Given a graph pair (G 1 , G 2 ), graph edit distance (GED) is defined as the minimum number of edit operations converting G 1 to G 2 . GED is a fundamental operation widely used in many applications, but its exact computation is NP-hard, so the approximation of GED has gained a lot of attention. Data-driven learning-based methods have been found to provide superior results compared to classical approximate algorithms, but they directly fit the coupling relationship between a pair of vertices from their vertex features. We argue that while pairwise vertex features can capture the coupling cost (discrepancy) of a pair of vertices, the vertex coupling matrix should be derived from the vertex-pair cost matrix through a more well-established method that is aware of the global context of the graph pair, such as optimal transport. In this paper, we propose an ensemble approach that integrates a supervised learning-based method and an unsupervised method, both based on optimal transport. Our learning method, GEDIOT, is based on inverse optimal transport that leverages a learnable Sinkhorn algorithm to generate the coupling matrix. Our unsupervised method, GEDGW, models GED computation as a linear combination of optimal transport and its variant, Gromov-Wasserstein discrepancy, for node and edge operations, respectively, which can be solved efficiently without needing the ground truth. Our ensemble method, GEDHOT, combines GEDIOT and GEDGW to further boost the performance. Extensive experiments demonstrate that our methods significantly outperform the existing methods in terms of the performance of GED computation, edit path generation, and model generalizability.

This paper considers statistical analysis on noisy datasets where near-duplicate elements need to be treated as identical ones. We focus on two basic problems, distinct elements and ℓ 0 -sampling, in the data stream model where the sequence of elements can only be scanned once using a limited space, under which a comprehensive data deduplication step before statistical analysis is not feasible. Previous streaming algorithms for these problems could only handle noisy datasets in O (1)-dimensional Euclidean spaces. In this paper, we propose sublinear-space streaming algorithms that work for noisy datasets in any metric space. We also give a lower bound result showing that solving the distinct elements problem on noisy datasets in general metric spaces is inherently more difficult than solving it on noiseless datasets and on noisy datasets in O (1)-dimensional Euclidean spaces.

A k -plex is a dense subgraph structure where every vertex can be disconnected with at most k vertices. Finding a maximum k -plex (M k P) in a big graph is a key primitive in many real applications such as community detection and biological network analysis. A lot of M k P algorithms have been actively proposed in recent years in top AI and DB conferences, featuring a broad range of sophisticated pruning techniques. In this paper, we study the various pruning techniques from nine recent M k P algorithms including kPlexT, Maple, Seesaw, DiseMKP, kPlexS, KpLeX, Maplex, BnB and BS by unifying them in a common framework called V-M k P. We summarize their proposed techniques into three categories, those for (1) branching, (2) upper bounding, and (3) reduction during subgraph exploration. We find that different pruning techniques can have drastically different performance impacts, but there exists a configuration of the techniques dependent on k that leads to the best performance in vast majority of the time. Interestingly, extensive experiments with our unified framework reveal that some techniques are not effective as claimed in the original works, and we also discover an unmentioned technique that is actually the major performance booster when k > 5. We also study problem variants such as finding all the M k Ps and finding the densest M k P (i.e., with the most edges) to cover community diversity, and effective algorithm parallelization. Our source code is released at https://github.com/akhlaqueak/MKP-Study.

Anomaly detection is a popular research topic in Artificial Intelligence and has been widely applied in network security, financial fraud detection, and industrial equipment failure detection. Isolation forest based methods are the base algorithms to detect anomalies in these scenarios for their simplicity and efficiency, which has been further exploited with multi-folk trees and learning mechanisms to realize the optimal isolation forest for high detection accuracy. However, the optimal isolation forest is time-consuming with the learning mechanisms, resulting in the task failing of time-constrained applications. Moreover, the original optimal isolation forest fails to construct the optimal tree structure restricted by the time complexity. To address the above challenges, we propose an efficient anomaly detection method called EEIF, which realizes the real e-folk structure of the optimal isolation forest in our practical algorithm design. Specifically, we design a distribution that perfectly matches the e-branch theory to construct the optimal isolation forest. Then, we design an FR clustering scheme to achieve fast training of the isolation forest with learning to hash and provide related proofs of accuracy and efficiency. Besides, a parallel algorithm is integrated into our method to reduce prediction time. Finally, extensive experiments are conducted on a large amount of real-world datasets and the results demonstrate that our method significantly improves efficiency while ensuring effectiveness, compared with the state-of-the-art methods.

