OpenRaiser/Intern-Atlas huggingface dataset:
A Faster Pseudopolynomial Time Algorithm for Subset Sum
Venue: arXiv cs.DS 2016
Year: 2016

Given a multiset $S$ of $n$ positive integers and a target integer $t$, the subset sum problem is to decide if there is a subset of $S$ that sums up to $t$. We present a new divide-and-conquer algorithm that computes all the realizable subset sums up to an integer $u$ in $\widetilde{O}\!\left(\min\{\sqrt{n}u,u^{4/3},σ\}\right)$, where $σ$ is the sum of all elements in $S$ and $\widetilde{O}$ hides polylogarithmic factors. This result improves upon the standard dynamic programming algorithm that runs in $O(nu)$ time. To the best of our knowledge, the new algorithm is the fastest general algorithm for this problem. We also present a modified algorithm for cyclic groups, which computes all the realizable subset sums within the group in $\widetilde{O}\!\left(\min\{\sqrt{n}m,m^{5/4}\}\right)$ time, where $m$ is the order of the group.
Finger Search in Grammar-Compressed Strings
Venue: arXiv cs.DS 2016
Year: 2016

Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly represent the grammar while supporting random access, that is, given a position in the original uncompressed string report the character at that position. In this paper we study the random access problem with the finger search property, that is, the time for a random access query should depend on the distance between a specified index $f$, called the \emph{finger}, and the query index $i$. We consider both a static variant, where we first place a finger and subsequently access indices near the finger efficiently, and a dynamic variant where also moving the finger such that the time depends on the distance moved is supported. Let $n$ be the size the grammar, and let $N$ be the size of the string. For the static variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and subsequently accessing in $O(\log D)$ time, where $D$ is the distance between the finger and the accessed index. For the dynamic variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and accessing and moving the finger in $O(\log D + \log \log N)$ time. Compared to the best linear space solution to random access, we improve a $O(\log N)$ query bound to $O(\log D)$ for the static variant and to $O(\log D + \log \log N)$ for the dynamic variant, while maintaining linear space. As an application of our results we obtain an improved solution to the longest common extension problem in grammar compressed strings. To obtain our results, we introduce several new techniques of independent interest, including a novel van Emde Boas style decomposition of grammars.
CoveringLSH: Locality-sensitive Hashing without False Negatives
Venue: arXiv cs.DS 2016
Year: 2016

We consider a new construction of locality-sensitive hash functions for Hamming space that is \emph{covering} in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius $r$. The construction is \emph{efficient} in the sense that the expected number of hash collisions between vectors at distance~$cr$, for a given $c>1$, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (STOC '98). The efficiency of the new construction essentially \emph{matches} their bound when the search radius is not too large --- e.g., when $cr = o(\log(n)/\log\log n)$, where $n$ is the number of points in the data set, and when $cr = \log(n)/k$ where $k$ is an integer constant. In general, it differs by at most a factor $\ln(4)$ in the exponent of the time bounds. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency.
Scientific Computing Meets Big Data Technology: An Astronomy Use Case
Venue: arXiv cs.DC 2016
Year: 2016

Scientific analyses commonly compose multiple single-process programs into a dataflow. An end-to-end dataflow of single-process programs is known as a many-task application. Typically, tools from the HPC software stack are used to parallelize these analyses. In this work, we investigate an alternate approach that uses Apache Spark -- a modern big data platform -- to parallelize many-task applications. We present Kira, a flexible and distributed astronomy image processing toolkit using Apache Spark. We then use the Kira toolkit to implement a Source Extractor application for astronomy images, called Kira SE. With Kira SE as the use case, we study the programming flexibility, dataflow richness, scheduling capacity and performance of Apache Spark running on the EC2 cloud. By exploiting data locality, Kira SE achieves a 2.5x speedup over an equivalent C program when analyzing a 1TB dataset using 512 cores on the Amazon EC2 cloud. Furthermore, we show that by leveraging software originally designed for big data infrastructure, Kira SE achieves competitive performance to the C implementation running on the NERSC Edison supercomputer. Our experience with Kira indicates that emerging Big Data platforms such as Apache Spark are a performant alternative for many-task scientific applications.
Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes
Venue: arXiv cs.IT 2016
Year: 2016

In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the low-complexity, highly parallel, and flexible systematic-encoding algorithm that we use and prove its correctness. Our hardware implementation results show that the overhead of adding code rate and length flexibility is little, and the impact on operation latency minor compared to code-specific versions. Finally, the flexible software encoder and decoder implementations are also shown to be able to maintain high throughput and low latency.
A New Framework for Distributed Submodular Maximization
Venue: arXiv cs.DS 2016
Year: 2016

