OpenRaiser/Intern-Atlas huggingface dataset:
Stable and Informative Spectral Signatures for Graph Matching
Venue: arXiv cs.CV 2018
Year: 2018

In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our approach relies on a rigorous analysis of stability of spectral signatures based on the graph Laplacian. In the case of the first order term, we derive an objective function that measures both the stability and informativeness of a given spectral signature. By optimizing this objective, we design new spectral node signatures tuned to a specific graph to be matched. We also introduce the pairwise heat kernel distance as a stable second order compatibility term; we justify its plausibility by showing that in a certain limiting case it converges to the classical adjacency matrix-based second order compatibility function. We have tested our approach on a set of synthetic graphs, the widely-used CMU house sequence, and a set of real images. These experiments show the superior performance of our first and second order compatibility terms as compared with the commonly used ones.
Capacity Scaling in MIMO Systems with General Unitarily Invariant Random Matrices
Venue: arXiv cs.IT 2018
Year: 2018

We investigate the capacity scaling of MIMO systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising $R$ receive and $T$ transmit antennas with $R>T$, we find the following: By removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on $R$, $T$ and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by $\sum_{t=1}^{T}\sum_{r=T+1}^{R}\frac{1}{r-t}$ nats. Under the same assumption, if $T,R\to \infty$ with the ratio $ϕ\triangleq T/R$ fixed, the rate loss normalized by $R$ converges almost surely to $H(ϕ)$ bits with $H(\cdot)$ denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.
Compressive Multiplexing of Correlated Signals
Venue: arXiv cs.IT 2018
Year: 2018

We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the $M$ signals, each bandlimited to $W/2$ Hz, can be approximated by a superposition of $R < M$ underlying signals, then the ensemble can be recovered by sampling at a rate within a logarithmic factor of $RW$ (as compared to the Nyquist rate of $MW$). This sampling theorem shows that the correlation structure of the signal ensemble can be exploited in the acquisition process even though it is unknown a priori. The reconstruction of the ensemble is recast as a low-rank matrix recovery problem from linear measurements. The architectures we are considering impose a certain type of structure on the linear operators. Although our results depend on the mixing forms being random, this imposed structure results in a very different type of random projection than those analyzed in the low-rank recovery literature to date.
Instruction sequences expressing multiplication algorithms
Venue: arXiv cs.PL 2018
Year: 2018

For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. We describe instruction sequences of this kind that compute the function on bit strings that models multiplication on natural numbers less than $2^N$ with respect to their binary representation by bit strings of length $N$, for a fixed but arbitrary $N > 0$, according to the long multiplication algorithm and the Karatsuba multiplication algorithm. We find among other things that the instruction sequence expressing the former algorithm is longer than the one expressing the latter algorithm only if the length of the bit strings involved is greater than $2^8$. We also go into the use of an instruction sequence with backward jump instructions for expressing the long multiplication algorithm. This leads to an instruction sequence that it is shorter than the other two if the length of the bit strings involved is greater than $2$.
On two Algorithmic Problems about Synchronizing Automata
Venue: arXiv cs.FL 2018
Year: 2018

Under the assumption $\mathcal{P} \neq \mathcal{NP}$, we prove that two natural problems from the theory of synchronizing automata cannot be solved in polynomial time. The first problem is to decide whether a given reachable partial automaton is synchronizing. The second one is, given an $n$-state binary complete synchronizing automaton, to compute its reset threshold within performance ratio less than $d \ln{(n)}$ for a specific constant $d>0$.
P is not equal to NP by Modus Tollens
Venue: arXiv cs.CC 2018
Year: 2018

An artificially designed Turing Machine algorithm $\mathbf{M}_{}^{o}$ generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption $\mathcal{P}=\mathcal{NP}$, we show that $\mathbf{M}_{}^{o}$ has a certain property, which, without the assumption, $\mathbf{M}_{}^{o}$ does not have. This leads to $\mathcal{P}\neq\mathcal{NP}$ $ $ by modus tollens.
Sublinear algorithms for local graph centrality estimation
Venue: arXiv cs.DS 2018
Year: 2018

