Information Technology Convergence and Services最新文献

{"title":"Classical algorithms and quantum limitations for maximum cut on high-girth graphs","authors":"B. Barak, Kunal Marwaha","doi":"10.4230/LIPIcs.ITCS.2022.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.14","url":null,"abstract":"We study the performance of local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) for the maximum cut problem, and their relationship to that of classical algorithms. (1) We prove that every (quantum or classical) one-local algorithm achieves on $D$-regular graphs of girth $>5$ a maximum cut of at most $1/2 + C/sqrt{D}$ for $C=1/sqrt{2} approx 0.7071$. This is the first such result showing that one-local algorithms achieve a value bounded away from the true optimum for random graphs, which is $1/2 + P_*/sqrt{D} + o(1/sqrt{D})$ for $P_* approx 0.7632$. (2) We show that there is a classical $k$-local algorithm that achieves a value of $1/2 + C/sqrt{D} - O(1/sqrt{k})$ for $D$-regular graphs of girth $>2k+1$, where $C = 2/pi approx 0.6366$. This is an algorithmic version of the existential bound of Lyons and is related to the algorithm of Aizenman, Lebowitz, and Ruelle (ALR) for the Sherrington-Kirkpatrick model. This bound is better than that achieved by the one-local and two-local versions of QAOA on high-girth graphs. (3) Through computational experiments, we give evidence that the ALR algorithm achieves better performance than constant-locality QAOA for random $D$-regular graphs, as well as other natural instances, including graphs that do have short cycles. Our experimental work suggests that it could be possible to extend beyond our theoretical constraints. This points at the tantalizing possibility that $O(1)$-local quantum maximum-cut algorithms might be *pointwise dominated* by polynomial-time classical algorithms, in the sense that there is a classical algorithm outputting cuts of equal or better quality *on every possible instance*. This is in contrast to the evidence that polynomial-time algorithms cannot simulate the probability distributions induced by local quantum algorithms.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123902307","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":"Limits of quantum speed-ups for computational geometry and other problems: Fine-grained complexity via quantum walks","authors":"H. Buhrman, B. Loff, Subhasree Patro, F. Speelman","doi":"10.4230/LIPIcs.ITCS.2022.31","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.31","url":null,"abstract":"Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question naturally arises: how much quantum speed-up is possible? The area of fine-grained complexity allows us to prove optimal lower-bounds on the complexity of various computational problems, based on the conjectured hardness of certain natural, well-studied problems. This theory has recently been extended to the quantum setting, in two independent papers by Buhrman, Patro, and Speelman (arXiv:1911.05686), and by Aaronson, Chia, Lin, Wang, and Zhang (arXiv:1911.01973). In this paper, we further extend the theory of fine-grained complexity to the quantum setting. A fundamental conjecture in the classical setting states that the 3SUM problem cannot be solved by (classical) algorithms in time O(n^{2-a}), for any a>0. We formulate an analogous conjecture, the Quantum-3SUM-Conjecture, which states that there exist no sublinear O(n^{1-b})-time quantum algorithms for the 3SUM problem. Based on the Quantum-3SUM-Conjecture, we show new lower-bounds on the time complexity of quantum algorithms for several computational problems. Most of our lower-bounds are optimal, in that they match known upper-bounds, and hence they imply tight limits on the quantum speedup that is possible for these problems.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114966262","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":"Interactive Communication in Bilateral Trade","authors":"Jieming Mao, R. Leme, Kangning Wang","doi":"10.4230/LIPIcs.ITCS.2022.105","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.105","url":null,"abstract":"We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123766140","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":"Nash-Bargaining-Based Models for Matching Markets: One-Sided and Two-Sided; Fisher and Arrow-Debreu","authors":"M. Hosseini, V. Vazirani","doi":"10.4230/LIPIcs.ITCS.2022.86","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.86","url":null,"abstract":"This paper addresses two deficiencies of models in the area of matching-based market design. The first arises from the recent realization that the most prominent solution that uses cardinal utilities, namely the Hylland-Zeckhauser (HZ) mechanism, is intractable; computation of even an approximate equilibrium is PPAD-complete. The second