-
Fine-Grained Cryptanalysis: Tight Conditional Bounds for Dense k-SUM and k-XOR J. ACM (IF 2.5) Pub Date : 2024-03-17 Itai Dinur, Nathan Keller, Ohad Klein
An average-case variant of the k-SUM conjecture asserts that finding k numbers that sum to 0 in a list of r random numbers, each of the order rk, cannot be done in much less than r⌈k/2⌉ time. On the other hand, in the dense regime of parameters, where the list contains more numbers and many solutions exist, the complexity of finding one of them can be significantly improved by Wagner’s k-tree algorithm
-
Twin-width IV: ordered graphs and matrices J. ACM (IF 2.5) Pub Date : 2024-03-11 Édouard Bonnet, Ugo Giocanti, Patrice Ossona de Mendez, Pierre Simon, Stéphan Thomassé, Szymon Toruńczyk
We establish a list of characterizations of bounded twin-width for hereditary classes of totally ordered graphs: as classes of at most exponential growth studied in enumerative combinatorics, as monadically NIP classes studied in model theory, as classes that do not transduce the class of all graphs studied in finite model theory, and as classes for which model checking first-order logic is fixed-parameter
-
Efficient Normalization of Linear Temporal Logic J. ACM (IF 2.5) Pub Date : 2024-03-06 Javier Esparza, Rubén Rubio, Salomon Sickert
In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form \(\bigwedge _{i=1}^n \mathbf {G}\mathbf {F} \varphi _i \vee \mathbf {F}\mathbf {G} \psi _i \), where φi and ψi contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to
-
Sketching approximability of all finite CSPs J. ACM (IF 2.5) Pub Date : 2024-02-29 Chi-Ning Chou, Alexander Golovnev, Madhu Sudan, Santhoshini Velusamy
A constraint satisfaction problem (CSP), \(\mathsf {Max-CSP}(\mathcal {F}) \), is specified by a finite set of constraints \(\mathcal {F} \subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace \) for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F} \) to subsequences of the n variables, and the goal is to find
-
Probabilistic Programming with Exact Conditions J. ACM (IF 2.5) Pub Date : 2024-02-11 Dario Stein, Sam Staton
We spell out the paradigm of exact conditioning as an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-based scoring known from languages such as Stan. We study exact conditioning in the cases of discrete and Gaussian probability, presenting prototypical languages for each case and giving semantics to them. We make use of categorical
-
The Space Complexity of Consensus from Swap J. ACM (IF 2.5) Pub Date : 2024-02-11 Sean Ovens
Nearly thirty years ago, it was shown that \(\Omega (\sqrt {n})\) read/write registers are needed to solve randomized wait-free consensus among n processes. This lower bound was improved to n registers in 2018, which exactly matches known algorithms. The \(\Omega (\sqrt {n})\) space complexity lower bound actually applies to a class of objects called historyless objects, which includes registers, test-and-set
-
Cerise: Program Verification on a Capability Machine in the Presence of Untrusted Code J. ACM (IF 2.5) Pub Date : 2024-02-11 Aïna Linn Georges*, Armaël Guéneau*, Thomas Van Strydonck, Amin Timany, Alix Trieu*, Dominique Devriese, Lars Birkedal
A capability machine is a type of CPU allowing fine-grained privilege separation using capabilities, machine words that represent certain kinds of authority. We present a mathematical model and accompanying proof methods that can be used for formal verification of functional correctness of programs running on a capability machine, even when they invoke and are invoked by unknown (and possibly malicious)
-
EFX Exists for Three Agents J. ACM (IF 2.5) Pub Date : 2024-02-11 Bhaskar Ray Chaudhury, Jugal Garg, Kurt Mehlhorn
We study the problem of distributing a set of indivisible goods among agents with additive valuations in a fair manner. The fairness notion under consideration is envy-freeness up to any good (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this article, we show constructively that
-
Optimal Auctions through Deep Learning: Advances in Differentiable Economics J. ACM (IF 2.5) Pub Date : 2024-02-11 Paul Dütting, Zhe Feng, Harikrishna Narasimhan, David C. Parkes, Sai Srivatsa Ravindranath
Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal design still remains elusive for settings with two or more items. In this work, we initiate the exploration of the use of tools from deep learning
-
Parallel Acyclic Joins: Optimal Algorithms and Cyclicity Separation J. ACM (IF 2.5) Pub Date : 2024-02-11 Xiao Hu, Yufei Tao
