The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite unions of conjunctive queries. Our main result states that the probabilistic query evaluation problem is #P-hard for all unbounded queries from this class. As bounded queries from this class are equivalent to a union of conjunctive queries, they are already classified by the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a complete data complexity dichotomy, between polynomial time and #P-hardness, on evaluating homomorphism-closed queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries over arity-two signatures, such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries. The dichotomy also applies to a restricted case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1. We show the main result by reducing from the problem of counting the valuations of positive partitioned 2-DNF formulae, or from the source-to-target reliability problem in an undirected graph, depending on properties of minimal models for the query.

Modular Path Queries with Arithmetic

We propose a new approach to querying graph databases. Our approach balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of minimal (e.g. shortest) and maximal (e.g. most valuable) paths satisfying given criteria. To express complex properties in a modular way, we introduce labelling-generating ontologies. The resulting formalism is computationally attractive - queries can be answered in non-deterministic logarithmic space in the size of the database.

Speeding Up Reachability Queries in Public Transport Networks Using Graph Partitioning

Computing path queries such as the shortest path in public transport networks is challenging because the path costs between nodes change over time. A reachability query from a node at a given start time on such a network retrieves all points of interest (POIs) that are reachable within a given cost budget. Reachability queries are essential building blocks in many applications, for example, group recommendations, ranking spatial queries, or geomarketing. We propose an efficient solution for reachability queries in public transport networks. Currently, there are two options to solve reachability queries. (1) Execute a modified version of Dijkstra’s algorithm that supports time-dependent edge traversal costs; this solution is slow since it must expand edge by edge and does not use an index. (2) Issue a separate path query for each single POI, i.e., a single reachability query requires answering many path queries. None of these solutions scales to large networks with many POIs. We propose a novel and lightweight reachability index. The key idea is to partition the network into cells. Then, in contrast to other approaches, we expand the network cell by cell. Empirical evaluations on synthetic and real-world networks confirm the efficiency and the effectiveness of our index-based reachability query solution.

Efficiently answering reachability and path queries on temporal bipartite graphs

Bipartite graphs are naturally used to model relationships between two different types of entities, such as people-location, author-paper, and customer-product. When modeling real-world applications like disease outbreaks, edges are often enriched with temporal information, leading to temporal bipartite graphs. While reachability has been extensively studied on (temporal) unipartite graphs, it remains largely unexplored on temporal bipartite graphs. To fill this research gap, in this paper, we study the reachability problem on temporal bipartite graphs. Specifically, a vertex u reaches a vertex w in a temporal bipartite graph G if u and w axe connected through a series of consecutive wedges with time constraints. Towards efficiently answering if a vertex can reach the other vertex, we propose an index-based method by adapting the idea of 2-hop labeling. Effective optimization strategies and parallelization techniques are devised to accelerate the index construction process. To better support real-life scenarios, we further show how the index is leveraged to efficiently answer other types of queries, e.g., single-source reachability query and earliest-arrival path query. Extensive experiments on 16 real-world graphs demonstrate the effectiveness and efficiency of our proposed techniques.