is the extreme paucity of models that use cardinal utilities. Our paper addresses both these issues by proposing Nash-bargaining-based matching market models. Since the Nash bargaining solution is captured by a convex program, efficiency follows. In addition, it possesses several desirable game-theoretic properties. Our approach yields a rich collection of models: for one-sided as well as two-sided markets, for Fisher as well as Arrow-Debreu settings, and for a wide range of utility functions, all the way from linear to Leontief. We give very fast implementations for these models using Frank-Wolfe and Cutting Plane algorithms. These help solve large instances with several thousand agents and goods in a matter of minutes on a PC, even for a one-sided matching market under piecewise-linear concave utility functions and a two-sided matching market under linear utility functions. In contrast, using HZ, going beyond even $n = 10$ is prohibitive. Several new ideas were needed, beyond the standard methods, to obtain these implementations. In particular, we present several lower bounding schemes, which not only help improve the convergence of our solution methods but also shed light on fairness properties of the Nash-bargaining-based models.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131091140","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":"Local Algorithms for Bounded Degree Sparsifiers in Sparse Graphs","authors":"Shay Solomon","doi":"10.4230/LIPIcs.ITCS.2018.52","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2018.52","url":null,"abstract":"In graph sparsification, the goal has almost always been of global nature: compress a graph into a smaller subgraph (sparsifier) that maintains certain features of the original graph. \u0000Algorithms can then run on the sparsifier, which in many cases leads to improvements in the overall runtime and memory. \u0000This paper studies sparsifiers that have bounded (maximum) degree, and are thus locally sparse, aiming to improve local measures of runtime and memory. To improve those local measures, it is important to be able to compute such sparsifiers locally. \u0000 \u0000We initiate the study of local algorithms for bounded degree sparsifiers in unweighted sparse graphs, focusing on the problems of vertex cover, matching, and independent set. Let eps > 0 be a slack parameter and alpha ge 1 be a density parameter. \u0000We devise local algorithms for computing: \u00001. A (1+eps)-vertex cover sparsifier of degree O(alpha / eps), for any graph of arboricity alpha.footnote{In a graph of arboricity alpha the average degree of any induced subgraph is at most 2alpha.} \u00002. A (1+eps)-maximum matching sparsifier and also a (1+eps)-maximal matching sparsifier of degree O(alpha / eps, for any graph of arboricity alpha. \u00003. A (1+eps)-independent set sparsifier of degree O(alpha^2 / eps), for any graph of average degree alpha. \u0000 \u0000Our algorithms require only a single communication round in the standard message passing model of distributed computing, \u0000and moreover, they can be simulated locally in a trivial way. \u0000As an immediate application we can extend results from distributed computing and local computation algorithms that apply to graphs of degree bounded by d to graphs of arboricity O(d / eps) or average degree O(d^2 / eps), at the expense of increasing the approximation guarantee by a factor of (1+eps). In particular, we can extend the plethora of recent local computation algorithms for approximate maximum and maximal matching from bounded degree graphs to bounded arboricity graphs with a negligible loss in the approximation guarantee. \u0000 \u0000The inherently local behavior of our algorithms can be used to amplify the approximation guarantee of any sparsifier in time roughly linear in its size, \u0000which has immediate applications in the area of dynamic graph algorithms. In particular, the state-of-the-art algorithm for \u0000maintaining (2-eps)-vertex cover (VC) is at least linear in the graph size, even in dynamic forests. We provide a reduction from the dynamic to the static case, showing that if a t-VC can be computed from scratch in time T(n) in any (sub)family of graphs with arboricity bounded by alpha, for an arbitrary t ge 1, \u0000then a (t+eps)-VC can be maintained with update time frac{T(n)}{O((n / alpha) cdot eps^2)}, for any eps > 0. For planar graphs this yields an algorithm for maintaining a (1+eps)-VC with constant update time for any constant eps > 0.