We study equi-join computation in the massively parallel computation (MPC) model. Currently, a main open question under this topic is whether it is possible to design an algorithm that can process any join with load O(N polylog N/p1/ρ*) — measured in the number of words communicated per machine — where N is the total number of tuples in the input relations, ρ* is the join’s fractional edge covering
-
Choiceless Polynomial Time with Witnessed Symmetric Choice J. ACM (IF 2.5) Pub Date : 2024-02-13 Moritz Lichter, Pascal Schweitzer
We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing Ptime, so that this extended logic has the following property: for every class of structures for which isomorphism is definable, the logic automatically captures Ptime. For the construction of this logic we extend CPT by a witnessed symmetric choice operator. This operator
-
Convergence of Datalog over (Pre-) Semirings J. ACM (IF 2.5) Pub Date : 2024-01-30 Mahmoud Abo Khamis, Hung Q. Ngo, Reinhard Pichler, Dan Suciu, Yisu Remy Wang
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big data systems require recursive computations beyond the Boolean space. In this paper we study the convergence of datalog when it is interpreted over an arbitrary semiring
-
A Compositional Theory of Linearizability J. ACM (IF 2.5) Pub Date : 2024-01-27 Arthur Oliveira Vale, Zhong Shao, Yixuan Chen
Compositionality is at the core of programming languages research and has become an important goal toward scalable verification of large systems. Despite that, there is no compositional account of linearizability, the gold standard of correctness for concurrent objects. In this paper, we develop a compositional semantics for linearizable concurrent objects. We start by showcasing a common issue, which
-
Byzantine Agreement with Optimal Resilience via Statistical Fraud Detection J. ACM (IF 2.5) Pub Date : 2024-01-02 Shang-En Huang, Seth Pettie, Leqi Zhu
Since the mid-1980s it has been known that Byzantine Agreement can be solved with probability 1 asynchronously, even against an omniscient, computationally unbounded adversary that can adaptively corrupt up to f < n/3 parties. Moreover, the problem is insoluble with f ≥ n/3 corruptions. However, Bracha’s [13] 1984 protocol (see also Ben-Or [8]) achieved f < n/3 resilience at the cost of exponential
-
Fitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor J. ACM (IF 2.5) Pub Date : 2024-01-02 Vincent Cohen-Addad, Debarati Das, Evangelos Kipouridis, Nikos Parotsidis, Mikkel Thorup
We consider the numerical taxonomy problem of fitting a positive distance function \({\mathcal {D}:{S\choose 2}\rightarrow \mathbb {R}_{\gt 0}} \) by a tree metric. We want a tree T with positive edge weights and including S among the vertices so that their distances in T match those in \(\mathcal {D} \). A nice application is in evolutionary biology where the tree T aims to approximate the branching
-
Learning to branch: Generalization guarantees and limits of data-independent discretization J. ACM (IF 2.5) Pub Date : 2023-12-25 Maria-Florina Balcan, Travis Dick, Tuomas Sandholm, Ellen Vitercik
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated
-
Faster Modular Composition J. ACM (IF 2.5) Pub Date : 2023-12-25 Vincent Neiger, Bruno Salvy, Éric Schost, Gilles Villard
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses On1.43 field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require On1.63 field operations in
-
Dominantly Truthful Peer Prediction Mechanisms with a Finite Number of Tasks J. ACM (IF 2.5) Pub Date : 2023-12-23 Yuqing Kong
In the setting where participants are asked multiple similar possibly subjective multi-choice questions (e.g. Do you like Panda Express? Y/N; do you like Chick-fil-A? Y/N), a series of peer prediction mechanisms have been designed to incentivize honest reports and some of them achieve dominantly truthfulness: truth-telling is a dominant strategy and strictly dominate other “non-permutation strategy”
-
Balanced Allocations with the Choice of Noise J. ACM (IF 2.5) Pub Date : 2023-11-30 Dimitrios Los, Thomas Sauerwald
We consider the allocation of m balls (jobs) into n bins (servers). In the standard Two-Choice process, at each step t=1,2,... ,m we first sample two randomly chosen bins, compare their two loads and then place a ball in the least loaded bin. It is well-known that for any m ⩾ n, this results in a gap (difference between the maximum and average load) of log2 log n + Θ (1) (with high probability). In
-