This paper introduces SyncSignature, the first fully parallelizable algorithmic framework for tree similarity joins under edit distance. SyncSignature makes use of implicit-synchronized signature generation schemes, which allow for an efficient and parallelizable candidate-generation procedure via hash join. Our experiments on large real-world datasets show that the proposed algorithms under the SyncSignature framework significantly outperform the state-of-the-art algorithm in the parallel computation environment. For datasets with big trees, they also exceed the state-of-the-art algorithms by a notable margin in the centralized/single-thread computation environment. To complement and guide the experimental study, we also provide a thorough theoretical analysis for all proposed signature generation schemes.

We study the problem of learning to cluster data points using an oracle which can answer same-cluster queries. Different from previous approaches, we do not assume that the total number of clusters is known at the beginning and do not require that the true clusters are consistent with a predefined objective function such as the K-means. These relaxations are critical from the practical perspective and, meanwhile, make the problem more challenging. We propose two algorithms with provable theoretical guarantees and verify their effectiveness via an extensive set of experiments on both synthetic and real-world data.

We study a fundamental problem in data analytics: similarity search under edit distance (or, edit similarity search for short). In this problem we try to build an index on a set of n strings S = s1, ..., sn, with the goal of answering the following two types of queries: (1) the threshold query: given a query string t and a threshold K, output all si ∈ S such that the edit distance between si and t is at most K; (2) the top-k query: given a query string t, output the k strings in S that are closest to t in terms of edit distance. Edit similarity search has numerous applications in bioinformatics, databases, data mining, information retrieval, etc., and has been studied extensively in the literature. In this paper we propose a novel algorithm for edit similarity search named MinSearch. The algorithm is randomized, and we can show mathematically that it outputs the correct answer with high probability for both types of queries. We have conducted an extensive set of experiments on MinSearch, and compared it with the best existing algorithms for edit similarity search. Our experiments show that MinSearch has a clear advantage (often in orders of magnitudes) against the best previous algorithms in query time, and MinSearch is always one of the best among all competitors in the indexing time and space usage. Finally, MinSearch achieves perfect accuracy for both types of queries on all datasets that we have tested.

We study the problem of computing similarity joins under edit distance on a set of strings. Edit similarity joins is a fundamental problem in databases, data mining and bioinformatics. It finds important applications in data cleaning and integration, collaborative filtering, genome sequence assembly, etc. This problem has attracted significant attention in the past two decades. However, all previous algorithms either cannot scale well to long strings and large similarity thresholds, or suffer from imperfect accuracy.

We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low dimensional LP-type problems appear frequently in various machine learning tasks such as robust regression, support vector machines, and core vector machines. As supporting large-scale machine learning queries in database systems has become an important direction for database research, obtaining efficient algorithms for low dimensional LP-type problems on massive datasets is of great value. In this paper we give both upper and lower bounds for LP-type problems in distributed and streaming models. Our bounds are almost tight when the dimensionality of the problem is a fixed constant.

We propose smooth q-gram, the first variant of q-gram that captures q-gram pair within a small edit distance. We apply smooth q-gram to the problem of detecting overlapping pairs of error-prone reads produced by single molecule real time sequencing (SMRT), which is the first and most critical step of the de novo fragment assembly of SMRT reads. We have implemented and tested our algorithm on a set of real world benchmarks. Our empirical results demonstrated the significant superiority of our algorithm over the existing q-gram based algorithms in accuracy.

In this paper we study how to perform distinct sampling in the streaming model where data contain near-duplicates. The goal of distinct sampling is to return a distinct element uniformly at random from the universe of elements, given that all the near-duplicates are treated as the same element. We also extend the result to the sliding window cases in which we are only interested in the most recent items. We present algorithms with provable theoretical guarantees for datasets in the Euclidean space, and also verify their effectiveness via an extensive set of experiments.

