Many data analytics systems store and process large datasets in partitions containing millions of rows. By mapping rows to partitions in an optimized way, it is possible to improve query performance by skipping over large numbers of irrelevant partitions during query processing. This mapping is referred to as a data layout. Recent works have shown that customizing the data layout to the anticipated query workload greatly improves query performance, but the performance benefits may disappear if the workload changes. Reorganizing data layouts to accommodate workload drift can resolve this issue, but reorganization costs could exceed query savings if not done carefully. In this paper, we present an algorithmic framework OReO that makes online reorganization decisions to balance the benefits of improved query performance with the costs of reorganization. Our framework extends results from Metrical Task Systems to provide a tight bound on the worst-case performance guarantee for online reorganization, without prior knowledge of the query workload. Through evaluation on real-world datasets and query workloads, our experiments demonstrate that online reorganization with OReO can lead to an up to 32% improvement in combined query and reorganization time compared to using a single, optimized data layout for the entire workload.

The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Though tight approximation algorithms for general matroid constraints exist in theory, the running times of such algorithms typically scale quadratically, and are not practical for truly large scale settings. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [Alina Ene and Huy L. Nguyen, 2019]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of 1-1/e-ε and both generalize and accelerate the results of Ene and Nguyen [Alina Ene and Huy L. Nguyen, 2019]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondrák [Ashwinkumar Badanidiyuru and Jan Vondrák, 2014]. To achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel Freeze operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [Stephen Alstrup et al., 2005] that maintains the maximum weight basis under insertions and deletions of elements in O(log n) time. This data structure needs to support certain subtree query and path update operations that are performed every insertion and deletion that are non-trivial to handle in conjunction. For the transversal matroid the Freeze operation corresponds to requiring the data structure to keep a certain set S of vertices matched, a property that we call S-stability. While there is a large body of work on dynamic matching algorithms, none are S-stable and maintain an approximate maximum weight matching under vertex updates. We give the first such algorithm for bipartite graphs with total running time linear (up to log factors) in the number of edges.

In search and retrieval, a critical subtask is the classification of user search queries into predefined categories. Traditional supervised multi-class classification algorithms usually treat each category independently. In practical applications however, the categories have implicit relationships. Categories are organized as a tree-based taxonomy, which can be viewed as a graph. In this work, we explore a novel and systematic way of leveraging semantic information for improving taxonomy-based categorization. We propose a class of graph-based network structures, which we call Categorical Graph Neural Networks (CaGNN). CaGNNs leverage relationship information between neighbor categories and overlay the semantic information for each category, thus improving the performance of query categorization. The CaGNN framework can integrate a baseline categorizer with any Graph Neural Network, such as the commonly used Graph Attention Network and Graph Convolutional Network. Over a query categorization dataset of 2k categories and another ad title categorization dataset of 5k categories, CaGNN improves categorizers’ performance significantly compared to a baseline Deep Neural Network model without the CaGNN structure. Notably top 3 prediction recall increases from 90.15% to 91.40% for the ad title categorization task, for which is quite significant at over 90% level for more than 5k categories. By inspecting the learned category embeddings and the flow of message passing, we show that CaGNN effectively encapsulates useful graph structural information. Online A/B testing result shows that an ad ranking model with CaGNN-based features has increased ad click-through rate by 1.81% and reduced defect rate by 2.64%. The model has been deployed to production.

This paper examines the approach taken by team gitastrophe in the CG:SHOP 2021 challenge. The challenge was to find a sequence of simultaneous moves of square robots between two given configurations that minimized either total distance travelled or makespan (total time). Our winning approach has two main components: an initialization phase that finds a good initial solution, and a k-opt local search phase which optimizes this solution. This led to a first place finish in the distance category and a third place finish in the makespan category.

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order.For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein~\cite{SMC19} gave a single-pass $(1-1/e-\varepsilon)$-approximation algorithm using only linear memory, but their exponential dependence on $\varepsilon$ makes it impractical even for $\varepsilon=0.1$.We simplify both the algorithm and the analysis, obtaining an exponential improvement in the $\varepsilon$-dependence (in particular, $O(k/\varepsilon)$ memory).Extending these techniques, we also give a simple $(1/e-\varepsilon)$-approximation for non-monotone functions in $O(k/\varepsilon)$ memory. For the monotone case, we also give a corresponding unconditional hardness barrier of $1-1/e+\varepsilon$ for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.

