OpenRaiser/Intern-Atlas huggingface dataset:
Bi-Factor Approximation Algorithms for Hard Capacitated $k$-Median Problems
Venue: arXiv cs.DS 2017
Year: 2017

The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established connections between clients and opened facilities. We consider the hard-capacitated version of the problem, where a single facility may only serve a limited number of clients and creating multiple copies of a facility is not allowed. We construct approximation algorithms slightly violating the capacities based on rounding a fractional solution to the standard LP. It is well known that the standard LP (even in the case of uniform capacities and opening costs) has unbounded integrality gap if we only allow violating capacities by a factor smaller than $2$, or if we only allow violating the number of facilities by a factor smaller than $2$. In this paper, we present the first constant-factor approximation algorithms for the hard-capacitated variants of the problem. For uniform capacities, we obtain a $(2+\varepsilon)$-capacity violating algorithm with approximation ratio $O(1/\varepsilon^2)$; our result has not yet been improved. Then, for non-uniform capacities, we consider the case of $k$-Median, which is equivalent to $k$-Facility Location with uniform opening cost of the facilities. Here, we obtain a $(3+\varepsilon)$-capacity violating algorithm with approximation ratio $O(1/\varepsilon)$.
For-all Sparse Recovery in Near-Optimal Time
Venue: arXiv cs.DS 2017
Year: 2017

An approximate sparse recovery system in $\ell_1$ norm consists of parameters $k$, $ε$, $N$, an $m$-by-$N$ measurement $Φ$, and a recovery algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates $x$ by $\widehat{\mathbf{x}} = \mathcal{R}(Φ\mathbf{x})$, which must satisfy $\|\widehat{\mathbf{x}}-\mathbf{x}\|_1 \leq (1+ε)\|\mathbf{x}-\mathbf{x}_k\|_1$. We consider the 'for all' model, in which a single matrix $Φ$, possibly 'constructed' non-explicitly using the probabilistic method, is used for all signals $\mathbf{x}$. The best existing sublinear algorithm by Porat and Strauss (SODA'12) uses $O(ε^{-3} k\log(N/k))$ measurements and runs in time $O(k^{1-α}N^α)$ for any constant $α> 0$. In this paper, we improve the number of measurements to $O(ε^{-2} k \log(N/k))$, matching the best existing upper bound (attained by super-linear algorithms), and the runtime to $O(k^{1+β}\textrm{poly}(\log N,1/ε))$, with a modest restriction that $ε\leq (\log k/\log N)^γ$, for any constants $β,γ> 0$. When $k\leq \log^c N$ for some $c>0$, the runtime is reduced to $O(k\textrm{poly}(N,1/ε))$. With no restrictions on $ε$, we have an approximation recovery system with $m = O(k/ε\log(N/k)((\log N/\log k)^γ+ 1/ε))$ measurements.
Minimum Bisection is NP-hard on Unit Disk Graphs
Venue: arXiv cs.CC 2017
Year: 2017

In this paper we prove that the \textsc{Min-Bisection} problem is NP-hard on \emph{unit disk graphs}, thus solving a longstanding open question.
Applications of Algorithmic Probability to the Philosophy of Mind
Venue: arXiv cs.AI 2017
Year: 2017

This paper presents formulae that can solve various seemingly hopeless philosophical conundrums. We discuss the simulation argument, teleportation, mind-uploading, the rationality of utilitarianism, and the ethics of exploiting artificial general intelligence. Our approach arises from combining the essential ideas of formalisms such as algorithmic probability, the universal intelligence measure, space-time-embedded intelligence, and Hutter's observer localization. We argue that such universal models can yield the ultimate solutions, but a novel research direction would be required in order to find computationally efficient approximations thereof.
Density decompositions of networks
Venue: arXiv cs.SI 2017
Year: 2017

We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network has exactly one density decomposition. The number of nodes in each partition defines a density distribution which we find is measurably similar to the degree distribution of given real networks (social, internet, etc.) and measurably dissimilar in synthetic networks (preferential attachment, small world, etc.).
A formally verified proof of the Central Limit Theorem
Venue: arXiv cs.MS 2017
Year: 2017

We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle's libraries for analysis and measure-theoretic probability. The proof of the theorem uses characteristic functions, which are a kind of Fourier transform, to demonstrate that, under suitable hypotheses, sums of random variables converge weakly to the standard normal distribution. We also discuss the libraries and infrastructure that supported the formalization, and reflect on some of the lessons we have learned from the effort.
Peeling potatoes near-optimally in near-linear time
Venue: arXiv cs.CG 2017
Year: 2017

