OpenRaiser/Intern-Atlas huggingface dataset:
Optimal Search Trees with 2-Way Comparisons
Venue: arXiv cs.DS 2021
Year: 2021

In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way comparisons (e.g., $<, \le, =, \ge$, and $>$). Until this paper, the problem of finding an optimal search tree using 2-way comparisons remained open -- poly-time algorithms were known only for restricted variants. We solve the general case, giving (i) an $O(n^4)$-time algorithm and (ii) an $O(n \log n)$-time additive-3 approximation algorithm. Also, for finding optimal binary split trees, we (iii) obtain a linear speedup and (iv) prove some previous work incorrect.
A First Look at Anycast CDN Traffic
Venue: arXiv cs.NI 2021
Year: 2021

Anycast routing is an IP solution that allows packets to be routed to the topologically nearest server. Over the last years it has been commonly adopted to manage some services running on top of UDP, e.g., public DNS resolvers, multicast rendez-vous points, etc. However, recently the Internet have witnessed the growth of new Anycast-enabled Content Delivery Networks (A-CDNs) such as CloudFlare and EdgeCast, which provide their web services (i.e., TCP traffic) entirely through anycast. To the best of our knowledge, little is known in the literature about the nature and the dynamic of such traffic. For instance, since anycast depends on the routing, the question is how stable are the paths toward the nearest server. To bring some light on this question, in this work we provide a first look at A-CDNs traffic by combining active and passive measurements. In particular, building upon our previous work, we use active measurements to identify and geolocate A-CDNs caches starting from a large set of IP addresses related to the top-100k Alexa websites. We then look at the traffic of those caches in the wild using a large passive dataset collected from a European ISP. We find that several A-CDN servers are encountered on a daily basis when browsing the Internet. Routes to A-CDN servers are very stable, with few changes that are observed on a monthly-basis (in contrast to more the dynamic traffic policies of traditional CDNs). Overall, A-CDNs are a reality worth further investigations.
Generating and Exploring S-Box Multivariate Quadratic Equation Systems with SageMath
Venue: arXiv cs.CR 2021
Year: 2021

A new method to derive Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box from its algebraic expressions with the aid of the computer mathematics software system SageMath is presented. We consolidate the deficiency of previously presented MQ metrics, supposed to quantify the resistance of S-boxes against algebraic attacks.
Detecting Real-World Influence Through Twitter
Venue: arXiv cs.SI 2021
Year: 2021

In this paper, we investigate the issue of detecting the real-life influence of people based on their Twitter account. We propose an overview of common Twitter features used to characterize such accounts and their activity, and show that these are inefficient in this context. In particular, retweets and followers numbers, and Klout score are not relevant to our analysis. We thus propose several Machine Learning approaches based on Natural Language Processing and Social Network Analysis to label Twitter users as Influencers or not. We also rank them according to a predicted influence level. Our proposals are evaluated over the CLEF RepLab 2014 dataset, and outmatch state-of-the-art ranking methods.
Trading off $t$-Resilience for Efficiency in Asynchronous Byzantine Reliable Broadcast
Venue: arXiv cs.DC 2021
Year: 2021

This paper presents a simple and efficient reliable broadcast algorithm for asynchronous message-passing systems made up of $n$ processes, among which up to $t<n/5$ may behave arbitrarily (Byzantine processes). This algorithm requires two communication steps and $n^2-1$ messages. When compared to Bracha's algorithm, which is resilience optimal ($t<n/3$) and requires three communication steps and $2n^2-n-1$ messages, the proposed algorithm shows an interesting tradeoff between communication efficiency and $t$-resilience.
An Extended Coding Theorem with Application to Quantum Complexities
Venue: arXiv cs.CC 2021
Year: 2021

This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.
An Integrated Framework to Recommend Personalized Retention Actions to Control B2C E-Commerce Customer Churn
Venue: arXiv cs.IR 2021
Year: 2021

Considering the level of competition prevailing in Business-to-Consumer (B2C) E-Commerce domain and the huge investments required to attract new customers, firms are now giving more focus to reduce their customer churn rate. Churn rate is the ratio of customers who part away with the firm in a specific time period. One of the best mechanism to retain current customers is to identify any potential churn and respond fast to prevent it. Detecting early signs of a potential churn, recognizing what the customer is looking for by the movement and automating personalized win back campaigns are essential to sustain business in this era of competition. E-Commerce firms normally possess large volume of data pertaining to their existing customers like transaction history, search history, periodicity of purchases, etc. Data mining techniques can be applied to analyse customer behaviour and to predict the potential customer attrition so that special marketing strategies can be adopted to retain them. This paper proposes an integrated model that can predict customer churn and also recommend personalized win back actions.
INSQ: An Influential Neighbor Set Based Moving kNN Query Processing System
Venue: arXiv cs.DB 2021
Year: 2021

