Abstract

Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al.~PODC 2019; Ghaffari-Uitto SODA 2019), we investigate the complexity of ruling set problems in this model. The MPC model has become very popular as a model for large-scale distributed computing and it comes with the constraint that the memory-per-machine is strongly sublinear in the input size. For graph problems, extremely fast MPC algorithms have been designed assuming Ω~(n) memory-per-machine, where n is the number of nodes in the graph (e.g., the O(loglogn) MIS algorithm of Ghaffari et al., PODC 2018). However, it has proven much more difficult to design fast MPC algorithms for graph problems in the low-memory MPC model, where the memory-per-machine is restricted to being strongly sublinear in the number of nodes, i.e., $O(n^eps)$ for $0 < eps < 1$. In this paper, we present an algorithm for the 2-ruling set problem, running in O~(log1/6Δ) rounds whp, in the low-memory MPC model. We then extend this result to β-ruling sets for any integer β>1. Specifically, we show that a β-ruling set can be computed in the low-memory MPC model with $O(n^eps)$ memory-per-machine in O~(β⋅log1/(2β+1−2)Δ) rounds, whp. From this it immediately follows that a β-ruling set for β=Ω(logloglogΔ)-ruling set can be computed in in just O(βloglogn) rounds whp. The above results assume a total memory of $tilde{O}(m + n^{1+eps})$. We also present algorithms for β-ruling sets in the low-memory MPC model assuming that the total memory over all machines is restricted to O~(m).

Abstract

We introduce PeeledHuman - a novel shape representation of the human body that is robust to self-occlusions. PeeledHuman encodes the human body as a set of Peeled Depth and RGB maps in 2D, obtained by performing raytracing on the 3D body model and extending each ray beyond its first intersection. This formulation allows us to handle self-occlusions efficiently compared to other representations. Given a monocular RGB image, we learn these Peeled maps in an end-to-end generative adversarial fashion using our novel framework - PeelGAN. We train PeelGAN using a 3D Chamfer loss and other 2D losses to generate multiple depth values per-pixel and a corresponding RGB field per-vertex in a dual-branch setup. In our simple non-parametric solution, the generated Peeled Depth maps are back-projected to 3D space to obtain a complete textured 3D shape. The corresponding RGB maps provide vertex …

Abstract

Product placement in retail has a significant impact on the sales revenue of retailers. Hence, research efforts are being made to improve retailer revenue using high-utility pattern mining based product placement approaches. However, none of these existing approaches has explored generalized high-utility itemset mining for determining product placement in retail. The knowledge of generalized high-utility itemsets extracted from user purchase transactional database in conjunction with a product taxonomy can provide new insights about customer purchase behaviour. This work proposes the generalized utility itemset (GUI) index for retrieving generalized high-utility (revenue) itemsets. We also present a framework, which leverages the GUI index towards retail product placement to improve revenue. Our performance study using real datasets shows the effectiveness of our proposed scheme w.r.t. two existing …

Abstract

Utility mining has been emerging as an important area in data mining. While existing works on utility mining for retail businesses have primarily focused on the problem of finding high-utility itemsets from transactional databases, they implicitly assume that each item occupies only one slot. Here, the slot size of a given item is the number of (integer) slots occupied by that item on the retail store shelves. However, in many real-world scenarios, the number of slots consumed by different items typically varies. Hence, this paper considers that a given item may physically occupy any fixed (integer) number of slots. Thus, we address the problem of efficiently determining the top-utility itemsets when a given number of slots is specified as input. The key contributions of our work are three fold. First, we present an efficient framework to determine the top-utility itemsets for different user-specified number of slots that need to be …

Abstract

Periodic-frequent pattern mining is a challenging problem of great importance in many applications. Most previous works focused on finding these patterns in binary temporal databases and did not take into account the quantities of items within the data. This paper proposes a novel model of fuzzy periodic-frequent pattern (FPFP) that may exist in a quantitative temporal database (QTD). Finding FPFPs in QTD is a non-trivial and challenging task due to its huge search space. A novel pruning technique, called improved maximum scalar cardinality, has been introduced to effectively reduce the search space and the computational cost of finding the desired itemsets. This technique facilitates the mining of FPFPs in real-world very large databases practicable. An efficient algorithm has also been presented to find all FPFPs in a QTD. Experimental results demonstrate that the proposed algorithm is efficient. We also …

Abstract

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entanglement detection criteria.

Abstract

We propose an improved framework for document representation using word embeddings. The existing models represent the document as a position vector in the same word embedding space. As a result, they are unable to capture the multiple aspects as well as the broad context in the document. Also, due to their low representational power, existing approaches perform poorly at document classification. Furthermore, the document vectors obtained using such methods have uninterpretable features. In this paper, we propose an improved document representation framework which captures multiple aspects of the document with interpretable features. In this framework, a document is represented in a different feature space by representing each dimension with a potential feature word with relatively high discriminating power. A given document is modeled as the distances between the feature words and the …

Abstract

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks

Abstract

We present a decentralized motion planning and collision avoidance algorithm for multi-robot payload transport systems (PTS). A PTS is a formation of loosely coupled non-holonomic robots that cooperatively transport a deformable payload. Each PTS is constrained to navigate safely in a dynamic environment by inter-formation, environmental, and intra-formation collision avoidance. Real-time collision avoidance for such systems is challenging due to the deformability of formations and high dimensional multi-robot non-convex workspace. We resolve the above challenges by embedding workspaces defined by a multi-robot collision avoidance algorithm and multi-scale repulsive potential fields as constraints within a decentralized convex optimization problem. Specifically, we present two main steps to plan the motion of each formation. First, we compute collision-free multi-scale convex workspaces over a planning

Abstract

Conformance checking of treatment plans in discharge summary data would facilitate the development of clinical decision support system, treatment plan quality assurance, and new treatment plan discovery. Conformance checking requires extraction of medical entities and relationships among them to form a computable representation of the treatment plan present in the discharge summary. We propose a workflow representation of patient’s discharge summary that is referred to as workflow instance. We employ a multi-layer perceptron neural network to extract relationships between medical entities to construct the workflow instance. The aim of this work is to check the conformance of the workflow instance against standard treatment plan. Standard treatment plans are extracted from the treatment guidelines provided on healthcare websites such as WebMD, Mayo Clinic, and Johns Hopkins. For each disease …