We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for this problem: in $O(n( \log^2 n + (1/\varepsilon^3) \log n + 1/\varepsilon^4))$ time we find a convex polygon contained in $P$ that, with probability at least $2/3$, has area at least $(1-\varepsilon)$ times the area of an optimal solution. We also obtain similar results for the variant of computing a convex polygon inside $P$ with maximum perimeter. To achieve these results we provide new results in geometric probability. The first result is a bound relating the probability that two points chosen uniformly at random inside $P$ are mutually visible and the area of the largest convex body inside $P$. The second result is a bound on the expected value of the difference between the perimeter of any planar convex body $K$ and the perimeter of the convex hull of a uniform random sample inside $K$.
Energy-Efficient Cooperative Cognitive Relaying Schemes for Cognitive Radio Networks
Venue: arXiv cs.NI 2017
Year: 2017

We investigate a cognitive radio network in which a primary user (PU) may cooperate with a cognitive radio user (i.e., a secondary user (SU)) for transmissions of its data packets. The PU is assumed to be a buffered node operating in a time-slotted fashion where the time is partitioned into equal-length slots. We develop two schemes which involve cooperation between primary and secondary users. To satisfy certain quality of service (QoS) requirements, users share time slot duration and channel frequency bandwidth. Moreover, the SU may leverage the primary feedback message to further increase both its data rate and satisfy the PU QoS requirements. The proposed cooperative schemes are designed such that the SU data rate is maximized under the constraint that the PU average queueing delay is maintained less than the average queueing delay in case of non-cooperative PU. In addition, the proposed schemes guarantee the stability of the PU queue and maintain the average energy emitted by the SU below a certain value. The proposed schemes also provide more robust and potentially continuous service for SUs compared to the conventional practice in cognitive networks where SUs transmit in the spectrum holes and silence sessions of the PUs. We include primary source burstiness, sensing errors, and feedback decoding errors to the analysis of our proposed cooperative schemes. The optimization problems are solved offline and require a simple 2-dimensional grid-based search over the optimization variables. Numerical results show the beneficial gains of the cooperative schemes in terms of SU data rate and PU throughput, average PU queueing delay, and average PU energy savings.
Joint Empirical Coordination of Source and Channel
Venue: arXiv cs.IT 2017
Year: 2017

In a decentralized and self-configuring network, the communication devices are considered as autonomous decision-makers that sense their environment and that implement optimal transmission schemes. It is essential that these autonomous devices cooperate and coordinate their actions, to ensure the reliability of the transmissions and the stability of the network. We study a point-to-point scenario in which the encoder and the decoder implement decentralized policies that are coordinated. The coordination is measured in terms of empirical frequency of symbols of source and channel. The encoder and the decoder perform a coding scheme such that the empirical distribution of the symbols is close to a target joint probability distribution. We characterize the set of achievable target probability distributions for a point-to-point source-channel model, in which the encoder is non-causal and the decoder is strictly causal i.e., it returns an action based on the observation of the past channel outputs. The objectives of the encoder and of the decoder, are captured by some utility function, evaluated with respect to the set of achievable target probability distributions. In this article, we investigate the maximization problem of a utility function that is common to both encoder and decoder. We show that the compression and the transmission of information are particular cases of the empirical coordination.
Geo-Social Group Queries with Minimum Acquaintance Constraint
Venue: arXiv cs.DB 2017
Year: 2017

The prosperity of location-based social networking services enables geo-social group queries for group-based activity planning and marketing. This paper proposes a new family of geo-social group queries with minimum acquaintance constraint (GSGQs), which are more appealing than existing geo-social group queries in terms of producing a cohesive group that guarantees the worst-case acquaintance level. GSGQs, also specified with various spatial constraints, are more complex than conventional spatial queries; particularly, those with a strict $k$NN spatial constraint are proved to be NP-hard. For efficient processing of general GSGQ queries on large location-based social networks, we devise two social-aware index structures, namely SaR-tree and SaR*-tree. The latter features a novel clustering technique that considers both spatial and social factors. Based on SaR-tree and SaR*-tree, efficient algorithms are developed to process various GSGQs. Extensive experiments on real-world Gowalla and Dianping datasets show that our proposed methods substantially outperform the baseline algorithms based on R-tree.
A Psychologically-Motivated Model of Opinion Change with Applications to American Politics
Venue: arXiv cs.MA 2017
Year: 2017

