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While large language models (LLMs) have made significant progress in processing and reasoning over knowledge graphs, current methods suffer from a high non-retrieval rate. This limitation reduces the accuracy of answering questions based on these graphs. Our analysis reveals that the combination of greedy search and forward reasoning is a major contributor to this issue. To overcome these challenges, we introduce the concept of super-relations, which enables both forward and backward reasoning by summarizing and connecting various relational paths within the graph. This holistic approach not only expands the search space, but also significantly improves retrieval efficiency. In this paper, we propose the ReKnoS framework, which aims to Reason over Knowledge Graphs with Super-Relations. Our framework’s key advantages include the inclusion of multiple relation paths through super-relations, enhanced forward and backward reasoning capabilities, and increased efficiency in querying LLMs. These enhancements collectively lead to a substantial improvement in the successful retrieval rate and overall reasoning performance. We conduct extensive experiments on a variety of datasets to evaluate ReKnoS, and the results demonstrate the superior performance of ReKnoS over existing state-of-the-art baselines, with an average accuracy gain of 2.92% across nine real-world datasets. 

We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem that is work-efficient, supports batches of updates, runs in polylogarithmic depth, and uses only linear total space. The existing algorithms for the problem either use super-linear space, do not come with strong theoretical bounds, or are not parallel. On the empirical side, we provide the first implementation of the cluster forest algorithm, the first linear-space and polylogarithmic update time algorithm for dynamic connectivity. Experimentally, we find that our algorithm uses up to 19.7× less space and is up to 6.2× faster than the level-set algorithm of Holm, de Lichten-berg, and Thorup, arguably the most widely-implemented dynamic connectivity algorithm with strong theoretical guarantees. 

We introduce the ParClusterers Benchmark Suite (PCBS)---a collection of highly scalable parallel graph clustering algorithms and benchmarking tools that streamline comparing different graph clustering algorithms and implementations. The benchmark includes clustering algorithms that target a wide range of modern clustering use cases, including community detection, classification, and dense subgraph mining. The benchmark toolkit makes it easy to run and evaluate multiple instances of different clustering algorithms with respect to both the running time and quality. We evaluate the PCBS algorithms empirically and find that they deliver both the state of the art quality and the running time. In terms of the running time, they are on average over 4x faster than the fastest library we compared to. In terms of quality, the correlation clustering algorithm [Shi et al., VLDB'21] optimizing for the LambdaCC objective, which does not have a direct counterpart in other libraries, delivers the highest quality in the majority of datasets that we used. 

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition is to generate a hierarchy among dense subgraphs at different resolutions. However, existing parallel algorithms for nucleus decomposition do not generate this hierarchy, and only compute the coreness values. This paper presents a scalable parallel algorithm for hierarchy construction, with practical optimizations, such as interleaving the coreness computation with hierarchy construction and using a concurrent union-find data structure in an innovative way to generate the hierarchy. We also introduce a parallel approximation algorithm for nucleus decomposition, which achieves much lower span in theory and better performance in practice. We prove strong theoretical bounds on the work and span (parallel time) of our algorithms. On a 30-core machine with two-way hyper-threading, our parallel hierarchy construction algorithm achieves up to a 58.84x speedup over the state-of-the-art sequential hierarchy construction algorithm by Sariyuce et al. and up to a 30.96x self-relative parallel speedup. On the same machine, our approximation algorithm achieves a 3.3x speedup over our exact algorithm, while generating coreness estimates with a multiplicative error of 1.33x on average.