We revisit the moving k nearest neighbor (MkNN) query, which computes one's k nearest neighbor set and maintains it while at move. Existing MkNN algorithms are mostly safe region based, which lack efficiency due to either computing small safe regions with a high recomputation frequency or computing larger safe regions but with a high cost for each computation. In this demonstration, we showcase a system named INSQ that adopts a novel algorithm called the Influential Neighbor Set (INS) algorithm to process the MkNN query in both two-dimensional Euclidean space and road networks. This algorithm uses a small set of safe guarding objects instead of safe regions. As long as the the current k nearest neighbors are closer to the query object than the safe guarding objects are, the current k nearest neighbors stay valid and no recomputation is required. Meanwhile, the region defined by the safe guarding objects is the largest possible safe region. This means that the recomputation frequency is also minimized and hence, the INS algorithm achieves high overall query processing efficiency.
The Rate-Distortion Risk in Estimation from Compressed Data
Venue: arXiv cs.IT 2021
Year: 2021

Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data is transmitted or stored prior to determining the downstream inference task. Given a bitrate constraint and a distortion measure between the data and its compressed version, let us consider the joint distribution achieving Shannon's rate-distortion (RD) function. Given an estimator and a loss function associated with the downstream inference task, define the rate-distortion risk as the expected loss under the RD-achieving distribution. We provide general conditions under which the operational risk in estimating from the compressed data is asymptotically equivalent to the RD risk. The main theoretical tools to prove this equivalence are transportation-cost inequalities in conjunction with properties of compression codes achieving Shannon's RD function. Whenever such equivalence holds, a recipe for designing estimators from datasets undergoing lossy compression without specifying the actual compression technique emerges: design the estimator to minimize the RD risk. Our conditions simplified in the special cases of discrete memoryless or multivariate normal data. For these scenarios, we derive explicit expressions for the RD risk of several estimators and compare them to the optimal source coding performance associated with full knowledge of the relation between the latent signal and the data.
Automatic Theorem Proving in Walnut
Venue: arXiv cs.FL 2021
Year: 2021

Walnut is a software package that implements a mechanical decision procedure for deciding certain combinatorial properties of some special words referred to as automatic words or automatic sequences. Walnut is written in Java and is open source. It is licensed under GNU General Public License.
Privacy Odometers and Filters: Pay-as-you-Go Composition
Venue: arXiv cs.CR 2021
Year: 2021

In this paper we initiate the study of adaptive composition in differential privacy when the length of the composition, and the privacy parameters themselves can be chosen adaptively, as a function of the outcome of previously run analyses. This case is much more delicate than the setting covered by existing composition theorems, in which the algorithms themselves can be chosen adaptively, but the privacy parameters must be fixed up front. Indeed, it isn't even clear how to define differential privacy in the adaptive parameter setting. We proceed by defining two objects which cover the two main use cases of composition theorems. A privacy filter is a stopping time rule that allows an analyst to halt a computation before his pre-specified privacy budget is exceeded. A privacy odometer allows the analyst to track realized privacy loss as he goes, without needing to pre-specify a privacy budget. We show that unlike the case in which privacy parameters are fixed, in the adaptive parameter setting, these two use cases are distinct. We show that there exist privacy filters with bounds comparable (up to constants) with existing privacy composition theorems. We also give a privacy odometer that nearly matches non-adaptive private composition theorems, but is sometimes worse by a small asymptotic factor. Moreover, we show that this is inherent, and that any valid privacy odometer in the adaptive parameter setting must lose this factor, which shows a formal separation between the filter and odometer use-cases.
Minimax Rate-Optimal Estimation of Divergences between Discrete Distributions
Venue: arXiv cs.IT 2021
Year: 2021