A New Minimax Theorem for Randomized Algorithms J. ACM (IF 2.5) Pub Date : 2023-11-30 Shalev Ben-David, Eric Blais
The celebrated minimax principle of Yao says that for any Boolean-valued function f with finite domain, there is a distribution μ over the domain of f such that computing f to error ε against inputs from μ is just as hard as computing f to error ε on worst-case inputs. Notably, however, the distribution μ depends on the target error level ε: the hard distribution which is tight for bounded error might
-
Toward a Better Understanding of Randomized Greedy Matching J. ACM (IF 2.5) Pub Date : 2023-11-30 Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang
There has been a long history of studying randomized greedy matching algorithms since the work by Dyer and Frieze [9]. We follow this trend and consider the problem formulated in the oblivious setting, in which the vertex set of a graph is known to the algorithm but not the edge set. The algorithm can make queries for the existence of the edge between any pair of vertices but must include the edge
-
Iceberg Hashing: Optimizing Many Hash-Table Criteria at Once J. ACM (IF 2.5) Pub Date : 2023-11-30 Michael A. Bender, Alex Conway, Martín Farach-Colton, William Kuszmaul, Guido Tagliavini
Despite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different trade-offs have been proposed. This article introduces
-
Pliability and Approximating Max-CSPs J. ACM (IF 2.5) Pub Date : 2023-11-30 Miguel Romero, Marcin Wrochna, Stanislav Živný
We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint graphs (with arbitrary constraints on an unbounded alphabet). Our result applies more generally to the maximum homomorphism problem between two rational-valued structures
-
Fast, Algebraic Multivariate Multipoint Evaluation in Small Characteristic and Applications J. ACM (IF 2.5) Pub Date : 2023-11-30 Vishwas Bhargava, Sumanta Ghosh, Mrinal Kumar, Chandra Kanta Mohapatra
Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem are also closely related to fast algorithms for other natural algebraic questions such as polynomial factorization and modular composition. And while nearly
-
Relative Error Streaming Quantiles J. ACM (IF 2.5) Pub Date : 2023-10-16 Graham Cormode, Zohar Karnin, Edo Liberty, Justin Thaler, Pavel Veselý
Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of n items from a data universe equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in n. Given the sketch and a query item y, one should be able to approximate its rank in the stream, i.e., the number of stream elements
-
First Price Auction is 1-1/e2 Efficient J. ACM (IF 2.5) Pub Date : 2023-10-14 Yaonan Jin, Pinyan Lu
We prove that the PoA of First Price Auctions is 1-1/e2 ≈ 0.8647, closing the gap between the best known bounds [0.7430, 0.8689].
-
Restorable Shortest Path Tiebreaking for Edge-Faulty Graphs J. ACM (IF 2.5) Pub Date : 2023-10-11 Greg Bodwin, Merav Parter
The restoration lemma by Afek et al. [3] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two original shortest paths. However, the lemma is tiebreaking-sensitive: if one selects a particular canonical shortest path for each node pair, it is no longer guaranteed that one can build replacement paths by concatenating
-
On Strongest Algebraic Program Invariants J. ACM (IF 2.5) Pub Date : 2023-10-11 Ehud Hrushovski, Joël Ouaknine, Amaury Pouly, James Worrell
A polynomial program is one in which all assignments are given by polynomial expressions and in which all branching is nondeterministic (as opposed to conditional). Given such a program, an algebraic invariant is one that is defined by polynomial equations over the program variables at each program location. Müller-Olm and Seidl have posed the question of whether one can compute the strongest algebraic
-
Proximity Gaps for Reed–Solomon Codes J. ACM (IF 2.5) Pub Date : 2023-10-11 Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, Shubhangi Saraf
A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are δ-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are δ-close to the property. In particular, no set in the collection has roughly half of its members δ-close to the property and the others δ-far from it. We show that the
-
Near-optimal Lower Bounds on Quantifier Depth and Weisfeiler–Lehman Refinement Steps J. ACM (IF 2.5) Pub Date : 2023-10-11 Christoph Berkholz, Jakob Nordström
