OpenRaiser/Intern-Atlas huggingface dataset:
Competitive Local Routing with Constraints
Venue: arXiv cs.CG 2017
Year: 2017

Let $P$ be a set of $n$ vertices in the plane and $S$ a set of non-crossing line segments between vertices in $P$, called constraints. Two vertices are visible if the straight line segment connecting them does not properly intersect any constraints. The constrained $Θ_m$-graph is constructed by partitioning the plane around each vertex into $m$ disjoint cones, each with aperture $θ= 2 π/m$, and adding an edge to the `closest' visible vertex in each cone. We consider how to route on the constrained $Θ_6$-graph. We first show that no deterministic 1-local routing algorithm is $o(\sqrt{n})$-competitive on all pairs of vertices of the constrained $Θ_6$-graph. After that, we show how to route between any two visible vertices of the constrained $Θ_6$-graph using only 1-local information. Our routing algorithm guarantees that the returned path is 2-competitive. Additionally, we provide a 1-local 18-competitive routing algorithm for visible vertices in the constrained half-$Θ_6$-graph, a subgraph of the constrained $Θ_6$-graph that is equivalent to the Delaunay graph where the empty region is an equilateral triangle. To the best of our knowledge, these are the first local routing algorithms in the constrained setting with guarantees on the length of the returned path.
Memory vectors for similarity search in high-dimensional spaces
Venue: arXiv cs.CV 2017
Year: 2017

We study an indexing architecture to store and search in a database of high-dimensional vectors from the perspective of statistical signal processing and decision theory. This architecture is composed of several memory units, each of which summarizes a fraction of the database by a single representative vector. The potential similarity of the query to one of the vectors stored in the memory unit is gauged by a simple correlation with the memory unit's representative vector. This representative optimizes the test of the following hypothesis: the query is independent from any vector in the memory unit vs. the query is a simple perturbation of one of the stored vectors. Compared to exhaustive search, our approach finds the most similar database vectors significantly faster without a noticeable reduction in search quality. Interestingly, the reduction of complexity is provably better in high-dimensional spaces. We empirically demonstrate its practical interest in a large-scale image search scenario with off-the-shelf state-of-the-art descriptors.
Graph-Based Minimum Dwell Time and Average Dwell Time Computations for Discrete-Time Switched Linear Systems
Venue: arXiv cs.SY 2017
Year: 2017

Discrete-time switched linear systems where switchings are governed by a digraph are considered. The minimum (or average) dwell time that guarantees the asymptotic stability can be computed by calculating the maximum cycle ratio (or maximum cycle mean) of a doubly weighted digraph where weights depend on the eigenvalues and eigenvectors of subsystem matrices. The graph-based method is applied to systems with defective subsystem matrices using Jordan decomposition. In the case of bimodal switched systems scaling algorithms that minimizes the condition number can be used to give a better minimum (or average) dwell time estimates.
Computability on the space of countable ordinals
Venue: arXiv cs.LO 2017
Year: 2017

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of countable ordinals via a representation in the sense of computable analysis. The computability structure is characterized by the computability of four specific operations, and we prove further relevant operations to be computable. Some alternative approaches are discussed, too. As an application in effective descriptive set theory, we can then state and prove computable uniform versions of the Lusin separation theorem and the Hausdorff-Kuratowski theorem. Furthermore, we introduce an operator on the Weihrauch lattice corresponding to iteration of some principle over a countable ordinal.
Social Participation Ontology: community documentation, enhancements and use examples
Venue: arXiv cs.CY 2017
Year: 2017

Participatory democracy advances in virtually all governments and especially in South America which exhibits a mixed culture and social predisposition. This article presents the "Social Participation Ontology" (OPS from the Brazilian name \emph{Ontologia de Participação Social}) implemented in compliance with the Web Ontology Language standard (OWL) for fostering social participation, specially in virtual platforms. The entities and links of OPS were defined based on an extensive collaboration of specialists. It is shown that OPS is instrumental for information retrieval from the contents of the portal, both in terms of the actors (at various levels) as well as mechanisms and activities. Significantly, OPS is linked to other OWL ontologies as an upper ontology and via FOAF and BFO as higher upper ontologies, which yields sound organization and access of knowledge and data. In order to illustrate the usefulness of OPS, we present results on ontological expansion and integration with other ontologies and data. Ongoing work involves further adoption of OPS by the official Brazilian federal portal for social participation and NGO s, and further linkage to other ontologies for social participation.
Spline Waveforms and Interference Analysis for 5G Random Access with Short Message Support
Venue: arXiv cs.IT 2017
Year: 2017

