Graphlets are small, connected, and non-isomorphic induced subgraphs that describe the topological structure of a graph. Counting graphlets is a fundamental task in graph mining and social network analysis. It has numerous applications in many fields, including dense subgraph discovery, anomaly detection, etc. Most existing work assumes a static graph. However, graphs are dynamic in the real world, which can be described as graph streams. Counting graphlets in graph streams is a challenge due to the streaming nature of the input. While there have been several studies on counting graphlets in graph streams, these works are limited to simple graphlets like triangles and butterflies. In this paper, we propose SGES algorithm to estimate more complex graphlets in graph streams. In SGES, we first propose an unbiased sampling strategy to maintain fixed-size sampled edges, which in turn allows us to unbiasedly estimate the number of subgraphs and then count graphlets based on the combinational relationship between the number of subgraphs and the number of graphlets. Extensive experiments over large real-world graph streams prove that our algorithm can obtain accurate estimation values of graphlet counts with high throughput.

In recent years, the integration of federated learning and deep learning technologies has become increasingly prevalent in privacy-preserved scenarios, such as smart health applications and automatic financial support. However, the inherent robustness issue in deep learning poses potential risks to federated learning systems when subjected to various attack methods. These attacks can inflict damage during the training and testing phases, perturbing models and inputs. To enhance the robustness of existing federated learning systems, we propose a novel framework called RobFL. This framework incorporates a unique feature learning module - feature center separation learning - that is specifically designed to increase the margins between different classes in the feature space, thereby augmenting the difficulty of attacks employing imperceptible perturbations on inputs. Furthermore, we design a malicious center detection method to detect malicious clients and mitigate their adverse impact. Extensive experiments substantiate the robustness of our proposed framework, RobFL, demonstrating its resilience against both evasion attacks and poisoning attacks.

A frequency bursting pattern (FBP) in temporal graphs represents some interaction behavior that accumulates its frequency at the fastest rate. Mining FBPs is essential to early warning of emergencies. However, existing studies on frequency-based pattern mining in graphs do not consider the temporal information and bursting features of a subgraph pattern. As a result, they may not provide effective and efficient mining algorithms for FBP discovery. In this paper, we study the problem of discovering top-k FBPs in temporal graphs. We present a novel model, referred to as maximal (m, θ)-bursting pattern, to describe FBPs in a temporal graph, which is a subgraph with a size larger than m that accumulates its frequency at the fastest rate during a time interval of length no less than θ. A naive solution for top-k FBPs discovery is to use the best-first search algorithm, where the burstiness threshold changes as more patterns are mined. However, this method will result in huge search space since we need to check every possible time interval for a candidate pattern in the temporal graph. To tackle this problem, we devise an online top-k framework in which k candidate results are maintained from the initial timestamp to the end in the temporal graph. Under the new framework, we further conceive two optimization strategies by exploiting incremental subgraph matching and Evolutionary Game Theory to boost the performance. Extensive experiment results on five real temporal graphs show that our algorithm has higher efficiency, effectiveness and scalability.

Abstract With the rapid development of information technologies, multi-source heterogeneous data has become an open problem, and the data is usually modeled as graphs since the graph structure is able to encode complex relationships among entities. However, in practical applications, such as network security analysis and public opinion analysis over social networks, the structure and the content of graph data are constantly evolving. Therefore, the ability to continuously monitor and detect interesting patterns on massive and dynamic graphs in real-time is crucial for many applications. Recently, a large group of excellent research works has also emerged. Nevertheless, these studies focus on different updates of graphs and apply different subgraph matching algorithms; thus, it is desirable to review these works comprehensively and give a thorough overview. In this paper, we systematically investigate the existing continuous subgraph matching techniques from the aspects of key techniques, representative algorithms, and performance evaluation. Furthermore, the typical applications and challenges of continuous subgraph matching over dynamic graphs, as well as the future development trends, are summarized and prospected.

RDF stream processing (RSP) has become a vibrant area of research in the Semantic Web community, which guarantees interoperability and opens up important applications. There have been efforts to extend RDF data and SPARQL query for representing streaming information and continuous querying functionalities. However, existing solutions will incur significant low throughput due to the recomputation of the results from scratch as the window slides. In this paper, we propose a novel graph-based framework, referred as IncTreeRDF, towards continuous SPARQL query evaluation over RDF data streams. Under the framework, the RDF data streams are modeled as streaming graphs; the SPARQL queries are translated into graph patterns and evaluated via continuous sub-graph pattern-matching over streaming RDF graphs. IncTreeRDF employs a query-centric auxiliary data structure called TStore to store some intermediate results, which supports fast incremental maintenance. Based on TStore, we can not only avoid re-computing matches of the query but also prune invalid updates. Besides, we define matching-free update, in which subgraph matching calculation can be avoided under this scenario. Extensive experimental results show that IncTreeRDF significantly outperforms existing competitors.

Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a dataset evolves over time, those existing methods have to update the model frequently to guarantee accuracy; such updating is computationally infeasible. In this paper, we propose a new formulation of SCO to handle evolving datasets. Specifically, we propose a new variant of the alternating direction method of multipliers (ADMM) to solve this problem efficiently. The guarantee of model accuracy is analyzed theoretically for two specific tasks: ridge regression and convex clustering. Extensive empirical studies confirm the effectiveness of our method.

\emphSeasonal periodicity is a frequent phenomenon for social interactions in temporal networks. A key property of this behavior is that it exhibits periodicity for multiple particular periods in temporal networks. Mining such seasonal-periodic patterns is significant since it can indicate interesting relationships between the individuals involved in the interactions. Unfortunately, most previous studies for periodic pattern mining ignore the seasonal feature. This motivates us to explore mining seasonal-periodic subgraphs, and the investigation presents a novel model, called maximal σ-periodic $ømega$-seasonal k-subgraph. It represents a subgraph with size larger than k and that appears at least σ times periodically in at least $ømega$ particular periods on the temporal graph. Since seasonal-periodic patterns do not satisfy the anti-monotonic property, we propose a weak version of support measure with an anti-monotonic property to reduce the search space efficiently. Then, we present an effective mining algorithm to seek all maximal σ-periodic $ømega$-seasonal k-subgraphs. Experimental results on real-life datasets show the effectiveness and efficiency of our approach.

Set reconciliation is a common and fundamental task in distributed systems. In many cases, given set A on $Host_A$ and set B on $Host_B$, applications need to identify those elements that appear in set A but not in set B, and vice versa. However, existing methods incur unsatisfactory space utilization and non-trivial false positives and false negatives. In this paper, we present a novel reconciliation method based on Cuckoo filter (CF). After exchanging the CFs each of which represents a set of elements, we query the local elements against the received CF to determine the elements that only belong to the local host and should be transmitted to the other host. The evaluation results indicate that the CF-based reconciliation method outperforms existing methods significantly.

An evolving pattern graph is defined by an initial pattern graph and a graph update stream consisting of edge insertions and deletions. Identifying and monitoring evolving graph patterns in the data graph is important in various application domains such as Cyberthreats surveillance. This motivates us to explore matching patterns with evolvement, and the investigation presents a novel algorithm \incepg for continuously matching of evolving patterns. Specially, we propose a concise representation \Index of partial matching solutions, and its execution model allows fast incremental maintenance. We also conceive an effective model for estimating step-wise cost of pattern evaluation to drive the matching process. Extensive experiments verify the superiority of \incepg.

The mission of set reconciliation (also called set synchronization) is to identify those elements which appear only in exactly one of two given sets. In this paper, we extend the set reconciliation problem into three design rationales: (i) multiset support; (ii) near 100% reconciliation accuracy; (iii) communication-friendly and time-saving. Prior reconciliation methods fail to realize the three rationales simultaneously. To this end, we redesign Trie and Fenwick Tree (FT), to near-accurately represent and reconcile two types of multisets that we refer to as unsorted and sorted multisets, respectively. Comprehensive evaluations are conducted to quantify the performance of our proposals. The trace-driven evaluations demonstrate that Trie and FT achieve near-accurate multiset reconciliation, with 4.31 and 2.96 times faster than the CBF-based method, respectively.

Uncertainty is intrinsic to a wide spectrum of real-life applications, which inevitably applies to graph data. Representative uncertain graphs are seen in bio-informatics, social networks, etc. This paper motivates the problem of frequent subgraph mining on single uncertain graphs, and investigates two different - probabilistic and expected - semantics in terms of support definitions. First, we present an enumeration-evaluation algorithm to solve the problem under probabilistic semantics. By showing the support computation under probabilistic semantics is #P-complete, we develop an approximation algorithm with accuracy guarantee for efficient problem-solving. To enhance the solution, we devise computation sharing techniques to achieve better mining performance. Afterwards, the algorithm is extended in a similar flavor to handle the problem under expected semantics, where checkpoint-based pruning and validation techniques are integrated. Experiment results on real-life datasets confirm the practical usability of the mining algorithms.

