Approximating Directed Steiner Problems via Tree Embedding

In the k-edge connected directed Steiner tree (k-DST) problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H of G that connects r to each terminal t by k edge-disjoint r,t-paths. This problem includes as special cases the well-known directed Steiner tree (DST) problem (the case k = 1) and the group Steiner tree (GST) problem. Despite having been studied and mentioned many times in literature, e.g., by Feldman et al. [SODA'09, JCSS'12], by Cheriyan et al. [SODA'12, TALG'14] and by Laekhanukit [SODA'14], there was no known non-trivial approximation algorithm for k-DST for k >= 2 even in the special case that an input graph is directed acyclic and has a constant number of layers. If an input graph is not acyclic, the complexity status of k-DST is not known even for a very strict special case that k= 2 and |T| = 2. In this paper, we make a progress toward developing a non-trivial approximation algorithm for k-DST. We present an O(D k^{D-1} log n)-approximation algorithm for k-DST on directed acyclic graphs (DAGs) with D layers, which can be extended to a special case of k-DST on "general graphs" when an instance has a D-shallow optimal solution, i.e., there exist k edge-disjoint r,t-paths, each of length at most D, for every terminal t. For the case k= 1 (DST), our algorithm yields an approximation ratio of O(D log h), thus implying an O(log^3 h)-approximation algorithm for DST that runs in quasi-polynomial-time (due to the height-reduction of Zelikovsky [Algorithmica'97]). Consequently, as our algorithm works for general graphs, we obtain an O(D k^{D-1} log n)-approximation algorithm for a D-shallow instance of the k-edge-connected directed Steiner subgraph problem, where we wish to connect every pair of terminals by k-edge-disjoint paths

Universal approach to deterministic spatial search via alternating quantum walks

Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel and universal approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum walks. The approach divides the search space into a series of subspaces and performs deterministic quantum searching on these subspaces. We highlight the flexibility of our approach by proving that for Johnson graphs, rook graphs, complete-square graphs and complete bipartite graphs, our quantum algorithms can find the marked vertex with $100\%$ success probability and achieve quadratic speedups over classical algorithms. This not only gives an alternative succinct way to prove the existing results, but also leads to new findings on more general graphs.Comment: The introduction has been revise

Assessing Face Validity of a Food Behavior Checklist for Limited-resource Filipinos

Diet-related chronic health conditions are prevalent in the Filipino American community; however, there is a lack of rigorously validated nutrition education evaluation tools in Tagalog for use in this population. This study aimed to develop and evaluate the face validity of a Tagalog-language food behavior checklist (FBC). A multi-step method was used, involving translation of questionnaire text from English to Tagalog by a team of professionals, creation of accompanying color photographs, cognitive testing with the target population, final review by the team of professionals, and assessment of readability. Subjects for cognitive testing were men (n=6) and women (n=14) 18 years or older in Hawai‘i who received or were eligible to receive Supplemental Nutrition Assistance Program (SNAP) benefits, self-identified as Filipino, and preferred Tagalog rather than English. Participants were recruited from churches, the Filipino Center, and other community sites. Cognitive interviews revealed several issues with text and photographs, such as preferences for specific terms, and images that did not adequately illustrate the text. Image changes were made to reflect items most commonly consumed. The team of professionals agreed with participant suggestions. Assessment of readability revealed a reading level appropriate for a low-literacy population of grade 5.9. The multi-step process, which allowed members of the target audience to reveal the appropriateness of the questionnaire, yielded a Tagalog-language FBC found to have adequate face validity. After further evaluation of validity and reliability, this tool may be used to evaluate behavior change resulting from the United States Department of Agriculture’s (USDA) nutrition education programs

End-to-End Bandwidth Guarantees Through Fair Local Spectrum Share in Wireless \u3cem\u3eAd-Hoc\u3c/em\u3e Networks

Sharing the common spectrum among the links in a vicinity is a fundamental problem in wireless ad-hoc networks. Lately, some scheduling approaches have been proposed that guarantee fair share of bandwidth among the links. The quality of service perceived by the applications however depends on the end-to-end bandwidth allocated to the multihop sessions. We propose an algorithm that provides provably maxmin fair end-to-end bandwidth to sessions. The algorithm combines a link scheduling that avoids collisions, a fair session service discipline per link, and a hop-by-hop window flow control. All the stages of the algorithm are implementable based on local information, except the link scheduling part that needs some network-wide coordination

TopoGraph: an end-to-end framework to build and analyze graph cubes

Graphs are a fundamental structure that provides an intuitive abstraction for modeling and analyzing complex and highly interconnected data. Given the potential complexity of such data, some approaches proposed extending decision-support systems with multidimensional analysis capabilities over graphs. In this paper, we introduce TopoGraph, an end-to-end framwork for building and analyzing graph cubes. TopoGraph extends the existing graph cube models by defining new types of dimensions and measures and organizing them within a multidimensional space that guarantees multidimensional integrity constraints. This results in defining three new types of graph cubes: property graph cubes, topological graph cubes, and graph-structured cubes. Afterwards, we define the algebraic OLAP operations for such novel cubes. We implement and experimentally validate TopoGraph with different types of real-world datasets.Peer ReviewedPostprint (author's final draft

Multidimensional Graph Neural Networks for Wireless Communications

Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies, lacking a systematical approach for modeling graph and selecting structure. Based on the observation that the mismatched permutation property from the policies and the information loss during the update of hidden representations have large impact on the learning performance and efficiency, in this paper we propose a unified framework to learn permutable wireless policies with multidimensional GNNs. To avoid the information loss, the GNNs update the hidden representations of hyper-edges. To exploit all possible permutations of a policy, we provide a method to identify vertices in a graph. We also investigate the permutability of wireless channels that affects the sample efficiency, and show how to trade off the training, inference, and designing complexities of GNNs. We take precoding in different systems as examples to demonstrate how to apply the framework. Simulation results show that the proposed GNNs can achieve close performance to numerical algorithms, and require much fewer training samples and trainable parameters to achieve the same learning performance as the commonly used convolutional neural networks

Scene graph generation: A comprehensive survey

Deep learning techniques have led to remarkable breakthroughs in the field of object detection and have spawned a lot of scene-understanding tasks in recent years. Scene graph has been the focus of research because of its powerful semantic representation and applications to scene understanding. Scene Graph Generation (SGG) refers to the task of automatically mapping an image or a video into a semantic structural scene graph, which requires the correct labeling of detected objects and their relationships. In this paper, a comprehensive survey of recent achievements is provided. This survey attempts to connect and systematize the existing visual relationship detection methods, to summarize, and interpret the mechanisms and the strategies of SGG in a comprehensive way. Deep discussions about current existing problems and future research directions are given at last. This survey will help readers to develop a better understanding of the current researches