We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, that we apply to the PageRank and Heat Kernel centralities, for building a low-variance score estimator through a local exploration of the graph. We obtain an algorithm that, given any node in any graph of $m$ arcs, with probability $(1-δ)$ computes a multiplicative $(1\pmε)$-approximation of its score by examining only $\tilde{O}(\min(m^{2/3} Δ^{1/3} d^{-2/3},\, m^{4/5} d^{-3/5}))$ nodes/arcs, where $Δ$ and $d$ are respectively the maximum and average outdegree of the graph (omitting for readability $\operatorname{poly}(ε^{-1})$ and $\operatorname{polylog}(δ^{-1})$ factors). A similar bound holds for computational complexity. We also prove a lower bound of $Ω(\min(m^{1/2} Δ^{1/2} d^{-1/2}, \, m^{2/3} d^{-1/3}))$ for both query complexity and computational complexity. Moreover, our technique yields a $\tilde{O}(n^{2/3})$ query complexity algorithm for the graph access model of [Brautbar et al., 2010], widely used in social network mining; we show this algorithm is optimal up to a sublogarithmic factor. These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node.
Tight Bounds for Restricted Grid Scheduling
Venue: arXiv cs.DS 2018
Year: 2018

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize the total size of all the bins used. Previously, a lower bound of 5/4 on the competitive ratio of this problem was achieved using jobs of size S and 2S-1. For these item sizes and maximum bin size 4S-3, we obtain asymptotically matching upper and lower bounds, which vary depending on the ratio of the number of small jobs to the number of large jobs.
A Datalog-based Computational Model for Coordination-free, Data-Parallel Systems
Venue: arXiv cs.DB 2018
Year: 2018

Cloud computing refers to maximizing efficiency by sharing computational and storage resources, while data-parallel systems exploit the resources available in the cloud to perform parallel transformations over large amounts of data. In the same line, considerable emphasis has been recently given to two apparently disjoint research topics: data-parallel, and eventually consistent, distributed systems. Declarative networking has been recently proposed to ease the task of programming in the cloud, by allowing the programmer to express only the desired result and leave the implementation details to the responsibility of the run-time system. In this context, we propose a study on a logic-programming-based computational model for eventually consistent, data-parallel systems, the keystone of which is provided by the recent finding that the class of programs that can be computed in an eventually consistent, coordination-free way is that of monotonic programs. This principle is called CALM and has been proven by Ameloot et al. for distributed, asynchronous settings. We advocate that CALM should be employed as a basic theoretical tool also for data-parallel systems, wherein computation usually proceeds synchronously in rounds and where communication is assumed to be reliable. It is general opinion that coordination-freedom can be seen as a major discriminant factor. In this work we make the case that the current form of CALM does not hold in general for data-parallel systems, and show how, using novel techniques, the satisfiability of the CALM principle can still be obtained although just for the subclass of programs called connected monotonic queries. We complete the study with considerations on the relationships between our model and the one employed by Ameloot et al., showing that our techniques subsume the latter when the synchronization constraints imposed on the system are loosened.
Structural Sparsity of Complex Networks: Bounded Expansion in Random Models and Real-World Graphs
Venue: arXiv cs.SI 2018
Year: 2018

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several common network models regarding their structural sparsity. We show that, with high probability, (1) graphs sampled with a prescribed s parse degree sequence; (2) perturbed bounded-degree graphs; (3) stochastic block models with small probabilities; result in graphs of bounded expansion. In contrast, we show that the Kleinberg and the Barabasi-Albert model have unbounded expansion. We support our findings with empirical measurements on a corpus of real-world networks.
Acyclic Edge Coloring through the Lovász Local Lemma
Venue: arXiv cs.DM 2018
Year: 2018

We give a probabilistic analysis of a Moser-type algorithm for the Lovász Local Lemma (LLL), adjusted to search for acyclic edge colorings of a graph. We thus improve the best known upper bound to acyclic chromatic index, also obtained by analyzing a similar algorithm, but through the entropic method (basically counting argument). Specifically we show that a graph with maximum degree $Δ$ has an acyclic proper edge coloring with at most $\lceil 3.74(Δ-1)\rceil+1 $ colors, whereas, previously, the best bound was $4(Δ-1)$. The main contribution of this work is that it comprises a probabilistic analysis of a Moser-type algorithm applied to events pertaining to dependent variables.
Polynomial size linear programs for problems in P
Venue: arXiv cs.DM 2018
Year: 2018

