OpenRaiser/Intern-Atlas huggingface dataset:
On Efficient Domination for Some Classes of $H$-Free Chordal Graphs
Venue: arXiv cs.DM 2019
Year: 2019

A vertex set $D$ in a finite undirected graph $G$ is an efficient dominating set (e.d.s. for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The Efficient Domination (ED) problem, which asks for the existence of an e.d.s.\ in $G$, is known to be \NP-complete even for very restricted graph classes such as for $2P_3$-free chordal graphs while it is solvable in polynomial time for $P_6$-free chordal graphs (and even for $P_6$-free graphs). A standard reduction from the \NP-complete Exact Cover problem shows that ED is \NP-complete for a very special subclass of chordal graphs generalizing split graphs. The reduction implies that ED is \NP-complete e.g.\ for double-gem-free chordal graphs while it is solvable in linear time for gem-free chordal graphs (by various reasons such as bounded clique-width, distance-hereditary graphs, chordal square etc.), and ED is \NP-complete for butterfly-free chordal graphs while it is solvable in linear time for $2P_2$-free graphs. We show that (weighted) ED can be solved in polynomial time for $H$-free chordal graphs when $H$ is net, extended gem, or $S_{1,2,3}$.
An $ω$-Algebra for Real-Time Energy Problems
Venue: arXiv cs.LO 2019
Year: 2019

We develop a $^*$-continuous Kleene $ω$-algebra of real-time energy functions. Together with corresponding automata, these can be used to model systems which can consume and regain energy (or other types of resources) depending on available time. Using recent results on $^*$-continuous Kleene $ω$-algebras and computability of certain manipulations on real-time energy functions, it follows that reachability and Büchi acceptance in real-time energy automata can be decided in a static way which only involves manipulations of real-time energy functions.
On the Role of a Market Maker in Networked Cournot Competition
Venue: arXiv cs.GT 2019
Year: 2019

We study Cournot competition among firms in a networked marketplace that is centrally managed by a market maker. In particular, we study a situation in which a market maker facilitates trade between geographically separate markets via a constrained transport network. Our focus is on understanding the consequences of the design of the market maker and on providing tools for optimal design. To that end we provide a characterization of the equilibrium outcomes of the game between the firms and the market maker. Our results highlight that the equilibrium structure is impacted dramatically by the market maker's objective - depending on the objective there may be a unique equilibrium, multiple equilibria, or no equilibria. Further, the game may be a potential game (as in the case of classical Cournot competition) or not. Beyond characterizing the equilibria of the game, we provide an approach for designing the market maker in order to optimize a design objective (e.g., social welfare) at the equilibrium of the game. Additionally, we use our results to explore the value of transport (trade) and the efficiency of the market maker (as compared to a single, aggregate market).
Pixel-wise Ear Detection with Convolutional Encoder-Decoder Networks
Venue: arXiv cs.CV 2019
Year: 2019

Object detection and segmentation represents the basis for many tasks in computer and machine vision. In biometric recognition systems the detection of the region-of-interest (ROI) is one of the most crucial steps in the overall processing pipeline, significantly impacting the performance of the entire recognition system. Existing approaches to ear detection, for example, are commonly susceptible to the presence of severe occlusions, ear accessories or variable illumination conditions and often deteriorate in their performance if applied on ear images captured in unconstrained settings. To address these shortcomings, we present in this paper a novel ear detection technique based on convolutional encoder-decoder networks (CEDs). For our technique, we formulate the problem of ear detection as a two-class segmentation problem and train a convolutional encoder-decoder network based on the SegNet architecture to distinguish between image-pixels belonging to either the ear or the non-ear class. The output of the network is then post-processed to further refine the segmentation result and return the final locations of the ears in the input image. Different from competing techniques from the literature, our approach does not simply return a bounding box around the detected ear, but provides detailed, pixel-wise information about the location of the ears in the image. Our experiments on a dataset gathered from the web (a.k.a. in the wild) show that the proposed technique ensures good detection results in the presence of various covariate factors and significantly outperforms the existing state-of-the-art.
A Novel Weight-Shared Multi-Stage CNN for Scale Robustness
Venue: arXiv cs.CV 2019
Year: 2019