One of the main drivers for new waveforms in future 5G wireless communication systems is to handle efficiently the variety of traffic types and requirements. In this paper, we introduce a new random access within the standard acquisition procedures to support sporadic traffic as an enabler of the Internet of Things (IoT). The major challenge hereby is to cope with the highly asynchronous access of different devices and to allow transmission of control signaling and payload "in one shot". We address this challenge by using a waveform design approach based on bi-orthogonal frequency division multiplexing where transmit orthogonality is replaced in favor of better temporal and spectral properties. We show that this approach allows data transmission in frequencies that otherwise have to remain unused. More precisely, we utilize frequencies previously used as guard bands, located towards the standard synchronous communication pipes as well as in between the typically small amount of resources used by each IoT device. We demonstrate the superiority of this waveform approach over the conventional random access using a novel mathematical approach and numerical experiments.
On the switch Markov chain for perfect matchings
Venue: arXiv cs.DS 2017
Year: 2017

We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We ask: for which classes of graphs is the Markov chain ergodic and for which is it rapidly mixing? We provide a precise answer to the ergodicity question and close bounds on the mixing question. We show for the first time that the mixing time of the switch chain is polynomial in the case of monotone graphs, a class that includes examples of interest in the statistical setting.
Object Proposal with Kernelized Partial Ranking
Venue: arXiv cs.CV 2017
Year: 2017

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm which however, incurs two major challenges: {\bf 1)} The ranking model often imposes pairwise constraints between each proposal, rendering the problem away from an efficient training/testing phase; {\bf 2)} Linear kernels are utilized due to the computational and memory bottleneck of training a kernelized model. In this paper, we remedy these two issues by suggesting a {\em kernelized partial ranking model}. In particular, we demonstrate that {\bf i)} our partial ranking model reduces the number of constraints from $O(n^2)$ to $O(nk)$ where $n$ is the number of all potential proposals for an image but we are only interested in top-$k$ of them that has the largest overlap with the ground truth; {\bf ii)} we permit non-linear kernels in our model which is often superior to the linear classifier in terms of accuracy. For the sake of mitigating the computational and memory issues, we introduce a consistent weighted sampling~(CWS) paradigm that approximates the non-linear kernel as well as facilitates an efficient learning. In fact, as we will show, training a linear CWS model amounts to learning a kernelized model. Extensive experiments demonstrate that equipped with the non-linear kernel and the partial ranking algorithm, recall at top-$k$ proposals can be substantially improved.
Efficiency and complexity of price competition among single-product vendors
Venue: arXiv cs.GT 2017
Year: 2017

Motivated by recent progress on pricing in the AI literature, we study marketplaces that contain multiple vendors offering identical or similar products and unit-demand buyers with different valuations on these vendors. The objective of each vendor is to set the price of its product to a fixed value so that its profit is maximized. The profit depends on the vendor's price itself and the total volume of buyers that find the particular price more attractive than the price of the vendor's competitors. We model the behaviour of buyers and vendors as a two-stage full-information game and study a series of questions related to the existence, efficiency (price of anarchy) and computational complexity of equilibria in this game. To overcome situations where equilibria do not exist or exist but are highly inefficient, we consider the scenario where some of the vendors are subsidized in order to keep prices low and buyers highly satisfied.
Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search
Venue: arXiv cs.DS 2017
Year: 2017

We present an optimal data structure for submatrix maximum queries in n x n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(loglogn) time. It also gives a matching lower bound, showing that O(loglogn) query-time is optimal for any data structure of size O(n polylog(n)). Our result concludes a line of improvements that started in SODA'12 with O(log^2 n) query-time and continued in ICALP'14 with O(log n) query-time. Finally, we show that partial Monge matrices can be handled in the same bounds as full Monge matrices. In both previous results, partial Monge matrices incurred additional inverse-Ackerman factors.
Envy-Free Pricing in Large Markets: Approximating Revenue and Welfare
Venue: arXiv cs.GT 2017
Year: 2017

