OpenRaiser/Intern-Atlas huggingface dataset:
Selling Multiple Correlated Goods: Revenue Maximization and Menu-Size Complexity (old title: "The Menu-Size Complexity of Auctions")
Venue: arXiv cs.GT 2018
Year: 2018

We consider the well known, and notoriously difficult, problem of a single revenue-maximizing seller selling two or more heterogeneous goods to a single buyer whose private values for the goods are drawn from a (possibly correlated) known distribution, and whose valuation is additive over the goods. We show that when there are two (or more) goods, _simple mechanisms_ -- such as selling the goods separately or as a bundle -- _may yield only a negligible fraction of the optimal revenue_. This resolves the open problem of Briest, Chawla, Kleinberg, and Weinberg (JET 2015) who prove the result for at least three goods in the related setup of a unit-demand buyer. We also introduce the menu size as a simple measure of the complexity of mechanisms, and show that the revenue may increase polynomially with _menu size_ and that no bounded menu size can ensure any positive fraction of the optimal revenue. The menu size also turns out to "pin down" the revenue properties of deterministic mechanisms.
The Ergodic Capacity of the Multiple Access Channel Under Distributed Scheduling - Order Optimality of Linear Receivers
Venue: arXiv cs.IT 2018
Year: 2018

Consider the problem of a Multiple-Input Multiple-Output (MIMO) Multiple-Access Channel (MAC) at the limit of large number of users. Clearly, in practical scenarios, only a small subset of the users can be scheduled to utilize the channel simultaneously. Thus, a problem of user selection arises. However, since solutions which collect Channel State Information (CSI) from all users and decide on the best subset to transmit in each slot do not scale when the number of users is large, distributed algorithms for user selection are advantageous. In this paper, we analyse a distributed user selection algorithm, which selects a group of users to transmit without coordinating between users and without all users sending CSI to the base station. This threshold-based algorithm is analysed for both Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers, and its expected sum-rate in the limit of large number of users is investigated. It is shown that for large number of users it achieves the same scaling laws as the optimal centralized scheme.
Broadcasting in Ad Hoc Multiple Access Channels
Venue: arXiv cs.NI 2018
Year: 2018

We study broadcast in multiple access channels in dynamic adversarial settings. There is an unbounded supply of anonymous stations attached to a synchronous channel. There is an adversary who injects packets into stations to be broadcast on the channel. The adversary is restricted by injection rate, burstiness, and by how many passive stations can be simultaneously activated by providing them with packets. We consider deterministic distributed broadcast algorithms, which are further categorized by their properties. We investigate for which injection rates can algorithms attain bounded packet latency, when adversaries are restricted to be able to activate at most one station per round. The rates of algorithms we present make the increasing sequence consisting of $\frac{1}{3}$, $\frac{3}{8}$ and $\frac{1}{2}$, reflecting the additional features of algorithms. We show that injection rate $\frac{3}{4}$ cannot be handled with bounded packet latency.
General Drift Analysis with Tail Bounds
Venue: arXiv cs.NE 2018
Year: 2018

Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, e.g., the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. Surprisingly, the probability of deviating by an $r$-factor in lower order terms of the expected time decreases exponentially with $r$ on all these problems. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Moreover, our theorem can be specialized into virtually all existing drift theorems with drift towards the target from the literature. Finally, user-friendly specializations of the general drift theorem are given.
Coping with Unreliable Workers in Internet-based Computing: An Evaluation of Reputation Mechanisms
Venue: arXiv cs.DC 2018
Year: 2018

We present reputation-based mechanisms for building reliable task computing systems over the Internet. The most characteristic examples of such systems are the volunteer computing and the crowdsourcing platforms. In both examples end users are offering over the Internet their computing power or their human intelligence to solve tasks either voluntarily or under payment. While the main advantage of these systems is the inexpensive computational power provided, the main drawback is the untrustworthy nature of the end users. Generally, this type of systems are modeled under the "master-worker" setting. A "master" has a set of tasks to compute and instead of computing them locally she sends these tasks to available "workers" that compute and report back the task results. We categorize these workers in three generic types: altruistic, malicious and rational. Altruistic workers that always return the correct result, malicious workers that always return an incorrect result, and rational workers that decide to reply or not truthfully depending on what increases their benefit. We design a reinforcement learning mechanism to induce a correct behavior to rational workers, while the mechanism is complemented by four reputation schemes that cope with malice. The goal of the mechanism is to reach a state of eventual correctness, that is, a stable state of the system in which the master always obtains the correct task results. Analysis of the system gives provable guarantees under which truthful behavior can be ensured. Finally, we observe the behavior of the mechanism through simulations that use realistic system parameters values. Simulations not only agree with the analysis but also reveal interesting trade-offs between various metrics and parameters. Finally, the four reputation schemes are assessed against the tolerance to cheaters.
Holographic Algorithms Beyond Matchgates
Venue: arXiv cs.DS 2018
Year: 2018

Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among problems with different descriptions via certain basis transformations. In this paper, we replace matchgates in the paradigm above by the affine type and the product type constraint functions, which are known to be tractable in general (not necessarily planar) graphs. More specifically, we present polynomial-time algorithms to decide if a given counting problem has a holographic reduction to another problem defined by the affine or product-type functions. Our algorithms also find a holographic transformation when one exists. We further present polynomial-time algorithms of the same decision and search problems for symmetric functions, where the complexity is measured in terms of the (exponentially more) succinct representations. The algorithm for the symmetric case also shows that the recent dichotomy theorem for Holant problems with symmetric constraints is efficiently decidable. Our proof techniques are mainly algebraic, e.g., using stabilizers and orbits of group actions.
Full-Diversity Space-Time Block Codes for Integer-Forcing Linear Receivers
Venue: arXiv cs.IT 2018
Year: 2018

In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding scheme. In this paper, we address the design of full-diversity STBCs for IF linear receivers. In particular, we are interested in characterizing the structure of STBCs that provide full-diversity with the IF receiver. Along that direction, we derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the restricted non-vanishing singular value (RNVS) property provide full-diversity for the IF receiver. Furthermore, we prove that all known STBCs with the non-vanishing determinant property provide full-diversity with IF receivers, as they guarantee the RNVS property. By using the formulation of RNVS property, we also prove the existence of a full-diversity STBC outside the class of perfect STBCs, thereby adding significant insights compared to the existing works on STBCs with IF decoding. Finally, we present extensive simulation results to demonstrate that linear designs with RNVS property provide full-diversity for IF receiver.
Approximation of smallest linear tree grammar
Venue: arXiv cs.DS 2018
Year: 2018

A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and r is the maximal rank of symbols in T (which is a constant in many applications). This is the first example of a grammar-based tree compression algorithm with a good, i.e. logarithmic in terms of the size of the input tree, approximation ratio. The analysis of the algorithm uses an extension of the recompression technique from strings to trees.
Adversarial Multiple Access Channels with Individual Injection Rates
Venue: arXiv cs.DC 2018
Year: 2018

We study deterministic distributed broadcasting in synchronous multiple-access channels. Packets are injected into $n$ nodes by a window-type adversary that is constrained by a window $w$ and injection rates individually assigned to all nodes. We investigate what queue size and packet latency can be achieved with the maximum aggregate injection rate of one packet per round, depending on properties of channels and algorithms. We give a non-adaptive algorithm for channels with collision detection and an adaptive algorithm for channels without collision detection that achieve $O(\min(n+w,w\log n))$ packet latency. We show that packet latency has to be either $Ω(w \max (1,\log_w n))$, when $w\le n$, or $Ω(w+n)$, when $w>n$, as a matching lower bound to these algorithms. We develop a non-adaptive algorithm for channels without collision detection that achieves $O(n+w)$ queue size and $O(nw)$ packet latency. This is in contrast with the adversarial model of global injection rates, in which non-adaptive algorithms with bounded packet latency do not exist (Chlebus et al. Distributed Computing 22(2): 93 - 116, 2009). Our algorithm avoids collisions produced by simultaneous transmissions; we show that any algorithm with this property must have $Ω(nw)$ packet latency.
Easy Accurate Reading and Writing of Floating-Point Numbers
Venue: arXiv cs.NA 2018
Year: 2018

Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than those previously published. The values are stable under repeated conversions between the formats. Unlike Java-1.8, the scientific representations generated use only the minimum number of mantissa digits needed to convert back to the original binary values.
Optimal detection of intersections between convex polyhedra
Venue: arXiv cs.CG 2018
Year: 2018