Agent-based models are versatile tools for studying how societal opinion change, including political polarization and cultural diffusion, emerges from individual behavior. This study expands agents' psychological realism using empirically-motivated rules governing interpersonal influence, commitment to previous beliefs, and conformity in social contexts. Computational experiments establish that these extensions produce three novel results: (a) sustained strong diversity of opinions within the population, (b) opinion subcultures, and (c) pluralistic ignorance. These phenomena arise from a combination of agents' intolerance, susceptibility and conformity, with extremist agents and social networks playing important roles. The distribution and dynamics of simulated opinions reproduce two empirical datasets on Americans' political opinions.
Object Detection Through Exploration With A Foveated Visual Field
Venue: arXiv cs.CV 2017
Year: 2017

We present a foveated object detector (FOD) as a biologically-inspired alternative to the sliding window (SW) approach which is the dominant method of search in computer vision object detection. Similar to the human visual system, the FOD has higher resolution at the fovea and lower resolution at the visual periphery. Consequently, more computational resources are allocated at the fovea and relatively fewer at the periphery. The FOD processes the entire scene, uses retino-specific object detection classifiers to guide eye movements, aligns its fovea with regions of interest in the input image and integrates observations across multiple fixations. Our approach combines modern object detectors from computer vision with a recent model of peripheral pooling regions found at the V1 layer of the human visual system. We assessed various eye movement strategies on the PASCAL VOC 2007 dataset and show that the FOD performs on par with the SW detector while bringing significant computational cost savings.
Sharing of Unlicensed Spectrum by Strategic Operators
Venue: arXiv cs.IT 2017
Year: 2017

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of spectrum which anyone can use for free without having to obtain a license. Major standards bodies are currently considering a proposal to retool and deploy Long Term Evolution (LTE) technologies in unlicensed bands below 6 GHz. This paper studies the fundamental questions of whether and how the unlicensed spectrum can be shared by intrinsically strategic operators without suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme which allows dynamic spectrum borrowing and lending between operators is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results to the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.
A Hoare-like logic of asserted single-pass instruction sequences
Venue: arXiv cs.LO 2017
Year: 2017

We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerned. The system is similar to Hoare logics, but takes into account that, by the presence of jump instructions, segments of single-pass instruction sequences may have multiple entry points and multiple exit points. It is intended to support a sound general understanding of the issues with Hoare-like logics for low-level programming languages.
A Public Key Cryptoscheme Using Bit-pairs and Probabilistic Mazes
Venue: arXiv cs.CR 2017
Year: 2017

This paper gives the definition and property of a bit-pair shadow, and devises the three algorithms of a public key cryptoscheme called JUOAN that is based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far, and regards a bit-pair as a manipulation unit. The authors demonstrate that the decryption algorithm is correct, deduce the probability that a plaintext solution is nonunique is nearly zero, analyze the security of the new cryptoscheme against extracting a private key from a public key and recovering a plaintext from a ciphertext on the assumption that an integer factorization problem, a discrete logarithm problem, and a low-density subset sum problem can be solved efficiently, and prove that the new cryptoscheme using random padding and random permutation is semantically secure. The analysis shows that the bit-pair method increases the density D of a related knapsack to a number more than 1, and decreases the modulus length lgM of the new cryptoscheme to 464, 544, or 640.
RENOIR - A Dataset for Real Low-Light Image Noise Reduction
Venue: arXiv cs.CV 2017
Year: 2017

Image denoising algorithms are evaluated using images corrupted by artificial noise, which may lead to incorrect conclusions about their performances on real noise. In this paper we introduce a dataset of color images corrupted by natural noise due to low-light conditions, together with spatially and intensity-aligned low noise images of the same scenes. We also introduce a method for estimating the true noise level in our images, since even the low noise images contain small amounts of noise. We evaluate the accuracy of our noise estimation method on real and artificial noise, and investigate the Poisson-Gaussian noise model. Finally, we use our dataset to evaluate six denoising algorithms: Active Random Field, BM3D, Bilevel-MRF, Multi-Layer Perceptron, and two versions of NL-means. We show that while the Multi-Layer Perceptron, Bilevel-MRF, and NL-means with soft threshold outperform BM3D on gray images with synthetic noise, they lag behind on our dataset.
Improved Algorithms for Parity and Streett objectives
Venue: arXiv cs.DS 2017
Year: 2017

