The distance-generalized core, also called ( k , h )-core, is defined as the maximal subgraph in which every vertex has at least k vertices at distance no longer than h. Compared with k -core, ( k , h )-core can identify more fine-grained subgraphs and, hence, is more useful for the applications such as network analysis and graph coloring. The state-of-the-art algorithms for ( k , h )-core decomposition are peeling algorithms, which iteratively delete the vertex with the minimum h -degree (i.e., the least number of neighbors within h hops). However, they suffer from some limitations, such as low parallelism and incapability of supporting dynamic graphs. To address these limitations, in this paper, we revisit the problem of ( k , h )-core decomposition. First, we introduce two novel concepts of pairwise h-attainability index and n-order H-index based on an insightful observation. Then, we thoroughly analyze the properties of n -order H-index and propose a parallelizable local algorithm for ( k , h )-core decomposition. Moreover, several optimizations are presented to accelerate the local algorithm. Furthermore, we extend the proposed local algorithm to address the ( k , h )-core maintenance problem for dynamic graphs. Experimental studies on real-world graphs show that, compared to the best existing solution, our proposed algorithms can reduce the ( k , h )-core decomposition time by 1--3 orders of magnitude and save the maintenance cost by 1--2 orders of magnitude.

Interactive graph search leverages human intelligence to categorize target labels in a hierarchy, which is useful for image classification, product categorization, and database search. However, many existing interactive graph search studies aim at identifying a single target optimally, and suffer from the limitations of asking too many questions and not being able to handle multiple targets. To address these two limitations, in this paper, we study a new problem of <u>b</u>udget constrained <u>i</u>nteractive <u>g</u>raph <u>s</u>earch for <u>m</u>ultiple targets called kBM-IGS problem. Specifically, given a set of multiple targets T in a hierarchy and two parameters k and b , the goal is to identify a k -sized set of selections S , such that the closeness between selections S and targets T is as small as possible, by asking at most a budget of b questions. We theoretically analyze the updating rules and design a penalty function to capture the closeness between selections and targets. To tackle the kBM-IGS problem, we develop a novel framework to ask questions using the best vertex with the largest expected gain, which provides a balanced trade-off between target probability and benefit gain. Based on the kBM-IGS framework, we first propose an efficient algorithm STBIS to handle the SingleTarget problem, which is a special case of kBM-IGS. Then, we propose a dynamic programming based method kBM-DP to tackle the MultipleTargets problem. To further improve efficiency, we propose two heuristic but efficient algorithms, kBM-Topk and kBM-DP+. Experiments on large real-world datasets with ground-truths verify both the effectiveness and efficiency of our algorithms.

The COVID-19 pandemic has caused the society lockdowns and a large number of deaths in many countries. Potential transmission cluster discovery is to find all suspected users with infections, which is greatly needed to fast discover virus transmission chains so as to prevent an outbreak of COVID-19 as early as possible. In this paper, we study the problem of potential transmission cluster discovery based on the spatio-temporal logs. Given a query of patient user q and a timestamp of confirmed infection t q , the problem is to find all potential infected users who have close social contacts to user q before time t q . We motivate and formulate the potential transmission cluster model, equipped with a detailed analysis of transmission cluster property and particular model usability. To identify potential clusters, one straightforward method is to compute all close contacts on-the-fly, which is simple but inefficient caused by scanning spatio-temporal logs many times. To accelerate the efficiency, we propose two indexing algorithms by constructing a multigraph index and an advanced BCG-index. Leveraging two well-designed techniques of spatio-temporal compression and graph partition on bipartite contact graphs, our BCG-index approach achieves a good balance of index construction and online query processing to fast discover potential transmission cluster. We theoretically analyze and compare the algorithm complexity of three proposed approaches. Extensive experiments on real-world check-in datasets and COVID-19 confirmed cases in the United States validate the effectiveness and efficiency of our potential transmission cluster model and algorithms.

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