We also show how to derandomize our algorithms at the cost of a subexponential multiplicative factor in the running time. Our derandomization is based on an efficient construction of a new pseudo-random object that might be of independent interest. Finally, we extend our methods to establish new combinatorial upper bounds and develop enumeration algorithms.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88548433","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":"Detecting an Odd Hole","authors":"M. Chudnovsky, A. Scott, P. Seymour, S. Spirkl","doi":"10.1145/3375720","DOIUrl":"https://doi.org/10.1145/3375720","url":null,"abstract":"We give a polynomial-time algorithm to test whether a graph contains an induced cycle with length more than three and odd.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76584893","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":"Near Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems","authors":"Nikhil R. Devanur, K. Jain, Balasubramanian Sivan, Christopher A. Wilkens","doi":"10.1145/3284177","DOIUrl":"https://doi.org/10.1145/3284177","url":null,"abstract":"We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every possible underlying distribution, obtains a 1−ε fraction of the profit obtained by an algorithm that knows the entire request sequence ahead of time. The factor ε approaches 0 when no single request consumes/contributes a significant fraction of the global consumption/contribution by all requests together. We show that the tradeoff we obtain here that determines how fast ε approaches 0, is near optimal: We give a nearly matching lower bound showing that the tradeoff cannot be improved much beyond what we obtain. Going beyond the model of a static underlying distribution, we introduce the adversarial stochastic input model, where an adversary, possibly in an adaptive manner, controls the distributions from which the requests are drawn at each step. Placing no restriction on the adversary, we design an algorithm that obtains a 1−ε fraction of the optimal profit obtainable w.r.t. the worst distribution in the adversarial sequence. Further, if the algorithm is given one number per distribution, namely the optimal profit possible for each of the adversary’s distribution, then we design an algorithm that achieves a 1−ε fraction of the weighted average of the optimal profit of each distribution the adversary picks. In the offline setting we give a fast algorithm to solve very large linear programs (LPs) with both packing and covering constraints. We give algorithms to approximately solve (within a factor of 1+ε) the mixed packing-covering problem with O(γ m log (n/δ)/ε2) oracle calls where the constraint matrix of this LP has dimension n× m, the success probability of the algorithm is 1−δ, and γ quantifies how significant a single request is when compared to the sum total of all requests. We discuss implications of our results to several special cases including online combinatorial auctions, network routing, and the adwords problem.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79007414","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":"The PCL Theorem","authors":"V. Bushkov, Dmytro Dziuma, P. Fatourou, R. Guerraoui","doi":"10.1145/3266141","DOIUrl":"https://doi.org/10.1145/3266141","url":null,"abstract":"We establish a theorem called the PCL theorem, which states that it is impossible to design a transactional memory algorithm that ensures (1) parallelism, i.e., transactions do not need to synchronize unless they access the same application objects, (2) very little consistency, i.e., a consistency condition, called weak adaptive consistency, introduced here and that is weaker than snapshot isolation, processor consistency, and any other consistency condition stronger than them (such as opacity, serializability, causal serializability, etc.), and (3) very little liveness, i.e., which transactions eventually commit if they run solo.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74574640","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":"Scaling Exponential Backoff","authors":"M. A. Bender, Jeremy T. Fineman, Seth Gilbert, Maxwell Young","doi":"10.1145/3276769","DOIUrl":"https://doi.org/10.1145/3276769","url":null,"abstract":"Randomized exponential backoff is a widely deployed technique for coordinating access to a shared resource. A good backoff protocol should, arguably, satisfy three natural properties: (1) it should provide constant throughput, wasting as little time as possible; (2) it should require few failed access attempts, minimizing the amount of wasted effort; and (3) it should be robust, continuing to work efficiently even if some of the access attempts fail for spurious reasons. Unfortunately, exponential backoff has some well-known limitations in two of these areas: it can suffer subconstant throughput under bursty traffic, and it is not robust to adversarial disruption. The goal of this article is to “fix” exponential backoff by making it scalable, particularly focusing on the case where processes arrive in an online, worst-case fashion. We present a relatively simple backoff protocol, Re-Backoff, that has, at its heart, a version of exponential backoff. It guarantees expected constant throughput with dynamic process arrivals and requires only an expected polylogarithmic number of access attempts per process. Re-Backoff is also robust to periods where the shared resource is unavailable for a period of time. If it is unavailable for D time slots, Re-Backoff provides the following guarantees. For n packets, the expected number of access attempts for successfully sending a packet is O(log2(n + D)). For the case of an infinite number of packets, we provide a similar result in terms of the maximum number of processes that are ever in the system concurrently.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83099544","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}