For a polyhedron $P$ in $\mathbb{R}^d$, denote by $|P|$ its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so that given two preprocessed polyhedra $P$ and $Q$ in $\mathbb{R}^d$, each translated and rotated, their intersection can be tested rapidly. For $d=3$ we show how to perform such a test in $O(\log |P| + \log |Q|)$ time after linear preprocessing time and space. This running time is the best possible and improves upon the last best known query time of $O(\log|P| \log|Q|)$ by Dobkin and Kirkpatrick (1990). We then generalize our method to any constant dimension $d$, achieving the same optimal $O(\log |P| + \log |Q|)$ query time using a representation of size $O(|P|^{\lfloor d/2\rfloor + \varepsilon})$ for any $\varepsilon>0$ arbitrarily small. This answers an even older question posed by Dobkin and Kirkpatrick 30 years ago. In addition, we provide an alternative $O(\log |P| + \log |Q|)$ algorithm to test the intersection of two convex polygons $P$ and $Q$ in the plane.
The False Premises and Promises of Bitcoin
Venue: arXiv cs.CE 2018
Year: 2018

Designed to compete with fiat currencies, bitcoin proposes it is a crypto-currency alternative. Bitcoin makes a number of false claims, including: solving the double-spending problem is a good thing; bitcoin can be a reserve currency for banking; hoarding equals saving, and that we should believe bitcoin can expand by deflation to become a global transactional currency supply. Bitcoin's developers combine technical implementation proficiency with ignorance of currency and banking fundamentals. This has resulted in a failed attempt to change finance. A set of recommendations to change finance are provided in the Afterword: Investment/venture banking for the masses; Venture banking to bring back what investment banks once were; Open-outcry exchange for all CDS contracts; Attempting to develop CDS type contracts on investments in startup and existing enterprises; and Improving the connection between startup tech/ideas, business organization and investment.
Distributed Energy Efficient Channel Allocation
Venue: arXiv cs.NI 2018
Year: 2018

Design of energy efficient protocols for modern wireless systems has become an important area of research. In this paper, we propose a distributed optimization algorithm for the channel assignment problem for multiple interfering transceiver pairs that cannot communicate with each other. We first modify the auction algorithm for maximal energy efficiency and show that the problem can be solved without explicit message passing using the carrier sense multiple access (CSMA) protocols. We then develop a novel scheme by converting the channel assignment problem into perfect matchings on bipartite graphs. The proposed scheme improves the energy efficiency and does not require any explicit message passing or a shared memory between the users. We derive bounds on the convergence rate and show that the proposed algorithm converges faster than the distributed auction algorithm and achieves near-optimal performance under Rayleigh fading channels. We also present an asymptotic performance analysis of the fast matching algorithm for energy efficient resource allocation and prove the optimality for large enough number of users and number of channels. Finally, we provide numerical assessments that confirm the energy efficiency gains compared to the state of the art.
Near-optimal sample compression for nearest neighbors
Venue: arXiv cs.LG 2018
Year: 2018

We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.
Strongly stable ideals and Hilbert polynomials
Venue: arXiv cs.SC 2018
Year: 2018

The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. A description of the main method and auxiliary tools is given.
Planar Graphs: Random Walks and Bipartiteness Testing
Venue: arXiv cs.DS 2018
Year: 2018

We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time testability was only known for planar graphs with bounded degree. Our algorithm is based on random walks. Since planar graphs have good separators, i.e., bad expansion, our analysis diverges from standard techniques that involve the fast convergence of random walks on expanders. We reduce the problem to the task of detecting an odd-parity cycle in a multigraph induced by constant-length cycles. We iteratively reduce the length of cycles while preserving the detection probability, until the multigraph collapses to a collection of easily discoverable self-loops. Our approach extends to arbitrary minor-free graphs. We also believe that our techniques will find applications to testing other properties in arbitrary minor-free graphs.
Optimal Spectrum Management in Two-User Interference Channels
Venue: arXiv cs.IT 2018
Year: 2018

In this work, we address the problem of optimal spectrum management in continuous frequency domain in multiuser interference channels. The objective is to maximize the weighted sum of user capacities. Our main results are as follows: (i) For frequency-selective channels, we prove that in an optimal solution, each user uses maximum power; this result also generalizes to the cases where the objective is to maximize the weighted product (i.e., proportional fairness) of user capacities. (ii) For the special case of two users in flat channels, we solve the problem optimally.
An algorithm for canonical forms of finite subsets of $\mathbb{Z}^d$ up to affinities
Venue: arXiv cs.DS 2018
Year: 2018