A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvoß proved the striking result that the Edmonds' matching polytope has exponential extension complexity. Here for each $n=|V|$ we describe a perfect matching polytope that is different from Edmonds' polytope and define a weaker notion of extended formulation. We show that the new polytope has a weak extended formulation (WEF) $Q$ of polynomial size. For each graph $G$ with $n$ vertices we can readily construct an objective function so that solving the resulting linear program over $Q$ decides whether or not $G$ has a perfect matching. The construction is uniform in the sense that, for each $n$, a single polytope is defined for the class of all graphs with $n$ nodes. The method extends to solve poly time optimization problems, such as the weighted matching problem. In this case a logarithmic (in the weight of the optimum solution) number of optimizations are made over the constructed WEF. The method described in the paper involves construction of a compiler that converts an algorithm given in a prescribed pseudocode into a polytope. It can therefore be used to construct a polytope for any decision problem in {\bf P} which can be solved by a given algorithm. Compared with earlier results of Dobkin-Lipton-Reiss and Valiant our method allows the construction of explicit linear programs directly from algorithms written for a standard register model, without intermediate transformations. We apply our results to obtain polynomial upper bounds on the non-negative rank of certain slack matrices related to membership testing of languages in {\bf P/Poly}.
Spoke-Darts for High-Dimensional Blue-Noise Sampling
Venue: arXiv cs.GR 2018
Year: 2018

Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution and the adaptability of the intermediate processes of our method are useful in these applications.
Near-Constant-Time Distributed Algorithms on a Congested Clique
Venue: arXiv cs.DC 2018
Year: 2018

This paper presents constant-time and near-constant-time distributed algorithms for a variety of problems in the congested clique model. We show how to compute a 3-ruling set in expected $O(\log \log \log n)$ rounds and using this, we obtain a constant-approximation to metric facility location, also in expected $O(\log \log \log n)$ rounds. In addition, assuming an input metric space of constant doubling dimension, we obtain constant-round algorithms to compute constant-factor approximations to the minimum spanning tree and the metric facility location problems. These results significantly improve on the running time of the fastest known algorithms for these problems in the congested clique setting.
Scalable Wake-up of Multi-Channel Single-Hop Radio Networks
Venue: arXiv cs.DS 2018
Year: 2018

We consider single-hop radio networks with multiple channels as a model of wireless networks. There are $n$ stations connected to $b$ radio channels that do not provide collision detection. A station uses all the channels concurrently and independently. Some $k$ stations may become active spontaneously at arbitrary times. The goal is to wake up the network, which occurs when all the stations hear a successful transmission on some channel. Duration of a waking-up execution is measured starting from the first spontaneous activation. We present a deterministic algorithm for the general problem that wakes up the network in $O(k\log^{1/b} k\log n)$ time, where $k$ is unknown. We give a deterministic scalable algorithm for the special case when $b>d \log \log n$, for some constant $d>1$, which wakes up the network in $O(\frac{k}{b}\log n\log(b\log n))$ time, with $k$ unknown. This algorithm misses time optimality by at most a factor of $O(\log n(\log b +\log\log n))$, because any deterministic algorithm requires $Ω(\frac{k}{b}\log \frac{n}{k})$ time. We give a randomized algorithm that wakes up the network within $O(k^{1/b}\ln \frac{1}ε)$ rounds with a probability that is at least $1-ε$, for any $0<ε<1$, where $k$ is known. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability $p$, independently across all channels and rounds. For this model, we give two deterministic algorithms for unknown~$k$: one wakes up the network in time $O(\log^{-1}(\frac{1}{p})\, k\log n\log^{1/b} k)$, and the other in time $O(\log^{-1}(\frac{1}{p}) \, \frac{k}{b} \log n\log(b\log n))$ but assuming the inequality $b>\log(128b\log n)$, both with a probability that is at least $1-1/\mbox{poly}(n)$.
Integer-Programming Ensemble of Temporal-Relations Classifiers
Venue: arXiv cs.CL 2018
Year: 2018

The extraction and understanding of temporal events and their relations are major challenges in natural language processing. Processing text on a sentence-by-sentence or expression-by-expression basis often fails, in part due to the challenge of capturing the global consistency of the text. We present an ensemble method, which reconciles the outputs of multiple classifiers of temporal expressions across the text using integer programming. Computational experiments show that the ensemble improves upon the best individual results from two recent challenges, SemEval-2013 TempEval-3 (Temporal Annotation) and SemEval-2016 Task 12 (Clinical TempEval).
A Constructive Proof on the Compositionality of Linearizability
Venue: arXiv cs.DC 2018
Year: 2018