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123674857","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":"Cursed yet Satisfied Agents","authors":"Yiling Chen, Alon Eden, Juntao Wang","doi":"10.4230/LIPIcs.ITCS.2022.44","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.44","url":null,"abstract":"In real-life auctions, a widely observed phenomenon is the winner’s curse—the winner’s high bid implies that the winner often overestimates the value of the good for sale, resulting in an incurred negative utility. The seminal work of Eyster and Rabin [Econometrica’05] introduced a behavioral model aimed to explain this observed anomaly. We term agents who display this bias “cursed agents”. We adopt their model in the interdependent value setting, and aim to devise mechanisms that prevent the agents from obtaining negative utility. We design mechanisms that are cursed ex-post incentive compatible, that is, incentivize agents to bid their true signal even though they are cursed, while ensuring that the outcome is ex-post individually rational (EPIR)—the price the agents pay is no more than the agents’ true value. Since the agents might over-estimate the value of the allocated good, such mechanisms might require the seller to make positive (monetary) transfers to the agents in order to prevent agents from over-paying for the good. While the revenue of the seller not requiring EPIR might increase when agents are cursed, when imposing EPIR, cursed agents will always pay less than fully rational agents (due to the positive transfers the seller makes). We devise revenue and welfare maximizing mechanisms for cursed agents. For revenue maximization, we give the optimal deterministic and anonymous mechanism. For welfare maximization, we require ex-post budget balance (EPBB), as positive transfers might cause the seller to have negative revenue. We propose a masking operation that takes any deterministic mechanism, and masks the allocation whenever the seller requires to make positive transfers. The masking operation ensures that the mechanism is both EPIR and EPBB. We show that in typical settings, EPBB implies that the mechanism cannot make any positive transfers. Thus, applying the masking operation on the fully efficient mechanism results in a socially optimal EPBB mechanism. This further implies that if the valuation function is the maximum of agents’ signals, the optimal EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave valuations, which include weighted-sum valuations and lp-norms, the welfare optimal EPBB mechanism obtains half of the optimal welfare as the number of agents grows large.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122241545","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":"Counting and Sampling Perfect Matchings in Regular Expanding Non-Bipartite Graphs","authors":"Farzam Ebrahimnejad, Ansh Nagda, S. Gharan","doi":"10.4230/LIPIcs.ITCS.2022.61","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.61","url":null,"abstract":"We show that the ratio of the number of near perfect matchings to the number of perfect matchings in d-regular strong expander (non-bipartite) graphs, with 2n vertices, is a polynomial in n, thus the Jerrum and Sinclair Markov chain [14] mixes in polynomial time and generates an (almost) uniformly random perfect matching. Furthermore, we prove that such graphs have at least Ω(d)n many perfect matchings, thus proving the Lovasz-Plummer conjecture [18] for this family of graphs. 2012 ACM Subject Classification Theory of computation → Expander graphs and randomness extractors; Mathematics of computing → Combinatoric problems; Mathematics of computing → Markov-chain Monte Carlo methods","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129176762","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 Reconstruction of Depth Three Arithmetic Circuits with Top Fan-In Two","authors":"Gaurav Sinha","doi":"10.4230/LIPIcs.ITCS.2022.118","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.118","url":null,"abstract":"We develop efficient randomized algorithms to solve the black-box reconstruction problem for polynomials over finite fields, computable by depth three arithmetic circuits with alternating addition/multiplication gates, such that output gate is an addition gate with in-degree two. These circuits compute polynomials of form $Gtimes(T_1 + T_2)$, where $G,T_1,T_2$ are product of affine forms, and polynomials $T_1,T_2$ have no common factors. Rank of such a circuit is defined as dimension of vector space spanned by all affine factors of $T_1$ and $T_2$. For any polynomial $f$ computable by such a circuit, $rank(f)$ is defined to be the minimum rank of any such circuit computing it. Our work develops randomized reconstruction algorithms which take as input black-box access to a polynomial $f$ (over finite field $mathbb{F}$), computable by such a circuit. Here are the results. 1 [Low rank]: When $5leq rank(f) = O(log^3 d)$, it runs in time $(nd^{log^3d}log |mathbb{F}|)^{O(1)}$, and, with high probability, outputs a depth three circuit computing $f$, with top addition gate having in-degree $leq d^{rank(f)}$. 