Convolutional neural networks (CNNs) have demonstrated remarkable results in image classification for benchmark tasks and practical applications. The CNNs with deeper architectures have achieved even higher performance recently thanks to their robustness to the parallel shift of objects in images as well as their numerous parameters and the resulting high expression ability. However, CNNs have a limited robustness to other geometric transformations such as scaling and rotation. This limits the performance improvement of the deep CNNs, but there is no established solution. This study focuses on scale transformation and proposes a network architecture called the weight-shared multi-stage network (WSMS-Net), which consists of multiple stages of CNNs. The proposed WSMS-Net is easily combined with existing deep CNNs such as ResNet and DenseNet and enables them to acquire robustness to object scaling. Experimental results on the CIFAR-10, CIFAR-100, and ImageNet datasets demonstrate that existing deep CNNs combined with the proposed WSMS-Net achieve higher accuracies for image classification tasks with only a minor increase in the number of parameters and computation time.
Cognitive Mapping and Planning for Visual Navigation
Venue: arXiv cs.CV 2019
Year: 2019

We introduce a neural architecture for navigation in novel environments. Our proposed architecture learns to map from first-person views and plans a sequence of actions towards goals in the environment. The Cognitive Mapper and Planner (CMP) is based on two key ideas: a) a unified joint architecture for mapping and planning, such that the mapping is driven by the needs of the task, and b) a spatial memory with the ability to plan given an incomplete set of observations about the world. CMP constructs a top-down belief map of the world and applies a differentiable neural net planner to produce the next action at each time step. The accumulated belief of the world enables the agent to track visited regions of the environment. We train and test CMP on navigation problems in simulation environments derived from scans of real world buildings. Our experiments demonstrate that CMP outperforms alternate learning-based architectures, as well as, classical mapping and path planning approaches in many cases. Furthermore, it naturally extends to semantically specified goals, such as 'going to a chair'. We also deploy CMP on physical robots in indoor environments, where it achieves reasonable performance, even though it is trained entirely in simulation.
Better Process Mapping and Sparse Quadratic Assignment
Venue: arXiv cs.DC 2019
Year: 2019

Communication and topology aware process mapping is a powerful approach to reduce communication time in parallel applications with known communication patterns on large, distributed memory systems. We address the problem as a quadratic assignment problem (QAP), and present algorithms to construct initial mappings of processes to processors, and fast local search algorithms to further improve the mappings. By exploiting assumptions that typically hold for applications and modern supercomputer systems such as sparse communication patterns and hierarchically organized communication systems, we obtain significantly more powerful algorithms for these special QAPs. Our multilevel construction algorithms employ perfectly balanced graph partitioning techniques and exploit the given communication system hierarchy in significant ways. We present improvements to a local search algorithm of Brandfass et al. (2013), and further decrease the running time by reducing the time needed to perform swaps in the assignment as well as by carefully constraining local search neighborhoods. We also investigate different algorithms to create the communication graph that is mapped onto the processor network. Experiments indicate that our algorithms not only dramatically speed up local search, but due to the multilevel approach also find much better solutions in practice.
Efficient Multitask Feature and Relationship Learning
Venue: arXiv cs.LG 2019
Year: 2019

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better generalization and interpretability, which proved to be useful for applications in many domains. In this paper, we consider a formulation of multitask learning that learns the relationships both between tasks and between features, represented through a task covariance and a feature covariance matrix, respectively. First, we demonstrate that existing methods proposed for this problem present an issue that may lead to ill-posed optimization. We then propose an alternative formulation, as well as an efficient algorithm to optimize it. Using ideas from optimization and graph theory, we propose an efficient coordinate-wise minimization algorithm that has a closed form solution for each block subproblem. Our experiments show that the proposed optimization method is orders of magnitude faster than its competitors. We also provide a nonlinear extension that is able to achieve better generalization than existing methods.
A Fixed-Parameter Perspective on #BIS
Venue: arXiv cs.CC 2019
Year: 2019

