Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing最新文献

{"title":"Local concentration inequalities and Tomaszewski’s conjecture","authors":"Nathan Keller, Ohad Klein","doi":"10.1145/3406325.3451011","DOIUrl":"https://doi.org/10.1145/3406325.3451011","url":null,"abstract":"We prove Tomaszewski’s conjecture (1986): Let f:{−1,1}n → ℝ be of the form f(x)= ∑i=1n ai xi. Then Pr[|f(x)| ≤ √Var[f]] ≥ 1/2. Our main novel tools are local concentration inequalities and an improved Berry-Esseen inequality for first-degree functions on the discrete cube. These tools are of independent interest, and may be useful in the study of linear threshold functions and of low degree Boolean functions.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115254612","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":"Efficient randomized DCAS","authors":"George Giakkoupis, Mehrdad Jafari Giv, Philipp Woelfel","doi":"10.1145/3406325.3451133","DOIUrl":"https://doi.org/10.1145/3406325.3451133","url":null,"abstract":"Double Compare-And-Swap (DCAS) is a tremendously useful synchronization primitive, which is also notoriously difficult to implement efficiently from objects that are provided by hardware. We present a randomized implementation of DCAS with O(logn) expected amortized step complexity against the oblivious adversary, where n is the number of processes in the system. This is the only algorithm to-date that achieves sub-linear step complexity. We achieve that by first implementing two novel algorithms as building blocks. One is a mechanism that allows processes to repeatedly agree on a random value among multiple proposed ones, and the other one is a restricted bipartite version of DCAS.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124474120","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":"Load balancing guardrails: keeping your heavy traffic on the road to low response times (invited paper)","authors":"Isaac Grosof, Ziv Scully, Mor Harchol-Balter","doi":"10.1145/3406325.3465359","DOIUrl":"https://doi.org/10.1145/3406325.3465359","url":null,"abstract":"This talk is about scheduling and load balancing in a multi-server system, with the goal of minimizing mean response time in a general stochastic setting. We will specifically concentrate on the common case of a load balancing system, where a front-end load balancer (a.k.a. dispatcher) dispatches requests to multiple back-end servers, each with their own queue. Much is known about load balancing in the case where the scheduling at the servers is First-Come-First-Served (FCFS). However, to minimize mean response time, we need to use Shortest-Remaining-Processing-Time (SRPT) scheduling at the servers. Unfortunately, there is almost nothing known about optimal dispatching when SRPT scheduling is used at the servers. To make things worse, it turns out that the traditional dispatching policies that are used in practice with FCFS servers often have poor performance in systems with SRPT servers. In this talk, we devise a simple fix that can be applied to any dispatching policy. This fix, called \"guardrails\" ensures that the dispatching policy yields optimal mean response time under heavy traffic, when used in a system with SRPT servers. Any dispatching policy, when augmented with guardrails becomes heavy-traffic optimal. Our results also yield the first analytical bounds on mean response time for load balancing systems with SRPT scheduling at the servers. Load balancing and scheduling are highly studied both in the stochastic and the worst-case scheduling communities. One aim of this talk is to contrast some differences in the approaches of the two communities when tackling multi-server scheduling problems.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123940489","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":"Separating words and trace reconstruction","authors":"Zachary Chase","doi":"10.1145/3406325.3451118","DOIUrl":"https://doi.org/10.1145/3406325.3451118","url":null,"abstract":"We prove that for any distinct x,y ∈ {0,1}n, there is a deterministic finite automaton with O(n1/3) states that accepts x but not y. This improves Robson’s 1989 bound of O(n2/5). Using a similar complex analytic technique, we improve the upper bound on worst case trace reconstruction, showing that any unknown string x ∈ {0,1}n can be reconstructed with high probability from exp(O(n1/5)) independently generated traces.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127982029","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":"Automating algebraic proof systems is NP-hard","authors":"Mika Göös, Jakob Nordström, T. Pitassi, Robert Robere, Dmitry Sokolov, Susanna F. de Rezende","doi":"10.1145/3406325.3451080","DOIUrl":"https://doi.org/10.1145/3406325.3451080","url":null,"abstract":"We show that algebraic proofs are hard to find: Given an unsatisfiable CNF formula F, it is NP-hard to find a refutation of F in the Nullstellensatz, Polynomial Calculus, or Sherali–Adams proof systems in time polynomial in the size of the shortest such refutation. Our work extends, and gives a simplified proof of, the recent breakthrough of Atserias and Müller (JACM 2020) that established an analogous result for Resolution.