We study the classic setting of envy-free pricing, in which a single seller chooses prices for its many items, with the goal of maximizing revenue once the items are allocated. Despite the large body of work addressing such settings, most versions of this problem have resisted good approximation factors for maximizing revenue; this is true even for the classic unit-demand case. In this paper we study envy-free pricing with unit-demand buyers, but unlike previous work we focus on large markets: ones in which the demand of each buyer is infinitesimally small compared to the size of the overall market. We assume that the buyer valuations for the items they desire have a nice (although reasonable) structure, i.e., that the aggregate buyer demand has a monotone hazard rate and that the values of every buyer type come from the same support. For such large markets, our main contribution is a 1.88 approximation algorithm for maximizing revenue, showing that good pricing schemes can be computed when the number of buyers is large. We also give a (e,2)-bicriteria algorithm that simultaneously approximates both maximum revenue and welfare, thus showing that it is possible to obtain both good revenue and welfare at the same time. We further generalize our results by relaxing some of our assumptions, and quantify the necessary tradeoffs between revenue and welfare in our setting. Our results are the first known approximations for large markets, and crucially rely on new lower bounds which we prove for the revenue-maximizing prices.
Efficient Straggler Replication in Large-scale Parallel Computing
Venue: arXiv cs.DC 2017
Year: 2017

In a cloud computing job with many parallel tasks, the tasks on the slowest machines (straggling tasks) become the bottleneck in the job completion. Computing frameworks such as MapReduce and Spark tackle this by replicating the straggling tasks and waiting for any one copy to finish. Despite being adopted in practice, there is little analysis of how replication affects the latency and the cost of additional computing resources. In this paper we provide a framework to analyze this latency-cost trade-off and find the best replication strategy by answering design questions such as: 1) when to replicate straggling tasks, 2) how many replicas to launch, and 3) whether to kill the original copy or not. Our analysis reveals that for certain execution time distributions, a small amount of task replication can drastically reduce both latency as well as the cost of computing resources. We also propose an algorithm to estimate the latency and cost based on the empirical distribution of task execution time. Evaluations using samples in the Google Cluster Trace suggest further latency and cost reduction compared to the existing replication strategy used in MapReduce.
LSTM: A Search Space Odyssey
Venue: arXiv cs.NE 2017
Year: 2017

Several variants of the Long Short-Term Memory (LSTM) architecture for recurrent neural networks have been proposed since its inception in 1995. In recent years, these networks have become the state-of-the-art models for a variety of machine learning problems. This has led to a renewed interest in understanding the role and utility of various computational components of typical LSTM variants. In this paper, we present the first large-scale analysis of eight LSTM variants on three representative tasks: speech recognition, handwriting recognition, and polyphonic music modeling. The hyperparameters of all LSTM variants for each task were optimized separately using random search, and their importance was assessed using the powerful fANOVA framework. In total, we summarize the results of 5400 experimental runs ($\approx 15$ years of CPU time), which makes our study the largest of its kind on LSTM networks. Our results show that none of the variants can improve upon the standard LSTM architecture significantly, and demonstrate the forget gate and the output activation function to be its most critical components. We further observe that the studied hyperparameters are virtually independent and derive guidelines for their efficient adjustment.
Analyzing Adaptive Cache Replacement Strategies
Venue: arXiv cs.DS 2017
Year: 2017

Adaptive Replacement Cache (ARC) and CLOCK with Adaptive Replacement (CAR) are state-of-the- art "adaptive" cache replacement algorithms invented to improve on the shortcomings of classical cache replacement policies such as LRU, LFU and CLOCK. By separating out items that have been accessed only once and items that have been accessed more frequently, both ARC and CAR are able to control the harmful effect of single-access items flooding the cache and pushing out more frequently accessed items. Both ARC and CAR have been shown to outperform their classical and popular counterparts in practice. Both algorithms are complex, yet popular. Even though they can be treated as online algorithms with an "adaptive" twist, a theoretical proof of the competitiveness of ARC and CAR remained unsolved for over a decade. We show that the competitiveness ratio of CAR (and ARC) has a lower bound of N + 1 (where N is the size of the cache) and an upper bound of 18N (4N for ARC). If the size of cache offered to ARC or CAR is larger than the one provided to OPT, then we show improved competitiveness ratios. The important implication of the above results are that no "pathological" worst-case request sequences exist that could deteriorate the performance of ARC and CAR by more than a constant factor as compared to LRU.
Robust Recovery of Positive Stream of Pulses
Venue: arXiv cs.IT 2017
Year: 2017