The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RHΠ_1. It is believed that #BIS does not have an efficient approximation algorithm but also that it is not NP-hard. We study the robustness of the intermediate complexity of #BIS by considering variants of the problem parameterised by the size of the independent set. We exhaustively map the complexity landscape for three problems, with respect to exact computation and approximation and with respect to conventional and parameterised complexity. The three problems are counting independent sets of a given size, counting independent sets with a given number of vertices in one vertex class and counting maximum independent sets amongst those with a given number of vertices in one vertex class. Among other things, we show that all of these problems are NP-hard to approximate within any polynomial ratio. (This is surprising because the corresponding problems without the size parameter are complete in #RHΠ_1, and hence are not believed to be NP-hard.) We also show that the first problem is #W[1]-hard to solve exactly but admits an FPTRAS, whereas the other two are W[1]-hard to approximate even within any polynomial ratio. Finally, we show that, when restricted to graphs of bounded degree, all three problems have efficient exact fixed-parameter algorithms.
Learning Compact Appearance Representation for Video-based Person Re-Identification
Venue: arXiv cs.CV 2019
Year: 2019

This paper presents a novel approach for video-based person re-identification using multiple Convolutional Neural Networks (CNNs). Unlike previous work, we intend to extract a compact yet discriminative appearance representation from several frames rather than the whole sequence. Specifically, given a video, the representative frames are selected based on the walking profile of consecutive frames. A multiple CNN architecture incorporated with feature pooling is proposed to learn and compile the features of the selected representative frames into a compact description about the pedestrian for identification. Experiments are conducted on benchmark datasets to demonstrate the superiority of the proposed method over existing person re-identification approaches.
On problems equivalent to (min,+)-convolution
Venue: arXiv cs.DS 2019
Year: 2019

In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower bounds -- reductions from a problem assumed to be hard. The hard problems include 3SUM, All-Pairs Shortest Path, SAT, Orthogonal Vectors, and others. In the $(\min,+)$-convolution problem, the goal is to compute a sequence $(c[i])^{n-1}_{i=0}$, where $c[k] = $ $\min_{i=0,\ldots,k} $ $\{a[i] $ $+$ $b[k-i]\}$, given sequences $(a[i])^{n-1}_{i=0}$ and $(b[i])_{i=0}^{n-1}$. This can easily be done in $O(n^2)$ time, but no $O(n^{2-\varepsilon})$ algorithm is known for $\varepsilon > 0$. In this paper, we undertake a systematic study of the $(\min,+)$-convolution problem as a hardness assumption. First, we establish the equivalence of this problem to a group of other problems, including variants of the classic knapsack problem and problems related to subadditive sequences. The $(\min,+)$-convolution problem has been used as a building block in algorithms for many problems, notably problems in stringology. It has also appeared as an ad hoc hardness assumption. Second, we investigate some of these connections and provide new reductions and other results. We also explain why replacing this assumption with the SETH might not be possible for some problems.
Optimal Time and Space Construction of Suffix Arrays and LCP Arrays for Integer Alphabets
Venue: arXiv cs.DS 2019
Year: 2019

Suffix arrays and LCP arrays are one of the most fundamental data structures widely used for various kinds of string processing. We consider two problems for a read-only string of length $N$ over an integer alphabet $[1, \dots, σ]$ for $1 \leq σ\leq N$, the string contains $σ$ distinct characters, the construction of the suffix array, and a simultaneous construction of both the suffix array and LCP array. For the word RAM model, we propose algorithms to solve both of the problems in $O(N)$ time by using $O(1)$ extra words, which are optimal in time and space. Extra words means the required space except for the space of the input string and output suffix array and LCP array. Our contribution improves the previous most efficient algorithms, $O(N)$ time using $σ+O(1)$ extra words by [Nong, TOIS 2013] and $O(N \log N)$ time using $O(1)$ extra words by [Franceschini and Muthukrishnan, ICALP 2007], for constructing suffix arrays, and it improves the previous most efficient solution that runs in $O(N)$ time using $σ+ O(1)$ extra words for constructing both suffix arrays and LCP arrays through a combination of [Nong, TOIS 2013] and [Manzini, SWAT 2004].
The parameterized space complexity of model-checking bounded variable first-order logic
Venue: arXiv cs.LO 2019
Year: 2019

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space $O(\log^2n)$. Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal.
Guarantees for Greedy Maximization of Non-submodular Functions with Applications
Venue: arXiv cs.DM 2019
Year: 2019