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algorithms for these problems. However, these results suffer from high number of rounds, suboptimal approximation ratios, or both. We develop a framework for bringing existing algorithms in the sequential setting to the distributed setting, achieving near optimal approximation ratios for many settings in only a constant number of MapReduce rounds. Our techniques also give a fast sequential algorithm for non-monotone maximization subject to a matroid constraint.
Minimum Energy to Send $k$ Bits Over Multiple-Antenna Fading Channels
Venue: arXiv cs.IT 2016
Year: 2016

This paper investigates the minimum energy required to transmit $k$ information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to $-1.59$ dB as $k$ goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that lack of CSI at the receiver causes a slowdown in the speed of convergence to $-1.59$ dB as $k\to\infty$ compared to the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to $-1.59$ dB is proportional to $((\log k) /k)^{1/3}$, whereas when perfect CSI is available at the receiver, this gap is proportional to $1/\sqrt{k}$. In both cases, the gap to $-1.59$ dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of $ - 1.5$ dB in the no-CSI case, one needs to transmit at least $7\times 10^7$ information bits, whereas $6\times 10^4$ bits suffice for the case of perfect CSI at the receiver.
Untangling AdaBoost-based Cost-Sensitive Classification. Part II: Empirical Analysis
Venue: arXiv cs.CV 2016
Year: 2016

A lot of approaches, each following a different strategy, have been proposed in the literature to provide AdaBoost with cost-sensitive properties. In the first part of this series of two papers, we have presented these algorithms in a homogeneous notational framework, proposed a clustering scheme for them and performed a thorough theoretical analysis of those approaches with a fully theoretical foundation. The present paper, in order to complete our analysis, is focused on the empirical study of all the algorithms previously presented over a wide range of heterogeneous classification problems. The results of our experiments, confirming the theoretical conclusions, seem to reveal that the simplest approach, just based on cost-sensitive weight initialization, is the one showing the best and soundest results, despite having been recurrently overlooked in the literature.
Assignment Problems of Different-Sized Inputs in MapReduce
Venue: arXiv cs.DB 2016
Year: 2016

A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this output. Reducers have a capacity, which limits the sets of inputs that they can be assigned. However, individual inputs may vary in terms of size. We consider, for the first time, mapping schemas where input sizes are part of the considerations and restrictions. One of the significant parameters to optimize in any MapReduce job is communication cost between the map and reduce phases. The communication cost can be optimized by minimizing the number of copies of inputs sent to the reducers. The communication cost is closely related to the number of reducers of constrained capacity that are used to accommodate appropriately the inputs, so that the requirement of how the inputs must meet in a reducer is satisfied. In this work, we consider a family of problems where it is required that each input meets with each other input in at least one reducer. We also consider a slightly different family of problems in which, each input of a list, X, is required to meet each input of another list, Y, in at least one reducer. We prove that finding an optimal mapping schema for these families of problems is NP-hard, and present a bin-packing-based approximation algorithm for finding a near optimal mapping schema.
On the GI-Completeness of a Sorting Networks Isomorphism
Venue: arXiv cs.CC 2016
Year: 2016

The subitemset isomorphism problem is really important and there are excellent practical solutions described in the literature. However, the computational complexity analysis and classification of the BZ (Bundala and Zavodny) subitemset isomorphism problem is currently an open problem. In this paper we prove that checking whether two sorting networks are BZ isomorphic to each other is GI-Complete; the general GI (Graph Isomorphism) problem is known to be in NP and LWPP, but widely believed to be neither P nor NP-Complete; recent research suggests that the problem is in QP. Moreover, we state the BZ sorting network isomorphism problem as a general isomorphism problem on itemsets --- because every sorting network is represented by Bundala and Zavodny as an itemset. The complexity classification presented in this paper applies sorting networks, as well as the general itemset isomorphism problem. The main consequence of our work is that currently no polynomial-time algorithm exists for solving the BZ sorting network subitemset isomorphism problem; however the CM (Choi and Moon) sorting network isomorphism problem can be efficiently solved in polynomial time.
A National Effort for Motivating Indian Students and Teachers towards Algorithmic Research
Venue: arXiv cs.CY 2016
Year: 2016

During 2008-2015, twenty-two introductory workshops on graph and geometric algorithms were organized for teachers and students (undergraduate, post-graduate and doctoral) of engineering colleges and universities at different states and union territories of India. The lectures were meant to provide exposure to the field of graph and geometric algorithms and to motivate the participants towards research. Fifty-eight professors from TIFR, IITs, IISc, IMSc, CMI, ISI Kolkata, and other institutes and universities delivered invited lectures on different topics in the design and analysis of algorithms, discrete applied mathematics, computer graphics, computer vision, and robotics. The first four workshops were funded by TIFR, BRNS and IIT Kharagpur, and the remaining workshops were funded by the NBHM. In this paper, we present the salient features of these workshops, and state our observations on the national impact of these workshops.
Discriminative Segmental Cascades for Feature-Rich Phone Recognition
Venue: arXiv cs.CL 2016
Year: 2016