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123978766","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":"Fiat–Shamir via list-recoverable codes (or: parallel repetition of GMW is not zero-knowledge)","authors":"Justin Holmgren, Alex Lombardi, R. Rothblum","doi":"10.1145/3406325.3451116","DOIUrl":"https://doi.org/10.1145/3406325.3451116","url":null,"abstract":"In a seminal work, Goldreich, Micali and Wigderson (CRYPTO ’86) demonstrated the wide applicability of zero-knowledge proofs by constructing such a proof system for the NP-complete problem of graph 3-coloring. A long-standing open question has been whether parallel repetition of their protocol preserves zero knowledge. In this work, we answer this question in the negative, assuming a standard cryptographic assumption (i.e., the hardness of learning with errors (LWE)). Leveraging a connection observed by Dwork, Naor, Reingold, and Stockmeyer (FOCS ’99), our negative result is obtained by making positive progress on a related fundamental problem in cryptography: securely instantiating the Fiat-Shamir heuristic for eliminating interaction in public-coin interactive protocols. A recent line of work has shown how to instantiate the heuristic securely, albeit only for a limited class of protocols. Our main result shows how to instantiate Fiat-Shamir for parallel repetitions of much more general interactive proofs. In particular, we construct hash functions that, assuming LWE, securely realize the Fiat-Shamir transform for the following rich classes of protocols: 1) The parallel repetition of any “commit-and-open” protocol (such as the GMW protocol mentioned above), when a specific (natural) commitment scheme is used. Commit-and-open protocols are a ubiquitous paradigm for constructing general purpose public-coin zero knowledge proofs. 2) The parallel repetition of any base protocol that (1) satisfies a stronger notion of soundness called round-by-round soundness, and (2) has an efficient procedure, using a suitable trapdoor, for recognizing “bad verifier randomness” that would allow the prover to cheat. Our results are obtained by establishing a new connection between the Fiat-Shamir transform and list-recoverable codes. In contrast to the usual focus in coding theory, we focus on a parameter regime in which the input lists are extremely large, but the rate can be small. We give a (probabilistic) construction based on Parvaresh-Vardy codes (FOCS ’05) that suffices for our applications.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124121689","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":"Statistical physics of random CSPs (tutorial)","authors":"Nike Sun","doi":"10.1145/3406325.3465352","DOIUrl":"https://doi.org/10.1145/3406325.3465352","url":null,"abstract":"I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase transitions and some understanding of solution geometry, particularly in the setting of the random regular NAE-SAT problem. In this lecture I will survey the physics heuristics, and explain how they lead to combinatorial models for the solution geometry, which form a basis of mathematical approaches to these problems. As time allows, I will discuss some of the mathematical techniques that have been introduced, particularly with regards to solving certain non-convex optimization problems that arise in moment method calculations.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125097484","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":"Simplicity creates inequity: implications for fairness, stereotypes, and interpretability (invited paper)","authors":"J. Kleinberg, S. Mullainathan","doi":"10.1145/3406325.3465356","DOIUrl":"https://doi.org/10.1145/3406325.3465356","url":null,"abstract":"Algorithms are increasingly used to aid, or in some cases supplant, human decision-making, particularly for decisions that hinge on predictions. As a result, two additional features in addition to prediction quality have generated interest: (i) to facilitate human interaction and understanding with these algorithms, we desire prediction functions that are in some fashion simple or interpretable; and (ii) because they influence consequential decisions, we also want them to produce equitable allocations. We develop a formal model to explore the relationship between the demands of simplicity and equity. Although the two concepts appear to be motivated by qualitatively distinct goals, we show a fundamental inconsistency between them. Specifically, we formalize a general framework for producing simple prediction functions, and in this framework we establish two basic results. First, every simple prediction function is strictly improvable: there exists a more complex prediction function that is both strictly more efficient and also strictly more equitable. Put another way, using a simple prediction function both reduces utility for disadvantaged groups and reduces overall welfare relative to other options. Second, we show that simple prediction functions necessarily create incentives to use information about individuals' membership in a disadvantaged group --- incentives that weren't present before simplification, and that work against these individuals. Thus, simplicity transforms disadvantage into bias against the disadvantaged group. Our results are not only about algorithms but about any process that produces simple models, and as such they connect to the psychology of stereotypes and to an earlier economics literature on statistical discrimination.