We study the minimax estimation of $α$-divergences between discrete distributions for integer $α\ge 1$, which include the Kullback--Leibler divergence and the $χ^2$-divergences as special examples. Dropping the usual theoretical tricks to acquire independence, we construct the first minimax rate-optimal estimator which does not require any Poissonization, sample splitting, or explicit construction of approximating polynomials. The estimator uses a hybrid approach which solves a problem-independent linear program based on moment matching in the non-smooth regime, and applies a problem-dependent bias-corrected plug-in estimator in the smooth regime, with a soft decision boundary between these regimes.
Unstructured Inversion of New Hope
Venue: arXiv cs.CR 2021
Year: 2021

Introduced as a new protocol first implemented in Google Chrome Canary, New Hope is engineered as post-quantum cryptography for the TLS 1.2 protocol. The structure of the exchange is lattice based, implementing Peikert's key encapsulation mechanism as a modified form of ring learning with errors. The search space used to introduce the closest-vector problem is generated by the intersection of a tesseract and hexadecachoron. This intersection results in a 24-cell Voronoi tessellation. With respect to this tessellation, New Hope may not withstand inversion attempts augmented with Grover's search algorithm.
Unifying task specification in reinforcement learning
Venue: arXiv cs.AI 2021
Year: 2021

Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of modularity can complicate generalization of the task specification, as well as obfuscate connections between different task settings, such as episodic and continuing. In this work, we introduce the RL task formalism, that provides a unification through simple constructs including a generalization to transition-based discounting. Through a series of examples, we demonstrate the generality and utility of this formalism. Finally, we extend standard learning constructs, including Bellman operators, and extend some seminal theoretical results, including approximation errors bounds. Overall, we provide a well-understood and sound formalism on which to build theoretical results and simplify algorithm use and development.
Quantum spectral analysis: frequency in time, with applications to signal and image processing
Venue: arXiv cs.CV 2021
Year: 2021

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it is based on Schrodinger equation, which is a partial differential equation that describes how the quantum state of a non-relativistic physical system changes with time. In classic world is named frequency in time (FIT), which is presented here in opposition and as a complement of traditional spectral analysis frequency-dependent based on Fourier theory. Besides, FIT is a metric, which assesses the impact of the flanks of a signal on its frequency spectrum, which is not taken into account by Fourier theory and even less in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N2) for images, c) it does not have phase uncertainties (indeterminate phase for magnitude = 0) as Discrete and Fast Fourier Transform (DFT, FFT, respectively), d) among others. In fact, FIT constitutes one side of a triangle (which from now on is closed) and it consists of the original signal in time, spectral analysis based on Fourier Theory and FIT. Thus a toolbox is completed, which it is essential for all applications of Digital Signal Processing (DSP) and Digital Image Processing (DIP); and, even, in the latter, FIT allows edge detection (which is called flank detection in case of signals), denoising, despeckling, compression, and superresolution of still images. Such applications include signals intelligence and imagery intelligence. On the other hand, we will present other DIP tools, which are also derived from the Schrodinger equation.
Multiwinner Approval Rules as Apportionment Methods
Venue: arXiv cs.GT 2021
Year: 2021

We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that they induce apportionment methods that are well-established in the literature on proportional representation. For instance, we show that Proportional Approval Voting induces the D'Hondt method and that Monroe's rule induces the largest reminder method. We also consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment methods satisfying these properties.
High-Multiplicity Election Problems
Venue: arXiv cs.GT 2021
Year: 2021

The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the electorate and their counts, i.e., high-multiplicity representation. We consider how this representation affects the complexity of election problems. High-multiplicity representation may be exponentially smaller than standard representation, and so many polynomial-time algorithms for election problems in standard representation become exponential-time. Surprisingly, for polynomial-time election problems, we are often able to either adapt the same approach or provide new algorithms to show that these problems remain polynomial-time in the high-multiplicity case; this is in sharp contrast to the case where each voter has a weight, where the complexity usually increases. In the process we explore the relationship between high-multiplicity scheduling and manipulation of high-multiplicity elections. And we show that for any fixed set of job lengths, high-multiplicity scheduling on uniform parallel machines is in P, which was previously known for only two job lengths. We did not find any natural case where a polynomial-time election problem does not remain in P when moving to high-multiplicity representation. However, we found one natural NP-hard election problem where the complexity does increase, namely winner determination for Kemeny elections.
Revenue Maximization in Incentivized Social Advertising
Venue: arXiv cs.SI 2021
Year: 2021