We prove near-optimal tradeoffs for quantifier depth (also called quantifier rank) versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every such sentence requires quantifier depth at least nΩ (k/log k). Our tradeoffs also apply to first-order counting logic and, by the known connection
-
The Topological Mu-Calculus: Completeness and Decidability J. ACM (IF 2.5) Pub Date : 2023-10-11 Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque
We study the topological μ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability, and finite model property over general topological spaces, as well as over T0 and TD spaces. We also investigate the relational μ-calculus, providing general completeness results for all natural fragments of the μ-calculus over many different classes of relational frames
-
Exponentially Faster Massively Parallel Maximal Matching J. ACM (IF 2.5) Pub Date : 2023-10-11 Soheil Behnezhad, Mohammadtaghi Hajiaghayi, David G. Harris
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, we still have a limited understanding of maximal matching which is one of the central problems of parallel and distributed computing. All known MPC algorithms for maximal matching either take polylogarithmic time which is considered inefficient, or
-
A Domain-theoretic Approach to Statistical Programming Languages J. ACM (IF 2.5) Pub Date : 2023-10-11 Jean Goubault-Larrecq, Xiaodong Jia, Clément Théron
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which allows for program transformations that permute the order of independent random draws, as one would expect. A similar property is not known for Jones and Plotkin’s
-
Cerise: Program Verification on a Capability Machine in the Presence of Untrusted Code J. ACM (IF 2.5) Pub Date : 2023-09-14 Aïna Linn Georges, Armaël Guéneau, Thomas Van Strydonck, Amin Timany, Alix Trieu, Dominique Devriese, Lars Birkedal
A capability machine is a type of CPU allowing fine-grained privilege separation using capabilities, machine words that represent certain kinds of authority. We present a mathematical model and accompanying proof methods that can be used for formal verification of functional correctness of programs running on a capability machine, even when they invoke and are invoked by unknown (and possibly malicious)
-
The Topological Mu-Calculus: Completeness and Decidability J. ACM (IF 2.5) Pub Date : 2023-09-07 Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque
We study the topological μ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and finite model property over general topological spaces, as well as over T0 and TD spaces. We also investigate the relational μ-calculus, providing general completeness results for all natural fragments of the μ-calculus over many different classes of relational frames.
-
The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness J. ACM (IF 2.5) Pub Date : 2023-08-12 Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, Rico Zenklusen
We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multiplayer model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming
-
On the Zeros of Exponential Polynomials J. ACM (IF 2.5) Pub Date : 2023-08-12 Ventsislav Chonev, Joel Ouaknine, James Worrell
We consider the problem of deciding the existence of real roots of real-valued exponential polynomials with algebraic coefficients. Such functions arise as solutions of linear differential equations with real algebraic coefficients. We focus on two problems: the Zero Problem, which asks whether an exponential polynomial has a real root, and the Infinite Zeros Problem, which asks whether such a function
-
Co-lexicographically Ordering Automata and Regular Languages - Part I J. ACM (IF 2.5) Pub Date : 2023-08-12 Nicola Cotumaccio, Giovanna D’Agostino, Alberto Policriti, Nicola Prezza
The states of a finite-state automaton 𝒩 can be identified with collections of words in the prefix closure of the regular language accepted by 𝒩. But words can be ordered, and among the many possible orders a very natural one is the co-lexicographic order. Such naturalness stems from the fact that it suggests a transfer of the order from words to the automaton’s states. This suggestion is, in fact
-
Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler–Leman Refinement Steps J. ACM (IF 2.5) Pub Date : 2023-07-20 Christoph Berkholz, Jakob Nordström
We prove near-optimal trade-offs for quantifier depth (also called quantifier rank) versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every such sentence requires quantifier depth at least nΩ(k/log k). Our trade-offs also apply to first-order counting logic, and by the known connection
-