Linearizability is the strongest correctness property for both shared memory and message passing systems. One of its useful features is the compositionality: a history (execution) is linearizable if and only if each object (component) subhistory is linearizable. In this paper, we propose a new hierarchical system model to address challenges in modular development of cloud systems. Object are defined by induction from the most fundamental atomic Boolean registers, and histories are represented as countable well-ordered structures of events to deal with both finite and infinite executions. Then, we present a new constructive proof on the compositionality theorem of linearizability inspired by Multiway Merge. This proof deduces a theoretically efficient algorithm which generates linearization in O(N*logP) running time with O(N) space, where P and N are process/event numbers respectively.
Salient Object Detection: A Benchmark
Venue: arXiv cs.CV 2018
Year: 2018

We extensively compare, qualitatively and quantitatively, 40 state-of-the-art models (28 salient object detection, 10 fixation prediction, 1 objectness, and 1 baseline) over 6 challenging datasets for the purpose of benchmarking salient object detection and segmentation methods. From the results obtained so far, our evaluation shows a consistent rapid progress over the last few years in terms of both accuracy and running time. The top contenders in this benchmark significantly outperform the models identified as the best in the previous benchmark conducted just two years ago. We find that the models designed specifically for salient object detection generally work better than models in closely related areas, which in turn provides a precise definition and suggests an appropriate treatment of this problem that distinguishes it from other problems. In particular, we analyze the influences of center bias and scene complexity in model performance, which, along with the hard cases for state-of-the-art models, provide useful hints towards constructing more challenging large scale datasets and better saliency models. Finally, we propose probable solutions for tackling several open problems such as evaluation scores and dataset bias, which also suggest future research directions in the rapidly-growing field of salient object detection.
On the Lexical Distinguishability of Source Code
Venue: arXiv cs.SE 2018
Year: 2018

Natural language is robust against noise. The meaning of many sentences survives the loss of words, sometimes many of them. Some words in a sentence, however, cannot be lost without changing the meaning of the sentence. We call these words "wheat" and the rest "chaff". The word "not" in the sentence "I do not like rain" is wheat and "do" is chaff. For human understanding of the purpose and behavior of source code, we hypothesize that the same holds. To quantify the extent to which we can separate code into "wheat" and "chaff", we study a large (100M LOC), diverse corpus of real-world projects in Java. Since methods represent natural, likely distinct units of code, we use the ~9M Java methods in the corpus to approximate a universe of "sentences." We extract their wheat by computing the function's minimal distinguishing subset (Minset). Our results confirm that functions contain work offers the first quantitative evidence for recent promising work on keyword-based programming and insight into how to develop a powerful, alternative programming model.
Dynamic DFS Tree in Undirected Graphs: breaking the $O(m)$ barrier
Venue: arXiv cs.DS 2018
Year: 2018

Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We address the problem of maintaining a DFS tree when the graph is undergoing {\em updates} (insertion and deletion of vertices or edges). We present the following results for this problem. (a) Fault tolerant DFS tree: There exists a data structure of size ${O}(m ~polylog~ n)$ such that given any set ${\cal F}$ of failed vertices or edges, a DFS tree of the graph $G\setminus {\cal F}$ can be reported in ${O}(n|{\cal F}| ~polylog~ n)$ time. (b) Fully dynamic DFS tree: There exists a fully dynamic algorithm for maintaining a DFS tree that takes worst case ${O}(\sqrt{mn} ~polylog~ n)$ time per update for any arbitrary online sequence of updates. (c) Incremental DFS tree: Given any arbitrary online sequence of edge insertions, we can maintain a DFS tree in ${O}(n ~polylog~ n)$ worst case time per edge insertion. These are the first $o(m)$ worst case time results for maintaining a DFS tree in a dynamic environment. Moreover, our fully dynamic algorithm provides, in a seamless manner, the first deterministic algorithm with $O(1)$ query time and $o(m)$ worst case update time for the dynamic subgraph connectivity, biconnectivity, and 2-edge connectivity.