Discriminative segmental models, such as segmental conditional random fields (SCRFs) and segmental structured support vector machines (SSVMs), have had success in speech recognition via both lattice rescoring and first-pass decoding. However, such models suffer from slow decoding, hampering the use of computationally expensive features, such as segment neural networks or other high-order features. A typical solution is to use approximate decoding, either by beam pruning in a single pass or by beam pruning to generate a lattice followed by a second pass. In this work, we study discriminative segmental models trained with a hinge loss (i.e., segmental structured SVMs). We show that beam search is not suitable for learning rescoring models in this approach, though it gives good approximate decoding performance when the model is already well-trained. Instead, we consider an approach inspired by structured prediction cascades, which use max-marginal pruning to generate lattices. We obtain a high-accuracy phonetic recognition system with several expensive feature types: a segment neural network, a second-order language model, and second-order phone boundary features.
Green Cognitive Relaying: Opportunistically Switching Between Data Transmission and Energy Harvesting
Venue: arXiv cs.IT 2016
Year: 2016

Energy efficiency has become an encouragement, and more than this, a requisite for the design of next-generation wireless communications standards. In current work, a dual-hop cognitive (secondary) relaying system is considered, incorporating multiple amplify-and-forward relays, a rather cost-effective solution. First, the secondary relays sense the wireless channel, scanning for a primary network activity, and then convey their reports to a secondary base station (SBS). Afterwards, the SBS, based on these reports and its own estimation, decides cooperatively the presence of primary transmission or not. In the former scenario, all the secondary nodes start to harvest energy from the transmission of primary node(s). In the latter scenario, the system initiates secondary communication via a best relay selection policy. Performance evaluation of this system is thoroughly investigated, by assuming realistic channel conditions, i.e., non-identical link-distances, Rayleigh fading, and outdated channel estimation. The detection and outage probabilities as well as the average harvested energy are derived as new closed-form expressions. In addition, an energy efficiency optimization problem is analytically formulated and solved, while a necessary condition in terms of power consumption minimization for each secondary node is presented. From a green communications standpoint, it turns out that energy harvesting greatly enhances the resources of secondary nodes, especially when primary activity is densely present.
Fourier descriptors based on the structure of the human primary visual cortex with applications to object recognition
Venue: arXiv cs.CV 2016
Year: 2016

In this paper we propose a supervised object recognition method using new global features and inspired by the model of the human primary visual cortex V1 as the semidiscrete roto-translation group $SE(2,N) = \mathbb Z_N\rtimes \mathbb R^2$. The proposed technique is based on generalized Fourier descriptors on the latter group, which are invariant to natural geometric transformations (rotations, translations). These descriptors are then used to feed an SVM classifier. We have tested our method against the COIL-100 image database and the ORL face database, and compared it with other techniques based on traditional descriptors, global and local. The obtained results have shown that our approach looks extremely efficient and stable to noise, in presence of which it outperforms the other techniques analyzed in the paper.
On the Stretch Factor of Convex Polyhedra whose Vertices are (Almost) on a Sphere
Venue: arXiv cs.CG 2016
Year: 2016

Let $P$ be a convex polyhedron in $\mathbb{R}^3$. The skeleton of $P$ is the graph whose vertices and edges are the vertices and edges of $P$, respectively. We prove that, if these vertices are on the unit-sphere, the skeleton is a $(0.999 \cdot π)$-spanner. If the vertices are very close to this sphere, then the skeleton is not necessarily a spanner. For the case when the boundary of $P$ is between two concentric spheres of radii $1$ and $R>1$, and the angles in all faces are at least $θ$, we prove that the skeleton is a $t$-spanner, where $t$ depends only on $R$ and $θ$. One of the ingredients in the proof is a tight upper bound on the geometric dilation of a convex cycle that is contained in an annulus.
Event-Driven Network Programming
Venue: arXiv cs.PL 2016
Year: 2016