Co-lexicographically Ordering Automata and Regular Languages - Part I J. ACM (IF 2.5) Pub Date : 2023-07-07 Nicola Cotumaccio, Giovanna D’Agostino, Alberto Policriti, Nicola Prezza
The states of a finite-state automaton \(\mathcal {N} \) can be identified with collections of words in the prefix closure of the regular language accepted by \(\mathcal {N} \). But words can be ordered, and among the many possible orders a very natural one is the co-lexicographic order. Such naturalness stems from the fact that it suggests a transfer of the order from words to the automaton’s states
-
On the Zeros of Exponential Polynomials J. ACM (IF 2.5) Pub Date : 2023-06-06 Ventsislav Chonev, Joel Ouaknine, James Worrell
We consider the problem of deciding the existence of real roots of real-valued exponential polynomials with algebraic coefficients. Such functions arise as solutions of linear differential equations with real algebraic coefficients. We focus on two problems: the Zero Problem, which asks whether an exponential polynomial has a real root, and the Infinite Zeros Problem, which asks whether such a function
-
Learning Equilibria in Matching Markets with Bandit Feedback J. ACM (IF 2.5) Pub Date : 2023-05-24 Meena Jagadeesan, Alexander Wei, Yixin Wang, Michael I. Jordan, Jacob Steinhardt
Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) are, unfortunately, of limited value in the learning setting, given that preferences are inherently uncertain and destabilizing while they are being learned. To
-
Chains, Koch Chains, and Point Sets with Many Triangulations J. ACM (IF 2.5) Pub Date : 2023-05-23 Daniel Rutschmann, Manuel Wettstein
We introduce the abstract notion of a chain, which is a sequence of n points in the plane, ordered by x-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations. We also describe an intriguing new and
-
The Price of Anarchy of Strategic Queuing Systems J. ACM (IF 2.5) Pub Date : 2023-05-23 Jason Gaitonde, Éva Tardos
Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. Classical work on such bounds in repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent beyond any influence on play from past history. This work studies such
-
Robustly Learning General Mixtures of Gaussians J. ACM (IF 2.5) Pub Date : 2023-05-23 Allen Liu, Ankur Moitra
This work represents a natural coalescence of two important lines of work — learning mixtures of Gaussians and algorithmic robust statistics. In particular, we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights and that the total variation distance between components is bounded away from zero. At
-
Rate-independent Computation in Continuous Chemical Reaction Networks J. ACM (IF 2.5) Pub Date : 2023-05-23 Ho-Lin Chen, David Doty, Wyatt Reeves, David Soloveichik
Understanding the algorithmic behaviors that are in principle realizable in a chemical system is necessary for a rigorous understanding of the design principles of biological regulatory networks. Further, advances in synthetic biology herald the time when we will be able to rationally engineer complex chemical systems and when idealized formal models will become blueprints for engineering. Coupled
-
Stochastic Games with Synchronization Objectives J. ACM (IF 2.5) Pub Date : 2023-05-23 Laurent Doyen
We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding stochasticity. The outcome of the game is a sequence of distributions over the graph states, representing the evolution of a population consisting of a continuum number
-
The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness J. ACM (IF 2.5) Pub Date : 2023-04-24 Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, Rico Zenklusen
We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming
-
On Exponential-Time Hypotheses, Derandomization, and Circuit Lower Bounds J. ACM (IF 2.5) Pub Date : 2023-04-20 LIJIE CHEN, RON D. ROTHBLUM, ROEI TELL, EYLON YOGEV
The Exponential-Time Hypothesis (\(\mathtt {ETH}\)) is a strengthening of the \(\mathcal {P} \ne \mathcal {NP}\) conjecture, stating that \(3\text{-}\mathtt {SAT}\) on \(n\) variables cannot be solved in (uniform) time \(2^{\epsilon \cdot n}\), for some \(\epsilon \gt 0\). In recent years, analogous hypotheses that are “exponentially-strong” forms of other classical complexity conjectures (such as
-
On Exponential-time Hypotheses, Derandomization, and Circuit Lower Bounds J. ACM (IF 2.5) Pub Date : 2023-04-20 Lijie Chen, Ron D. Rothblum, Roei Tell, Eylon Yogev