The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is robust in the presence of noise (or model mismatch). Particularly, the recovery error is proportional to the noise level. We further show that the error grows exponentially with the density of the delays and also depends on the localization properties of the pulse.
Discrete uncertainty principles and sparse signal processing
Venue: arXiv cs.IT 2017
Year: 2017

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.
Localization in mobile networks via virtual convex hulls
Venue: arXiv cs.SY 2017
Year: 2017

In this paper, we develop a \textit{distributed} algorithm to localize an arbitrary number of agents moving in a bounded region of interest. We assume that the network contains \textit{at least one} agent with known location (hereinafter referred to as an anchor), and each agent measures a noisy version of its motion and the distances to the nearby agents. We provide a~\emph{geometric approach}, which allows each agent to: (i) continually update the distances to the locations where it has exchanged information with the other nodes in the past; and (ii) measure the distance between a neighbor and any such locations. Based on this approach, we provide a \emph{linear update} to find the locations of an arbitrary number of mobile agents when they follow some convexity in their deployment and motion. Since the agents are mobile, they may not be able to find nearby nodes (agents and/or anchors) to implement a distributed algorithm. To address this issue, we introduce the notion of a \emph{virtual convex hull} with the help of the aforementioned geometric approach. In particular, each agent keeps track of a virtual convex hull of other nodes, which may not physically exist, and updates its location with respect to its neighbors in the virtual hull. We show that the corresponding localization algorithm, in the absence of noise, can be abstracted as a Linear Time-Varying (LTV) system, with non-deterministic system matrices, which asymptotically tracks the true locations of the agents. We provide simulations to verify the analytical results and evaluate the performance of the algorithm in the presence of noise on the motion as well as on the distance measurements.
The Parametric Closure Problem
Venue: arXiv cs.DS 2017
Year: 2017

We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights vary. We give polynomial time solutions to many important special cases of this problem including semiorders, reachability orders of bounded-treewidth graphs, partial orders of bounded width, and series-parallel partial orders. Our result for series-parallel orders provides a significant generalization of a previous result of Carlson and Eppstein on bicriterion subtree problems.
Multi-GPU Graph Analytics
Venue: arXiv cs.DC 2017
Year: 2017

We present a single-node, multi-GPU programmable graph processing library that allows programmers to easily extend single-GPU graph algorithms to achieve scalable performance on large graphs with billions of edges. Directly using the single-GPU implementations, our design only requires programmers to specify a few algorithm-dependent concerns, hiding most multi-GPU related implementation details. We analyze the theoretical and practical limits to scalability in the context of varying graph primitives and datasets. We describe several optimizations, such as direction optimizing traversal, and a just-enough memory allocation scheme, for better performance and smaller memory consumption. Compared to previous work, we achieve best-of-class performance across operations and datasets, including excellent strong and weak scalability on most primitives as we increase the number of GPUs in the system.
Tensor theta norms and low rank recovery
Venue: arXiv cs.IT 2017
Year: 2017

We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather well-understand by now, almost no theory is available for the extension to higher order tensors due to various theoretical and computational difficulties arising for tensor decompositions. In fact, nuclear norm minimization for matrix recovery is a tractable convex relaxation approach, but the extension of the nuclear norm to tensors is in general NP-hard to compute. In this article, we introduce convex relaxations of the tensor nuclear norm which are computable in polynomial time via semidefinite programming. Our approach is based on theta bodies, a concept from computational algebraic geometry similar to the Lasserre relaxations. We introduce polynomial ideals which are generated by the second order minors corresponding to different matricizations of the tensor (where the tensor entries are treated as variables) such that the nuclear norm ball is the convex hull of the algebraic variety of the ideal. The $k$-th theta body for such an ideal generates a new norm which we call the $θ_k$-norm. We show that in the matrix case, these norms reduce to the nuclear norm. For tensors of order $d \geq 3$ however, we obtain new norms. The sequence of the corresponding unit-$θ_k$-norm balls converges asymptotically to the unit tensor nuclear norm ball. By providing the Gröbner basis for the ideals, we explicitly give semidefinite programs for the computation of the $θ_k$-norm and for the minimization of the $θ_k$-norm under an affine constraint. Numerical experiments for order-3 tensor recovery via $θ_1$-norm minimization suggest that our approach successfully reconstructs tensors of low rank from incomplete linear (random) measurements.
Persistently Exciting Tube MPC
Venue: arXiv cs.SY 2017
Year: 2017

This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part.