In this paper we describe an algorithm for the computation of canonical forms of finite subsets of $\mathbb{Z}^d$, up to affinities over $\mathbb{Z}$. For fixed dimension $d$, this algorithm has worst-case asymptotic complexity $O(n \log^2 n \, s\,μ(s))$, where $n$ is the number of points in the given subset, $s$ is an upper bound to the size of the binary representation of any of the $n$ points, and $μ(s)$ is an upper bound to the number of operations required to multiply two $s$-bit numbers. In particular, the problem is fixed-parameter tractable with respect to the dimension $d$. This problem arises e.g. in the context of computation of invariants of finitely presented groups with abelianized group isomorphic to $\mathbb{Z}^d$. In that context one needs to decide whether two Laurent polynomials in $d$ indeterminates, considered as elements of the group ring over the abelianized group, are equivalent with respect to a change of basis.
Doing-it-All with Bounded Work and Communication
Venue: arXiv cs.DC 2018
Year: 2018

We consider the Do-All problem, where $p$ cooperating processors need to complete $t$ similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of work complexity (also known as total available processor steps) and communication complexity (total number of point-to-point messages). When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work $O( t + p \log p\, (\sqrt{p\log p}+\sqrt{t\log t}\, ) )$ and a nonconstructive algorithm that has work $O(t +p \log^2 p)$. The latter result is close to the lower bound $Ω(t + p \log p/ \log \log p)$ on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by $c\,p$, for some positive constant $c < 1$. We also present a nonconstructive algorithm that has effort $O(t + p ^{1.77})$.
Non-myopic learning in repeated stochastic games
Venue: arXiv cs.GT 2018
Year: 2018

In repeated stochastic games (RSGs), an agent must quickly adapt to the behavior of previously unknown associates, who may themselves be learning. This machine-learning problem is particularly challenging due, in part, to the presence of multiple (even infinite) equilibria and inherently large strategy spaces. In this paper, we introduce a method to reduce the strategy space of two-player general-sum RSGs to a handful of expert strategies. This process, called Mega, effectually reduces an RSG to a bandit problem. We show that the resulting strategy space preserves several important properties of the original RSG, thus enabling a learner to produce robust strategies within a reasonably small number of interactions. To better establish strengths and weaknesses of this approach, we empirically evaluate the resulting learning system against other algorithms in three different RSGs.
An easy subexponential bound for online chain partitioning
Venue: arXiv cs.DS 2018
Year: 2018

Bosek and Krawczyk exhibited an online algorithm for partitioning an online poset of width $w$ into $w^{14\lg w}$ chains. We improve this to $w^{6.5 \lg w + 7}$ with a simpler and shorter proof by combining the work of Bosek & Krawczyk with work of Kierstead & Smith on First-Fit chain partitioning of ladder-free posets. We also provide examples illustrating the limits of our approach.
Eigenvectors of Orthogonally Decomposable Functions
Venue: arXiv cs.LG 2018
Year: 2018

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely orthogonal tensor decompositions, Independent Component Analysis (ICA), topic models, spectral clustering, and Gaussian mixture learning---we generalize the eigendecomposition from quadratic forms to a broad class of "orthogonally decomposable" functions. We identify a key role of convexity in our extension, and we generalize two traditional characterizations of eigenvectors: First, the eigenvectors of a quadratic form arise from the optima structure of the quadratic form on the sphere. Second, the eigenvectors are the fixed points of the power iteration. In our setting, we consider a simple first order generalization of the power method which we call gradient iteration. It leads to efficient and easily implementable methods for basis recovery. It includes influential Machine Learning methods such as cumulant-based FastICA and the tensor power iteration for orthogonally decomposable tensors as special cases. We provide a complete theoretical analysis of gradient iteration using the structure theory of discrete dynamical systems to show almost sure convergence and fast (super-linear) convergence rates. The analysis also extends to the case when the observed function is only approximately orthogonally decomposable, with bounds that are polynomial in dimension and other relevant parameters, such as perturbation size. Our perturbation results can be considered as a non-linear version of the classical Davis-Kahan theorem for perturbations of eigenvectors of symmetric matrices.