The Exponential-Time Hypothesis (ETH) is a strengthening of the 𝒫 ≠ 𝒩𝒫 conjecture, stating that 3-SAT on n variables cannot be solved in (uniform) time 2εċn, for some ε > 0. In recent years, analogous hypotheses that are “exponentially strong” forms of other classical complexity conjectures (such as 𝒩𝒫⊈ ℬ𝒫𝒫 or co𝒩𝒫⊈𝒩𝒫) have also been introduced and have become widely influential. In this
-
Lower Bounds for Semialgebraic Range Searching and Stabbing Problems J. ACM (IF 2.5) Pub Date : 2023-04-18 Peyman Afshani, Pingan Cheng
In the semialgebraic range searching problem, we are given a set of n points in ℝd, and we want to preprocess the points such that for any query range belonging to a family of constant complexity semialgebraic sets (Tarski cells), all the points intersecting the range can be reported or counted efficiently. When the ranges are composed of simplices, the problem is well-understood: It can be solved
-
Intermediate Value Linearizability: A Quantitative Correctness Criterion J. ACM (IF 2.5) Pub Date : 2023-04-18 Arik Rinberg, Idit Keidar
Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched counter counts events in batches. This article focuses on correctness criteria for concurrent implementations of such objects. Specifically, we consider quantitative
-
Almost Optimal Exact Distance Oracles for Planar Graphs J. ACM (IF 2.5) Pub Date : 2023-03-25 Panagiotis Charalampopoulos, Paweł Gawrychowski, Yaowei Long, Shay Mozes, Seth Pettie, Oren Weimann, Christian Wulff-Nilsen
We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q, and since the mid-1990s all results had polynomial time-space tradeoffs, e.g., Q = ~ Θ(n/√ S) or Q = ~Θ(n5/2/S3/2). In this article we show that there is no polynomial tradeoff between time and space and that
-
Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents J. ACM (IF 2.5) Pub Date : 2023-03-25 Ivan Geffner, Joseph Y. Halpern
Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a (k, t)-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4(k+t), where an equilibrium is (k, t)-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff
-
Separating Rank Logic from Polynomial Time J. ACM (IF 2.5) Pub Date : 2023-03-25 Moritz Lichter
In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ2i cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism
-
A Correctness and Incorrectness Program Logic J. ACM (IF 2.5) Pub Date : 2023-03-25 Roberto Bruni, Roberto Giacobazzi, Roberta Gori, Francesco Ranzato
Abstract interpretation is a well-known and extensively used method to extract over-approximate program invariants by a sound program analysis algorithm. Soundness means that no program errors are lost and it is, in principle, guaranteed by construction. Completeness means that the abstract interpreter reports no false alarms for all possible inputs, but this is extremely rare because it needs a very
-
Universal almost Optimal Compression and Slepian-wolf Coding in Probabilistic Polynomial Time J. ACM (IF 2.5) Pub Date : 2023-03-21 Bruno Bauwens*, Marius Zimand
In a lossless compression system with target lengths, a compressor 𝒞 maps an integer m and a binary string x to an m-bit code p, and if m is sufficiently large, a decompressor 𝒟 reconstructs x from p. We call a pair (m,x) achievable for (𝒞,𝒟) if this reconstruction is successful. We introduce the notion of an optimal compressor 𝒞opt by the following universality property: For any compressor-decompressor
-
A Universal Law of Robustness via Isoperimetry J. ACM (IF 2.5) Pub Date : 2023-03-21 Sébastien Bubeck, Mark Sellke
Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with many more parameters than what this classical theory would suggest. We propose a partial theoretical explanation for this phenomenon. We prove that for a broad class
-
A New Algorithm for Euclidean Shortest Paths in the Plane J. ACM (IF 2.5) Pub Date : 2023-03-21 Haitao Wang
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously, Hershberger and Suri (in SIAM Journal on Computing, 1999) gave an algorithm of O(n log n) time and O(n log n) space, where n is the total number of vertices of all obstacles
-
On the Need for Large Quantum Depth J. ACM (IF 2.5) Pub Date : 2023-01-16 Nai-Hui Chia, Kai-Min Chung, Ching-Yi Lai
Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates. A natural approach to leverage these quantum computers is interleaving them with classical computers. Understanding the capabilities and limits of this hybrid approach is an essential topic in quantum computation. Most notably, the quantum Fourier transform can be implemented by a hybrid of logarithmic-depth