We consider statistical estimations of a matrix product over the integers in a distributed setting, where we have two parties Alice and Bob; Alice holds a matrix A and Bob holds a matrix B, and they want to estimate statistics of $A \cdot B$. We focus on the well-studied $\ell_p$-norm, distinct elements ($p = 0$), $\ell_0$-sampling, and heavy hitter problems. The goal is to minimize both the communication cost and the number of rounds of communication. This problem is closely related to the fundamental set-intersection join problem in databases: when $p = 0$ the problem corresponds to the size of the set-intersection join. When $p = ınfty$ the output is simply the pair of sets with the maximum intersection size. When $p = 1$ the problem corresponds to the size of the corresponding natural join. We also consider the heavy hitters problem which corresponds to finding the pairs of sets with intersection size above a certain threshold, and the problem of sampling an intersecting pair of sets uniformly at random.

In this paper we study skyline queries in the distributed computational model, where we have s remote sites and a central coordinator; each site holds a piece of data, and the coordinator wants to compute the skyline of the union of the s datasets. The computation is in terms of rounds, and the goal is to minimize both the total communication cost and the round cost.

We study the problem of edit similarity joins, where given a set of strings and a threshold value K, we want to output all pairs of strings whose edit distances are at most K. Edit similarity join is a fundamental problem in data cleaning/integration, bioinformatics, collaborative filtering and natural language processing, and has been identified as a primitive operator for database systems. This problem has been studied extensively in the literature. However, we have observed that all the existing algorithms fall short on long strings and large distance thresholds.

Linear sketching algorithms have been widely used for processing large-scale distributed and streaming datasets. Their popularity is largely due to the fact that linear sketches can be naturally composed in the distributed model and be efficiently updated in the streaming model. The errors of linear sketches are typically expressed in terms of the sum of coordinates of the input vector excluding those largest ones, or, the mass on the tail of the vector. Thus, the precondition for these algorithms to perform well is that the mass on the tail is small, which is, however, not always the case - in many real-world datasets the coordinates of the input vector have a bias , which will generate a large mass on the tail. In this paper we propose linear sketches that are bias- aware . We rigorously prove that they achieve strictly better error guarantees than the corresponding existing sketches, and demonstrate their practicality and superiority via an extensive experimental evaluation on both real and synthetic datasets.

We study the problem of estimating distinct elements in the data stream model, which has a central role in traffic monitoring, query optimization, data mining and data integration. Different from all previous work, we study the problem in the noisy data setting, where two different looking items in the stream may reference the same entity (determined by a distance function and a threshold value), and the goal is to estimate the number of distinct entities in the stream. In this paper, we formalize the problem of robust distinct elements, and develop space and time-efficient streaming algorithms for datasets in the Euclidean space, using a novel technique we call bucket sampling. We also extend our algorithmic framework to other metric spaces by establishing a connection between bucket sampling and the theory of locality sensitive hashing. Moreover, we formally prove that our algorithms are still effective under small distinct elements ambiguity. Our experiments demonstrate the practicality of our algorithms.

Given a set-comparison predicate P and given two lists of sets A = (A1,...,Am) and B = (B1,...,Bm), with all Ai, Bj ⊆ [n], the P-set join A bowtieP B is defined to be the set {(i, j) in [m] x [m] | P(Ai,Bj)}. When P(Ai,Bj) is the condition "Ai ∩ Bj ≠ is empty " we call this the set-intersection-notempty join (a.k.a. the composition of A and B); when P(Ai,Bj) is "Ai ∩ Bj is empty" we call it the set-disjointness join; when P(Ai,Bj) is "Ai = Bj" we call it the set-equality join; when P(Ai,Bj) is "|Ai ∩ Bj| ≥ T" for a given threshold T, we call it the set-intersection threshold join. Assuming A and B are stored at two different sites in a distributed environment, we study the (randomized) communication complexity of computing these, and related, set-joins A bowtieP B, as well as the (randomized) communication complexity of computing the exact and approximate value of their size k = |A bowtieP B|. Combined, our analyses shed new insights into the quantitative differences between these different set-joins. Furthermore, given the close affinity of the natural join and the set-intersection-not-empty join, our results also yield communication complexity results for computing the natural join in a distributed environment.