Software-defined networking (SDN) programs must simultaneously describe static forwarding behavior and dynamic updates in response to events. Event-driven updates are critical to get right, but difficult to implement correctly due to the high degree of concurrency in networks. Existing SDN platforms offer weak guarantees that can break application invariants, leading to problems such as dropped packets, degraded performance, security violations, etc. This paper introduces EVENT-DRIVEN CONSISTENT UPDATES that are guaranteed to preserve well-defined behaviors when transitioning between configurations in response to events. We propose NETWORK EVENT STRUCTURES (NESs) to model constraints on updates, such as which events can be enabled simultaneously and causal dependencies between events. We define an extension of the NetKAT language with mutable state, give semantics to stateful programs using NESs, and discuss provably-correct strategies for implementing NESs in SDNs. Finally, we evaluate our approach empirically, demonstrating that it gives well-defined consistency guarantees while avoiding expensive synchronization and packet buffering.
Strategyproof Quota Mechanisms for Multiple Assignment Problems
Venue: arXiv cs.GT 2016
Year: 2016

We study the problem of allocating multiple objects to agents without transferable utilities, where each agent may receive more than one object according to a quota. Under lexicographic preferences, we characterize the set of strategyproof, non-bossy, and neutral quota mechanisms and show that under a mild Pareto efficiency condition, serial dictatorship quota mechanisms are the only mechanisms satisfying these properties. Dropping the neutrality requirement, this class of quota mechanisms further expands to sequential dictatorship quota mechanisms. We then extend quota mechanisms to randomized settings, and show that the random serial dictatorship quota mechanisms (RSDQ) are envyfree, strategyproof, and ex post efficient for any number of agents and objects and any quota system, proving that the well-studied Random Serial Dictatorship (RSD) satisfies envyfreeness when preferences are lexicographic.
Fundamental Bounds on Radio Localization Precision in the Far Field
Venue: arXiv cs.IT 2016
Year: 2016

This paper experimentally and theoretically investigates the fundamental bounds on radio localization precision of far-field Received Signal Strength (RSS) measurements. RSS measurements are proportional to power-flow measurements time-averaged over periods long compared to the coherence time of the radiation. Our experiments are performed in a novel localization setup using 2.4GHz quasi-monochromatic radiation, which corresponds to a mean wavelength of 12.5cm. We experimentally and theoretically show that RSS measurements are cross-correlated over a minimum distance that approaches the diffraction limit, which equals half the mean wavelength of the radiation. Our experiments show that measuring RSS beyond a sampling density of one sample per half the mean wavelength does not increase localization precision, as the Root-Mean-Squared-Error (RMSE) converges asymptotically to roughly half the mean wavelength. This adds to the evidence that the diffraction limit determines (1) the lower bound on localization precision and (2) the sampling density that provides optimal localization precision. We experimentally validate the theoretical relations between Fisher information, Cramér-Rao Lower Bound (CRLB) and uncertainty, where uncertainty is lower bounded by diffraction as derived from coherence and speckle theory. When we reconcile Fisher Information with diffraction, the CRLB matches the experimental results with an accuracy of 97-98%.
An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings
Venue: arXiv cs.CG 2016
Year: 2016

Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order type of $P$, which describes the orientation (clockwise or counterclockwise) of every ordered triple in $P$. Given only the order type, the radial system is uniquely determined and can easily be obtained. The converse, however, is not true. Indeed, let $R$ be the radial system of $P$, and let $T(R)$ be the set of all order types with radial system $R$ (we define $T(R) = \emptyset$ for the case that $R$ is not a valid radial system). Aichholzer et al. (Reconstructing Point Set Order Types from Radial Orderings, in ISAAC 2014) show that $T(R)$ may contain up to $n-1$ order types. They also provide polynomial-time algorithms to compute $T(R)$ when only $R$ is given. We describe a new algorithm for finding $T(R)$. The algorithm constructs the convex hulls of all possible point sets with the radial system $R$. After that, orientation queries on point triples can be answered in constant time. A representation of this set of convex hulls can be found in $O(n)$ queries to the radial system, using $O(n)$ additional processing time. This is optimal. Our results also generalize to abstract order types.
Dependability Analysis of Control Systems using SystemC and Statistical Model Checking
Venue: arXiv cs.SE 2016
Year: 2016

Stochastic Petri nets are commonly used for modeling distributed systems in order to study their performance and dependability. This paper proposes a realization of stochastic Petri nets in SystemC for modeling large embedded control systems. Then statistical model checking is used to analyze the dependability of the constructed model. Our verification framework allows users to express a wide range of useful properties to be verified which is illustrated through a case study.
New Criteria for MRD and Gabidulin Codes and some Rank-Metric Code Constructions
Venue: arXiv cs.IT 2016
Year: 2016

In this work we present a new criterion to check if a given rank-metric code is a maximum rank distance (MRD) code. Moreover, we derive a criterion to check if a given MRD code is a generalized Gabidulin code. We then use these results to come up with constructions of linear MRD codes of dimension 2 that are not generalized Gabidulin codes.