We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $α$ and the submodularity ratio $γ$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\frac{1}α(1- e^{-γα})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.
Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces
Venue: arXiv cs.CG 2019
Year: 2019

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant.
On low rank-width colorings
Venue: arXiv cs.DS 2019
Year: 2019

We introduce the concept of low rank-width colorings, generalising the notion of low tree-depth colorings introduced by Nešetřil and Ossona de Mendez in [Grad and classes with bounded expansion I. Decompositions. EJC, 2008]. We say that a class $\mathcal{C}$ of graphs admits low rank-width colourings if there exist functions $N\colon \mathbb{N}\rightarrow\mathbb{N}$ and $Q\colon \mathbb{N}\rightarrow\mathbb{N}$ such that for all $p\in \mathbb{N}$, every graph $G\in \mathcal{C}$ can be vertex colored with at most $N(p)$ colors such that the union of any $i\leq p$ color classes induces a subgraph of rank-width at most $Q(i)$. Graph classes admitting low rank-width colorings strictly generalize graph classes admitting low tree-depth colorings and graph classes of bounded rank-width. We prove that for every graph class $\mathcal{C}$ of bounded expansion and every positive integer $r$, the class $\{G^r\colon G\in \mathcal{C}\}$ of $r$th powers of graphs from $\mathcal{C}$, as well as the classes of unit interval graphs and bipartite permutation graphs admit low rank-width colorings. All of these classes have unbounded rank-width and do not admit low tree-depth colorings. We also show that the classes of interval graphs and permutation graphs do not admit low rank-width colorings. As interesting side properties, we prove that every graph class admitting low rank-width colorings has the Erdős-Hajnal property and is $χ$-bounded.
Packing Short Plane Spanning Graphs in Complete Geometric Graphs
Venue: arXiv cs.CG 2019
Year: 2019

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is very long (when compared to the minimum length needed to obtain a spanning graph). We consider two different approaches: first we show an almost optimal centralized approach to extract two graphs. Then we show a constant factor approximation for a distributed model in which each point can compute its adjacencies using only local information. In both cases the obtained layers are plane
A Unified Effective Capacity Performance Analysis of Lp-norm Diversity Reception over Arbitrary and Correlated Generalized Fading Channels
Venue: arXiv cs.IT 2019
Year: 2019

The effective capacity (EC) has been recently established as a rigorous alternative to the classical Shannon's ergodic capacity since it accounts for the delay constraints imposed by future wireless applications and their impact on the overall system performance. This paper presents a novel moment generating function (MGF)-based framework for the unified EC performance analysis of a generic Lp-norm diversity combining scheme operating over arbitrary and correlated generalized fading channels and a maximum delay constraint. The Lp-norm diversity is a generic diversity structure which includes as special cases various well-known diversity schemes such as equal gain combining (EGC) and maximal ratio combining (MRC). For MRC, the proposed methodology reduces to a previously published MGF-based approach for the evaluation of the EC, whereas, for EGC, analytical approach presented is novel and the associated performance evaluation results have not been published previously in the open technical literature. Based on this methodology, novel analytical closed-form expressions for the EC performance of dual branch Lp-norm diversity receivers operating over Gamma shadowed generalized Nakagami-m fading channels are deduced. For diversity order greater than two, a novel analytical approach for the asymptotic EC performance analysis is also developed and evaluated, revealing how basic system parameters affect the overall system performance. The overall mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results thus confirming the correctness of the proposed unified analytical methodology.
Collapsibility to a subcomplex of a given dimension is NP-complete
Venue: arXiv cs.CG 2019
Year: 2019

In this paper we extend the works of Tancer and of Malgouyres and Francés, showing that $(d,k)$-collapsibility is NP-complete for $d\geq k+2$ except $(2,0)$. By $(d,k)$-collapsibility we mean the following problem: determine whether a given $d$-dimensional simplicial complex can be collapsed to some $k$-dimensional subcomplex. The question of establishing the complexity status of $(d,k)$-collapsibility was asked by Tancer, who proved NP-completeness of $(d,0)$ and $(d,1)$-collapsibility (for $d\geq 3$). Our extended result, together with the known polynomial-time algorithms for $(2,0)$ and $d=k+1$, answers the question completely.