Skill estimation mechanisms, colloquially known as rating systems, play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and video games. The system’s simplicity allows us to prove theoretical bounds on its robustness and runtime. In addition, we show that it is incentive-compatible: a player who seeks to maximize their rating will never want to underperform. Experimentally, the rating system surpasses existing systems in prediction accuracy, and computes faster than existing systems by up to an order of magnitude.

Over the past decade, Determinantal Point Processes (DPPs) have proven to be a mathematically elegant framework for modeling diversity. Given a set of items N, DPPs define a probability distribution over subsets of N, with sets of larger diversity having greater probability. Recently, DPPs have achieved success in the domain of recommendation systems, as a method to enforce diversity of recommendations in addition to relevance. In large-scale recommendation applications however, the input typically comes in the form of a stream too large to fit into main memory. However, the natural greedy algorithm for DPP-based recommendations is memory intensive, and cannot be used in a streaming setting.

In large-data applications, it is desirable to design algorithms with a high degree of parallelization. In the context of submodular optimization, adaptive complexity has become a widely-used measure of an algorithm’s “sequentiality”. Algorithms in the adaptive model proceed in rounds, and can issue polynomially many queries to a function f in each round. The queries in each round must be independent, produced by a computation that depends only on query results obtained in previous rounds.

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and there are several methods for scaling subgraph counting to large graphs. Many real-world networks have a notion of strength of connection between nodes, which is often modeled by a weighted graph, but existing scalable algorithms for pattern mining are designed for unweighted graphs. Here, we develop deterministic and random sampling algorithms that enable the fast discovery of the 3-cliques (triangles) of largest weight, as measured by the generalized mean of the triangle's edge weights. For example, one of our proposed algorithms can find the top-1000 weighted triangles of a weighted graph with billions of edges in thirty seconds on a commodity server, which is orders of magnitude faster than existing "fast" enumeration schemes. Our methods open the door towards scalable pattern mining in weighted graphs.

Pattern counting in graphs is fundamental to several network sci- ence tasks, and there is an abundance of scalable methods for estimating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer structure, and incorporating temporal information in particular has become a key part of network analysis. Consequently, temporal motifs, which are generalizations of small subgraph patterns that incorporate temporal ordering on edges, are an emerging part of the network analysis toolbox. However, there are no algorithms for fast estimation of temporal motifs counts; moreover, we show that even counting simple temporal star motifs is NP-complete. Thus, there is a need for fast and approximate algorithms. Here, we present the first frequency estimation algorithms for counting temporal motifs. More specifically, we develop a sampling framework that sits as a layer on top of existing exact counting algorithms and enables fast and accurate memory-efficient estimates of temporal motif counts. Our results show that we can achieve one to two orders of magnitude speedups over existing algorithms with minimal and controllable loss in accuracy on a number of datasets.

MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and submodular optimization problems. We develop new techniques for designing greedy and local ratio algorithms in this setting. Our randomized local ratio technique gives $2$-approximations for weighted vertex cover and weighted matching, and an f -approximation for weighted set cover, all in a constant number of MapReduce rounds. Our randomized greedy technique gives algorithms for maximal independent set, maximal clique, and a (1+ε)1n Δ-approximation for weighted set cover. We also give greedy algorithms for vertex colouring with $(1+o(1))Δ colours and edge colouring with (1+o(1))Δ colours.

SYM-ILDL is a numerical software package that computes incomplete LDL T (ILDL) factorizations of symmetric indefinite and real skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by Li and Saad [2005]. Our code is economical in terms of storage, and it deals with real skew-symmetric matrices as well as symmetric ones. The package is written in C++ and is templated, is open source, and includes a M atlab ™ interface. The code includes built-in RCM and AMD reordering, two equilibration strategies, threshold Bunch-Kaufman pivoting, and rook pivoting, as well as a wrapper to MC64, a popular matching-based equilibration and reordering algorithm. We also include two built-in iterative solvers: SQMR, preconditioned with ILDL, and MINRES, preconditioned with a symmetric positive definite preconditioner based on the ILDL factorization.