The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on $n$ vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time $O(n^{5/2})$ and for (2) k-pair Streett objectives in graphs in time $O(n^2 + nk \log n)$. For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.
GYM: A Multiround Join Algorithm In MapReduce
Venue: arXiv cs.DB 2017
Year: 2017

Multiround algorithms are now commonly used in distributed data processing systems, yet the extent to which algorithms can benefit from running more rounds is not well understood. This paper answers this question for a spectrum of rounds for the problem of computing the equijoin of $n$ relations. Specifically, given any query $Q$ with width $\w$, {\em intersection width} $\iw$, input size $\mathrm{IN}$, output size $\mathrm{OUT}$, and a cluster of machines with $M$ memory available per machine, we show that: (1) $Q$ can be computed in $O(n)$ rounds with $O(n\frac{(\mathrm{IN}^{\w} + \mathrm{OUT})^2}{M})$ communication cost. (2) $Q$ can be computed in $O(\log(n))$ rounds with $O(n\frac{(\mathrm{IN}^{\max(\w, 3\iw)} + \mathrm{OUT})^2}{M})$ communication cost. \end{itemize} Intersection width is a new notion of queries and generalized hypertree decompositions (GHDs) of queries we introduce to capture how connected the adjacent cyclic components of the GHDs are. We achieve our first result by introducing a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any GHD of $Q$ with width $\w$ and depth $d$, and computes $Q$ in $O(d + \log(n))$ rounds and $O(n\frac{(\mathrm{IN}^{\w} + \mathrm{OUT})^2}{M})$ communication cost. We achieve our second result by showing how to construct GHDs of $Q$ with width $\max(\w, 3\iw)$ and depth $O(\log(n))$. We describe another technique to construct GHDs with longer widths and shorter depths, demonstrating a spectrum of tradeoffs one can make between communication and the number of rounds.
Should We Train Scientific Generalists?
Venue: arXiv cs.CY 2017
Year: 2017

I examine the topic of training scientific generalists. To focus the discussion, I propose the creation of a new graduate program, analogous in structure to existing MD/PhD programs, aimed at training a critical mass of scientific researchers with substantial intellectual breadth. In addition to completing the normal requirements for a PhD, students would undergo an intense, several year training period designed to expose them to the core vocabulary of multiple subjects at the graduate level. After providing some historical and philosophical context for this proposal, I outline how such a program could be implemented with little institutional overhead by existing research universities. Finally, I discuss alternative possibilities for training generalists by taking advantage of contemporary developments in online learning and open science.
Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory
Venue: arXiv cs.OH 2017
Year: 2017

Aim of this paper is to provide preliminary elements for discussion about the implications of the Hierarchy Theory of Evolution on the design and evolution of artificial systems and socio-technical organizations. In order to achieve this goal, a number of analogies are drawn between the System of Leibniz; the socio-technical architecture known as Fractal Social Organization; resilience and related disciplines; and Hierarchy Theory. In so doing we hope to provide elements for reflection and, hopefully, enrich the discussion on the above topics with considerations pertaining to related fields and disciplines, including computer science, management science, cybernetics, social systems, and general systems theory.
Dual Algorithms
Venue: arXiv cs.CE 2017
Year: 2017

The cubic spline interpolation method, the Runge--Kutta method, and the Newton-Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some examples are presented. Among them, we use the dual Newton--Raphson method to obtain the derivatives of the output angle in the RRRCR spatial mechanism; we use the dual normal cubic spline interpolation algorithm to obtain the thermal diffusivity using photothermal techniques; and we use the dual Runge--Kutta method to obtain the derivatives of functions depending on the solution of the Duffing equation.
An Expected Linear-Time Algorithm for the Farthest-Segment Voronoi Diagram
Venue: arXiv cs.CG 2017
Year: 2017

We present an expected linear-time algorithm to construct the farthest-segment Voronoi diagram, given the sequence of its faces at infinity. This sequence forms a Davenport-Schinzel sequence of order 3 and it can be computed in O(n log n) time, where n is the number of input segments. The farthest-segment Voronoi diagram is a tree, with disconnected Voronoi regions, of total complexity Theta(n) in the worst case. Disconnected regions pose a major difficulty in deriving linear-time construction algorithms for such tree-like Voronoi diagrams. In this paper we present a new approach towards this direction.