This paper studies multi-way join queries over temporal data, where each tuple is associated with a valid time interval indicating when the tuple is valid. A temporal join requires that joining tuples' valid intervals intersect. Previous work on temporal joins has focused on joining two relations, but pairwise processing is often inefficient because it may generate unnecessarily large intermediate results. This paper investigates how to efficiently process complex temporal joins involving multiple relations. We also consider a useful extension, durable temporal joins, which further selects results with long enough valid intervals so they are not merely transient patterns.

A way of finding interesting or exceptional records from instant-stamped temporal data is to consider their "durability, " or, intuitively speaking, how well they compare with other records that arrived earlier or later, and how long they retain their supremacy. For example, people are naturally fascinated by claims with long durability, such as: "On January 22, 2006, Kobe Bryant dropped 81 points against Toronto Raptors. Since then, this scoring record has yet to be broken." In general, given a sequence of instant-stamped records, suppose that we can rank them by a user-specified scoring function f, which may consider multiple attributes of a record to compute a single score for ranking. This paper studies durable top-k queries, which find records whose scores were within top-k among those records within a "durability window" of given length, e.g., a 10-year window starting/ending at the timestamp of the record. The parameter k, the length of the durability window, and parameters of the scoring function (which capture user preference) can all be given at the query time. We illustrate why this problem formulation yields more meaningful answers in some practical situations than other similar types of queries considered previously. We propose new algorithms for solving this problem, and provide a comprehensive theoretical analysis on the complexities of the problem itself and of our algorithms. Our algorithms vastly outperform various baselines (by up to two orders of magnitude on real and synthetic datasets).

We consider a class of queries called durability prediction queries that arise commonly in predictive analytics, where we use a given predictive model to answer questions about possible futures to inform our decisions. Examples of durability prediction queries include "what is the probability that this financial product will keep losing money over the next 12 quarters before turning in any profit?" and "what is the chance for our proposed server cluster to fail the required service-level agreement before its term ends?" We devise a general method called Multi-Level Splitting Sampling (MLSS) that can efficiently handle complex queries and complex models---including those involving black-box functions---as long as the models allow us to simulate possible futures step by step. Our method addresses the inefficiency of standard Monte Carlo (MC) methods by applying the idea of importance splitting to let one "promising" sample path prefix generate multiple "offspring" paths, thereby directing simulation efforts toward more promising paths. We propose practical techniques for designing splitting strategies, freeing users from manual tuning. Experiments show that our approach is able to achieve unbiased estimates and the same error guarantees as standard MC while offering an order-of-magnitude cost reduction.

Estimation of the accuracy of a large-scale knowledge graph (KG) often requires humans to annotate samples from the graph. How to obtain statistically meaningful estimates for accuracy evaluation while keeping human annotation costs low is a problem critical to the development cycle of a KG and its practical applications. Surprisingly, this challenging problem has largely been ignored in prior research. To address the problem, this paper proposes an efficient sampling and evaluation framework, which aims to provide quality accuracy evaluation with strong statistical guarantee while minimizing human efforts. Motivated by the properties of the annotation cost function observed in practice, we propose the use of cluster sampling to reduce the overall cost. We further apply weighted and two-stage sampling as well as stratification for better sampling designs. We also extend our framework to enable efficient incremental evaluation on evolving KG, introducing two solutions based on stratified sampling and a weighted variant of reservoir sampling. Extensive experiments on real-world datasets demonstrate the effectiveness and efficiency of our proposed solution. Compared to baseline approaches, our best solutions can provide up to 60% cost reduction on static KG evaluation and up to 80% cost reduction on evolving KG evaluation, without loss of evaluation quality.

Many datasets have a temporal dimension and contain a wealth of historical information. When using such data to make decisions, we often want to examine not only the current snapshot of the data but also its history. For example, given a result object of a snapshot query, we can ask for its "durability," or intuitively, how long (or how often) it was valid in the past. This paper considers durable top-k queries, which look for objects whose values were among the top k for at least some fraction of the times during a given interval---e.g., stocks that were among the top 20 most heavily traded for at least 80% of the trading days during the last quarter of 2017. We present a comprehensive suite of techniques for solving this problem, ranging from exact algorithms where k is fixed in advance, to approximate methods that work for any k and are able to exploit workload and data characteristics to improve accuracy while capping index cost. We show that our methods vastly outperform baseline and previous methods using both real and synthetic datasets.

In many applications, the system needs to selectively present a small subset of answers to users. The set of all possible answers can be seen as an elevation surface over a domain, where the elevation measures the quality of each answer, and the dimensions of the domain correspond to attributes of the answers with which similarity between answers can be measured. This paper considers the problem of finding a diverse set of k high-quality representatives for such a surface. We show that existing methods for diversified top- k and weighted clustering problems are inadequate for this problem. We propose k -DHR as a better formulation for the problem. We show that k -DHR has a submodular and monotone objective function, and we develop efficient algorithms for solving k -DHR with provable guarantees. We conduct extensive experiments to demonstrate the usefulness of the results produced by k -DHR for applications in computational lead-finding and fact-checking, as well as the efficiency and effectiveness of our algorithms.