2 [High rank]: When $rank(f) = Omega(log^3 d)$, it runs in time $(ndlog |mathbb{F}|)^{O(1)}$, and, with high probability, outputs a depth three circuit computing $f$, with top addition gate having in-degree two. Ours is the first blackbox reconstruction algorithm for this circuit class, that runs in time polynomial in $log |mathbb{F}|$. This problem has been mentioned as an open problem in [GKL12] (STOC 2012)","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131421533","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":"Matroid Secretary is Equivalent to Contention Resolution","authors":"S. Dughmi","doi":"10.4230/LIPIcs.ITCS.2022.58","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.58","url":null,"abstract":"We show that the matroid secretary problem is equivalent to correlated contention resolution in the online random-order model. Specifically, the matroid secretary conjecture is true if and only if every matroid admits an online random-order contention resolution scheme which, given an arbitrary (possibly correlated) prior distribution over subsets of the ground set, matches the balance ratio of the best offline scheme for that distribution up to a constant. We refer to such a scheme as universal. Our result indicates that the core challenge of the matroid secretary problem lies in resolving contention for positively correlated inputs, in particular when the positive correlation is benign in as much as offline contention resolution is concerned. Our result builds on our previous work which establishes one direction of this equivalence, namely that the secretary conjecture implies universal random-order contention resolution, as well as a weak converse, which derives a matroid secretary algorithm from a random-order contention resolution scheme with only partial knowledge of the distribution. It is this weak converse that we strengthen in this paper: We show that universal random-order contention resolution for matroids, in the usual setting of a fully known prior distribution, suffices to resolve the matroid secretary conjecture in the affirmative. Our proof is the composition of three reductions. First, we use duality arguments to reduce the matroid secretary problem to the matroid prophet secretary problem with arbitrarily correlated distributions. Second, we introduce a generalization of contention resolution we term labeled contention resolution, to which we reduce the correlated matroid prophet secretary problem. Finally, we combine duplication of elements with limiting arguments to reduce labeled contention resolution to classical contention resolution.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121126350","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":"More Dominantly Truthful Multi-Task Peer Prediction with a Finite Number of Tasks","authors":"Yuqing Kong","doi":"10.4230/LIPIcs.ITCS.2022.95","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.95","url":null,"abstract":"In the setting where we ask participants multiple similar possibly subjective multi-choice questions (e.g. Do you like Bulbasaur? Y/N; do you like Squirtle? Y/N), peer prediction aims to design mechanisms that encourage honest feedback without verification. A series of works have successfully designed multi-task peer prediction mechanisms where reporting truthfully is better than any other strategy (dominantly truthful), while they require an infinite number of tasks. A recent work proposes the first multi-task peer prediction mechanism, Determinant Mutual Information (DMI)-Mechanism, where not only is dominantly truthful but also works for a finite number of tasks (practical). However, the existence of other practical dominantly-truthful multi-task peer prediction mechanisms remains to be an open question. This work answers the above question by providing 1. a new family of information-monotone information measures: volume mutual information (VMI), where DMI is a special case; 2. a new family of practical dominantly-truthful multi-task peer prediction mechanisms, VMI-Mechanisms. To illustrate the importance of VMI-Mechanisms, we also provide a tractable effort incentive optimization goal. We show that DMI-Mechanism may not be not optimal but we can construct a sequence of VMI-Mechanisms that are approximately optimal. The main technical highlight in this paper is a novel geometric information measure, Volume Mutual Information, that is based on a simple idea: we can measure an object A's information amount by the number of objects that is less informative than A. Different densities over the object lead to different information measures. This also gives Determinant Mutual Information a simple geometric interpretation.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125426147","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}