Strengthening ties towards a highly-connected world

Online social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms.

A CCA-PKE Secure-Cryptosystem Resilient to Randomness Reset and Secret-Key Leakage

In recent years, several new notions of security have begun receiving consideration for public-key cryptosystems, beyond the standard of security against adaptive chosen ciphertext attack (CCA2). Among these are security against randomness reset attacks, in which the randomness used in encryption is forcibly set to some previous value, and against constant secret-key leakage attacks, wherein the constant factor of a secret key’s bits is leaked. In terms of formal security definitions, cast as attack games between a challenger and an adversary, a joint combination of these attacks means that the adversary has access to additional encryption queries under a randomness of his own choosing along with secret-key leakage queries. This implies that both the encryption and decryption processes of a cryptosystem are being tampered under this security notion. In this paper, we attempt to address this problem of a joint combination of randomness and secret-key leakage attacks through two cryptosystems that incorporate hash proof system and randomness extractor primitives. The first cryptosystem relies on the random oracle model and is secure against a class of adversaries, called non-reversing adversaries. We remove the random oracle oracle assumption and the non-reversing adversary requirement in our second cryptosystem, which is a standard model that relies on a proposed primitive called LM lossy functions. These functions allow up to M lossy branches in the collection to substantially lose information, allowing the cryptosystem to use this loss of information for several encryption and challenge queries. For each cryptosystem, we present detailed security proofs using the game-hopping procedure. In addition, we present a concrete instantation of LM lossy functions in the end of the paper—which relies on the DDH assumption.

Sign-rank Can Increase under Intersection

The communication class UPP cc is a communication analog of the Turing Machine complexity class PP . It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f , let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPP cc ( f ) = O (log n ), and UPP cc ( f ∧ f ) = Θ (log 2 n ). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPP cc , the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity n Omega Ω(log n ) . This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time.

A General Framework for Approximating Min Sum Ordering Problems

We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of min sum set cover, several scheduling and search problems, and problems in Boolean function evaluation. We define a new problem, called the min sum ordering problem (MSOP), which generalizes all these problems using a cost and a weight function defined on subsets of a finite set. Assuming a polynomial time α-approximation algorithm for the problem of finding a subset whose ratio of weight to cost is maximal, we show that under very minimal assumptions, there is a polynomial time [Formula: see text]-approximation algorithm for MSOP. This approximation result generalizes a proof technique used for several distinct problems in the literature. We apply this to obtain a number of new approximation results. Summary of Contribution: This paper provides a general framework for min sum ordering problems. Within the realm of theoretical computer science, these problems include min sum set cover and its generalizations, as well as problems in Boolean function evaluation. On the operations research side, they include problems in search theory and scheduling. We present and analyze a very general algorithm for these problems, unifying several previous results on various min sum ordering problems and resulting in new constant factor guarantees for others.

An Optimal Approximation for Submodular Maximization Under a Matroid Constraint in the Adaptive Complexity Model

An Exponentially Faster Algorithm for Submodular Maximization Under a Matroid Constraint This paper studies the problem of submodular maximization under a matroid constraint. It is known since the 1970s that the greedy algorithm obtains a constant-factor approximation guarantee for this problem. Twelve years ago, a breakthrough result by Vondrák obtained the optimal 1 − 1/e approximation. Previous algorithms for this fundamental problem all have linear parallel runtime, which was considered impossible to accelerate until recently. The main contribution of this paper is a novel algorithm that provides an exponential speedup in the parallel runtime of submodular maximization under a matroid constraint, without loss in the approximation guarantee.

Competitive Algorithms for Online Multidimensional Knapsack Problems

In this paper, we study the online multidimensional knapsack problem (called OMdKP) in which there is a knapsack whose capacity is represented in m dimensions, each dimension could have a different capacity. Then, n items with different scalar profit values and m-dimensional weights arrive in an online manner and the goal is to admit or decline items upon their arrival such that the total profit obtained by admitted items is maximized and the capacity of knapsack across all dimensions is respected. This is a natural generalization of the classic single-dimension knapsack problem and finds several relevant applications such as in virtual machine allocation, job scheduling, and all-or-nothing flow maximization over a graph. We develop two algorithms for OMdKP that use linear and exponential reservation functions to make online admission decisions. Our competitive analysis shows that the linear and exponential algorithms achieve the competitive ratios of O(θα ) and O(łogł(θα)), respectively, where α is the ratio between the aggregate knapsack capacity and the minimum capacity over a single dimension and θ is the ratio between the maximum and minimum item unit values. We also characterize a lower bound for the competitive ratio of any online algorithm solving OMdKP and show that the competitive ratio of our algorithm with exponential reservation function matches the lower bound up to a constant factor.

Power of Bonus in Pricing for Crowdsourcing

We consider a simple form of pricing for a crowdsourcing system, where pricing policy is published a priori, and workers then decide their task acceptance. Such a pricing form is widely adopted in practice for its simplicity, e.g., Amazon Mechanical Turk, although additional sophistication to pricing rule can enhance budget efficiency. With the goal of designing efficient and simple pricing rules, we study the impact of the following two design features in pricing policies: (i) personalization tailoring policy worker-by-worker and (ii) bonus payment to qualified task completion. In the Bayesian setting, where the only prior distribution of workers' profiles is available, we first study the Price of Agnosticism (PoA) that quantifies the utility gap between personalized and common pricing policies. We show that PoA is bounded within a constant factor under some mild conditions, and the impact of bonus is essential in common pricing. These analytic results imply that complex personalized pricing can be replaced by simple common pricing once it is equipped with a proper bonus payment. To provide insights on efficient common pricing, we then study the efficient mechanisms of bonus payment for several profile distribution regimes which may exist in practice. We provide primitive experiments on Amazon Mechanical Turk, which support our analytical findings.

On a More Accurate Half-Discrete Mulholland-Type Inequality Involving One Multiple Upper Limit Function

By the use of the weight functions, the symmetry property, and Hermite-Hadamard’s inequality, a more accurate half-discrete Mulholland-type inequality involving one multiple upper limit function is given. The equivalent conditions of the best possible constant factor related to multiparameters are studied. Furthermore, the equivalent forms, several inequalities for the particular parameters, and the operator expressions are provided.

A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series

In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series. Based on the obtained inequality, we discuss the equivalent statements of the best possible constant factor related to several parameters. Moreover, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

Mapping Autistic Wayfinding in Urban Environments

Needs and preferences in wayfinding tasks of people with autism spectrum disorders (ASD) have been a topic of ongoing discussion in the scientific literature over the last decades. While different tasks have revealed both autistic strengths (e.g., encoding and recall of route information) and weaknesses (e.g., understanding allocentric representations), ASD spatial behaviour is not fully understood yet. In this paper we focus on spatial uncertainty, which is the discrepancy between a-priori expectation and in-situ experience and thus a constant factor in ASD wayfinding tasks. As a matter of course, spatial uncertainty is inevitable, always resulting from a dynamic interaction of situational qualities (e.g., noise or smell). Nevertheless, mapping uncertainty and the underlying spatial patterns in an organized way might help users from the ASD spectrum to better prepare for the different levels of expectable uncertainty in route. We propose a framework of conceptualizing, measuring, and mapping spatial uncertainty from an autistic viewpoint. The discussion of this framework is based on a qualitative analysis of the spatial behaviour of B, a five-year-old child with ASD and nonverbal communication, in an urban environment. We compare the level of spatial uncertainty of the routes developed by B against the routes indicated by ourselves.