Set reconciliation is a fundamental problem in distributed databases, where two parties each holding a set of elements wish to find their difference, so as to establish data consistency. Efficient algorithms exist for this problem with communication cost proportional only to the difference of the two sets, as opposed to the cardinality of the sets themselves. However, all existing work on set reconciliation considers two elements to be the same only if they are exactly equal. We observe that, in many applications, the elements correspond to objects on which a distance function can be defined, e.g., points in the Euclidean space, and close points often actually represent the same object. During the reconciliation, the algorithm should only find the truly different elements in the two sets while tolerating small perturbations. In this paper, we propose the robust set reconciliation problem, and take a principled approach to address this issue via the earth mover's distance. We have developed a communication and time-efficient algorithm with provable guarantees on the quality of the reconciliation. This is then complemented with an essentially matching lower bound showing the optimality of the algorithm. Our experimental results on both synthetic and real data sets have demonstrated that our algorithm also performs very well in practice.

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the count-tracking problem, where there are k players, each holding a counter ni that gets incremented over time, and the goal is to track an ∑-approximation of their sum n=∑ini continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is θ(k/ε • log N), where N is the final value of n when the tracking finishes, we show that with randomization, the communication cost can be reduced to θ(√k/ε • log N). Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: frequency-tracking and rank-tracking, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.

A fundamental problem in data management is to draw a sample of a large data set, for approximate query answering, selectivity estimation, and query planning. With large, streaming data sets, this problem becomes particularly difficult when the data is shared across multiple distributed sites. The challenge is to ensure that a sample is drawn uniformly across the union of the data while minimizing the communication needed to run the protocol and track parameters of the evolving data. At the same time, it is also necessary to make the protocol lightweight, by keeping the space and time costs low for each participant. In this paper, we present communication-efficient protocols for sampling (both with and without replacement) from k distributed streams. These apply to the case when we want a sample from the full streams, and to the sliding window cases of only the W most recent items, or arrivals within the last w time units. We show that our protocols are optimal, not just in terms of the communication used, but also that they use minimal or near minimal (up to logarithmic factors) time to process each new item, and space to operate.

The hash table, especially its external memory version, is one of the most important index structures in large databases. Assuming a truly random hash function, it is known that in a standard external hash table with block size b, searching for a particular key only takes expected average t_q=1+1/2Ω(b) disk accesses for any load factor α bounded away from $1$. However, such near-perfect performance is achieved only when b is known and the hash table is particularly tuned for working with such a blocking. In this paper we study if it is possible to build a cache-oblivious hash table that works well with any blocking. Such a hash table will automatically perform well across all levels of the memory hierarchy and does not need any hardware-specific tuning, an important feature in autonomous databases.

We consider the the problem of tracking heavy hitters and quantiles in the distributed streaming model. The heavy hitters and quantiles are two important statistics for characterizing a data distribution. Let A be a multiset of elements, drawn from the universe U={1,...,u}. For a given 0 ≤ Φ ≤ 1, the Φ-heavy hitters are those elements of A whose frequency in A is at least Φ |A|; the Φ-quantile of A is an element x of U such that at most Φ|A| elements of A are smaller than A and at most (1-Φ)|A| elements of A are greater than x. Suppose the elements of A are received at k remote sites over time, and each of the sites has a two-way communication channel to a designated coordinator, whose goal is to track the set of Φ-heavy hitters and the Φ-quantile of A approximately at all times with minimum communication. We give tracking algorithms with worst-case communication cost O(k/ε ⋅ log n) for both problems, where n is the total number of items in A, and ε is the approximation error. This substantially improves upon the previous known algorithms. We also give matching lower bounds on the communication costs for both problems, showing that our algorithms are optimal. We also consider a more general version of the problem where we simultaneously track the Φ-quantiles for all 0 ≤ Φ ≤ 1.

Computing statistical information on probabilistic data has attracted a lot of attention recently, as the data generated from a wide range of data sources are inherently fuzzy or uncertain. In this paper, we study an important statistical query on probabilistic data: finding the frequent items. One straightforward approach to identify the frequent items in a probabilistic data set is to simply compute the expected frequency of an item and decide if it exceeds a certain fraction of the expected size of the whole data set. However, this simple definition misses important information about the internal structure of the probabilistic data and the interplay among all the uncertain entities. Thus, we propose a new definition based on the possible world semantics that has been widely adopted for many query types in uncertain data management, trying to find all the items that are likely to be frequent in a randomly generated possible world. Our approach naturally leads to the study of ranking frequent items based on confidence as well.