Incentivized social advertising, an emerging marketing model, provides monetization opportunities not only to the owners of the social networking platforms but also to their influential users by offering a "cut" on the advertising revenue. We consider a social network (the host) that sells ad-engagements to advertisers by inserting their ads, in the form of promoted posts, into the feeds of carefully selected "initial endorsers" or seed users: these users receive monetary incentives in exchange for their endorsements. The endorsements help propagate the ads to the feeds of their followers. In this context, the problem for the host is is to allocate ads to influential users, taking into account the propensity of ads for viral propagation, and carefully apportioning the monetary budget of each of the advertisers between incentives to influential users and ad-engagement costs, with the rational goal of maximizing its own revenue. We consider a monetary incentive for the influential users, which is proportional to their influence potential. We show that revenue maximization in incentivized social advertising corresponds to the problem of monotone submodular function maximization, subject to a partition matroid constraint on the ads-to-seeds allocation, and submodular knapsack constraints on the advertisers' budgets. This problem is NP-hard and we devise 2 greedy algorithms with provable approximation guarantees, which differ in their sensitivity to seed user incentive costs. Our approximation algorithms require repeatedly estimating the expected marginal gain in revenue as well as in advertiser payment. By exploiting a connection to the recent advances made in scalable estimation of expected influence spread, we devise efficient and scalable versions of the greedy algorithms.
A Brief Introduction to Shannon's Information Theory
Venue: arXiv cs.IT 2021
Year: 2021

This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues usually not addressed in the literature are discussed here as well. In particular, we show that it seems we can define channel capacity differently which allows us to potentially transmit more messages in a fixed sufficient long time duration. However, for a channel carrying a finite number of letters, the channel capacity unfortunately remains the same as the Shannon limit.
On Higher-Order Probabilistic Subrecursion
Venue: arXiv cs.LO 2021
Year: 2021

We study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like Gödel's $\mathbb{T}$ with various forms of probabilistic choice operators may result in calculi which are not equivalent as for the class of distributions they give rise to, although they all guarantee almost-sure termination. Along the way, we introduce a probabilistic variation of the classic reducibility technique, and we prove that the simplest form of probabilistic choice leaves the expressive power of $\mathbb{T}$ essentially unaltered. The paper ends with some observations about the functional expressive power: expectedly, all the considered calculi capture the functions which $\mathbb{T}$ itself represents, at least when standard notions of observations are considered.
Combination Networks with End-user-caches: Novel Achievable and Converse Bounds under Uncoded Cache Placement
Venue: arXiv cs.IT 2021
Year: 2021

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the users' local caches. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size $M$ and the network load $R$ for networks where a server with $N$ files is connected to $H$ relays (without caches), which in turn are connected to $K$ users equipped with caches of $M$ files. When each user is connected to a different subset of $r$ relays, i.e., $K = \binom{H}{r}$, the system is referred to as a {\it combination network with end-user-caches}. In this work, converse bounds are derived for the practically motivated case of {\it uncoded} cache contents, that is, bits of the various files are directly pushed into the user caches without any coding. In this case, once the cache contents and the user demands are known, the problem reduces to a general index coding problem.This paper shows that relying on a well-known "acyclic index coding converse bound" results in converse bounds that are not tight for combination networks with end-user-caches. A novel converse bound that leverages the network topology is proposed, which is the tightest converse bound known to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived. Several novel caching schemes are proposed, based on the Maddah-Ali and Niesen cache placement. The proposed schemes are proved: (i) to be (order) optimal for some $(N,M,H,r)$ parameters regimes under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations.
Secure Multi-Source Multicast
Venue: arXiv cs.IT 2021
Year: 2021

The principal mission of Multi-Source Multicast (MSM) is to disseminate all messages from all sources in a network to all destinations. MSM is utilized in numerous applications. In many of them, securing the messages disseminated is critical. A common secure model is to consider a network where there is an eavesdropper which is able to observe a subset of the network links, and seek a code which keeps the eavesdropper ignorant regarding all the messages. While this is solved when all messages are located at a single source, Secure MSM (SMSM) is an open problem, and the rates required are hard to characterize in general. In this paper, we consider Individual Security, which promises that the eavesdropper has zero mutual information with each message individually. We completely characterize the rate region for SMSM under individual security, and show that such a security level is achievable at the full capacity of the network, that is, the cut-set bound is the matching converse, similar to non-secure MSM. Moreover, we show that the field size is similar to non-secure MSM and does not have to be larger due to the security constraint.