The mission of set reconciliation (also called set synchronization) is to identify those elements which appear only in exactly one of two given sets. In this paper, we extend the set reconciliation problem into three design rationales: (i) multiset support; (ii) near 100 percent reconciliation accuracy; and (iii) communication-friendly and time-saving. These three rationales, if realized, will lead to unprecedented benefits for the set reconciliation paradigm. Generally, prior reconciliation methods are mainly designed for simple sets and thus remain inapplicable for multisets. Methods based on probabilistic data structures, e.g., the Counting Bloom Filter (CBF), support efficient representation, and multiplicity queries. Based on these probabilistic data structures, approximate multiset reconciliation can be enabled. However, they often cannot achieve a statisfying accuracy, due to potential hash collisions. The reconciliations enabled by logs or lists incur high time-complexity and communication overhead. Therefore, existing reconciliation methods, fail to realize the three rationales simultaneously. To this end, we redesign Trie and Fenwick Tree (FT), to near-accurately represent and reconcile two types of multisets that we refer to as unsorted and sorted multisets, respectively. Moreover, to further reduce the communication overhead during the reconciliation process, we design a partial transmission strategy when exchanging two Tries or FTs. Comprehensive evaluations are conducted to quantify the performance of our proposals. The trace-driven evaluations demonstrate that Trie and FT achieve near-accurate multiset reconciliation, with 4.31 and 2.96 times faster than the CBF-based method, respectively. The simulations based on synthetic datasets further indicate that our proposals outperform the CBF-based method in terms of accuracy and communication overhead at most time.

In this paper, we study the set reconciliation problem, in which each member of a node pair has a set of objects and seeks to deliver its unique objects to the other member. How could each node compute the set difference, however, is challenging in the set reconciliation problem. To address such an issue, we propose a lightweight but efficient method that only requires the pair of nodes to represent objects using a counting Bloom filter (CBF) of size $(O(d))$ and exchange with each other, where $(d)$ denotes the total size of the set differences. A receiving node then subtracts the received CBF from its local one via minus operation proposed in this paper. The resultant CBF can approximately represent the union of the set differences and thus the set difference to each node can be identified after querying the resultant CBF. In this paper, we propose a novel estimator through which each node can accurately estimate not only the value of $(d)$ but also the size of the set difference to each node. Such an estimation result can be used to optimize the parameter setting of the CBF to achieve less false positives and false negatives. Comprehensive analysis and evaluation demonstrates that our method is more efficient than prior BF-based methods in terms of achieving the same accuracy with less communication cost. Moreover, our reconciliating method needs no prior context logs and it is very useful in networking and distributed applications.

Bloom filter is effective, space-efficient data structure for concisely representing a data set and supporting approximate membership queries. Traditionally, researchers often believe that it is possible that a Bloom filter returns a false positive, but it will never return a false negative under well-behaved operations. By investigating the mainstream variants, however, we observe that a Bloom filter does return false negatives in many scenarios. In this work, we show that the undetectable incorrect deletion of false positive items and detectable incorrect deletion of multiaddress items are two general causes of false negative in a Bloom filter. We then measure the potential and exposed false negatives theoretically and practically. Inspired by the fact that the potential false negatives are usually not fully exposed, we propose a novel Bloom filter scheme, which increases the ratio of bits set to a value larger than one without decreasing the ratio of bits set to zero. Mathematical analysis and comprehensive experiments show that this design can reduce the number of exposed false negatives as well as decrease the likelihood of false positives. To the best of our knowledge, this is the first work dealing with both the false positive and false negative problems of Bloom filter systematically when supporting standard usages of item insertion, query, and deletion operations.

A Bloom filter is an effective, space-efficient data structure for concisely representing a set, and supporting approximate membership queries. Traditionally, the Bloom filter and its variants just focus on how to represent a static set and decrease the false positive probability to a sufficiently low level. By investigating mainstream applications based on the Bloom filter, we reveal that dynamic data sets are more common and important than static sets. However, existing variants of the Bloom filter cannot support dynamic data sets well. To address this issue, we propose dynamic Bloom filters to represent dynamic sets, as well as static sets and design necessary item insertion, membership query, item deletion, and filter union algorithms. The dynamic Bloom filter can control the false positive probability at a low level by expanding its capacity as the set cardinality increases. Through comprehensive mathematical analysis, we show that the dynamic Bloom filter uses less expected memory than the Bloom filter when representing dynamic sets with an upper bound on set cardinality, and also that the dynamic Bloom filter is more stable than the Bloom filter due to infrequent reconstruction when addressing dynamic sets without an upper bound on set cardinality. Moreover, the analysis results hold in stand-alone applications, as well as distributed applications.