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129429798","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":"Simple and fast derandomization from very hard functions: eliminating randomness at almost no cost","authors":"Lijie Chen, R. Tell","doi":"10.1145/3406325.3451059","DOIUrl":"https://doi.org/10.1145/3406325.3451059","url":null,"abstract":"Extending the classical “hardness-to-randomness” line-of-works, Doron, Moshkovitz, Oh, and Zuckerman (FOCS 2020) recently proved that derandomization with near-quadratic time overhead is possible, under the assumption that there exists a function in DTIME[2n] that cannot be computed by randomized SVN circuits of size 2(1−є)· n for a small є. In this work we extend their inquiry and answer several open questions that arose from their work. For a time function T(n), consider the following assumption: Non-uniformly secure one-way functions exist, and for δ=δ(є) and k=kT(є) there exists a problem in DTIME[2k· n] that is hard for algorithms that run in time 2(k−δ)· n and use 2(1−δ)· n bits of advice. Under this assumption, we show that: 1. (Worst-case derandomization.) Probabilistic algorithms that run in time T(n) can be deterministically simulated in time n· T(n)1+є. 2. (Average-case derandomization.) For polynomial time functions T(n)=poly(n), we can improve the derandomization time to nє· T(n) if we allow the derandomization to succeed only on average, rather than in the worst-case. 3. (Conditional optimality.) For worst-case derandomization, the multiplicative time overhead of n is essentially optimal, conditioned on a counting version of the non-deterministic strong exponential-time hypothesis (i.e., on #NSETH). Lastly, we present an alternative proof for the result of Doron, Moshkovitz, Oh, and Zuckerman that is simpler and more versatile. In fact, we show how to simplify the analysis not only of their construction, but of any construction that “extracts randomness from a pseudoentropic string”.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124880840","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":"Log-concave polynomials IV: approximate exchange, tight mixing times, and near-optimal sampling of forests","authors":"Nima Anari, Kuikui Liu, S. Gharan, C. Vinzant, T. Vuong","doi":"10.1145/3406325.3451091","DOIUrl":"https://doi.org/10.1145/3406325.3451091","url":null,"abstract":"We prove tight mixing time bounds for natural random walks on bases of matroids, determinantal distributions, and more generally distributions associated with log-concave polynomials. For a matroid of rank k on a ground set of n elements, or more generally distributions associated with log-concave polynomials of homogeneous degree k on n variables, we show that the down-up random walk, started from an arbitrary point in the support, mixes in time O(klogk). Our bound has no dependence on n or the starting point, unlike the previous analyses of Anari et al. (STOC 2019), Cryan et al. (FOCS 2019), and is tight up to constant factors. The main new ingredient is a property we call approximate exchange, a generalization of well-studied exchange properties for matroids and valuated matroids, which may be of independent interest. In particular, given a distribution µ over size-k subsets of [n], our approximate exchange property implies that a simple local search algorithm gives a kO(k)-approximation of maxS µ(S) when µ is generated by a log-concave polynomial, and that greedy gives the same approximation ratio when µ is strongly Rayleigh. As an application, we show how to leverage down-up random walks to approximately sample random forests or random spanning trees in a graph with n edges in time O(nlog2 n). The best known result for sampling random forest was a FPAUS with high polynomial runtime recently found by Anari et al. (STOC 2019), Cryan et al. (FOCS 2019). For spanning tree, we improve on the almost-linear time algorithm by Schild (STOC 2018). Our analysis works on weighted graphs too, and is the first to achieve nearly-linear running time for these problems. Our algorithms can be naturally extended to support approximately sampling from random forests of size between k1 and k2 in time O(n log2 n), for fixed parameters k1, k2.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126854037","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}