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Register a new userExpressive Path Queries on Graph with Data
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Added by
Pablo Barcelo
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Graph data models have recently become popular owing to their applications, e.g., in social networks and the semantic web. Typical navigational query languages over graph databases - such as Conjunctive Regular Path Queries (CRPQs) - cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable to WL in terms of expressive power.
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We investigate the query evaluation problem for fixed queries over fully dynamic databases, where tuples can be inserted or deleted. The task is to design a dynamic algorithm that immediately reports the new result of a fixed query after every database update. We consider queries in first-order logic (FO) and its extension with modulo-counting quantifiers (FO+MOD), and show that they can be efficiently evaluated under updates, provided that the dynamic database does not exceed a certain degree bound. In particular, we construct a data structure that allows to answer a Boolean FO+MOD query and to compute the size of the result of a non-Boolean query within constant time after every database update. Furthermore, after every update we are able to immediately enumerate the new query result with constant delay between the output tuples. The time needed to build the data structure is linear in the size of the database. Our results extend earlier work on the evaluation of first-order queries on static databases of bounded degree and rely on an effective Hanf normal form for FO+MOD recently obtained by Heimberg, Kuske, and Schweikardt (LICS 2016).
A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time 11 a.m. and duration 7 mins. Temporal graphs can be used to model many networks with time-related activities, but efficient algorithms for analyzing temporal graphs are severely inadequate. We study fundamental problems such as answering reachability and time-based path queries in a temporal graph, and propose an efficient indexing technique specifically designed for processing these queries in a temporal graph. Our results show that our method is efficient and scalable in both index construction and query processing.
Structural indexing is an approach to accelerating query evaluation, whereby data objects are partitioned and indexed reflecting the precise expressive power of a given query language. Each partition block of the index holds exactly those objects that are indistinguishable with respect to queries expressible in the language. Structural indexes have proven successful for XML, RDF, and relational data management. In this paper we study structural indexing for conjunctive path queries (CPQ). CPQ forms the core of contemporary graph query languages such as SPARQL, Cypher, PGQL, and G-CORE. CPQ plays the same fundamental role with respect to contemporary graph query languages as the classic conjunctive queries play for SQL. We develop the first practical structural indexes for this important query language. In particular, we propose a structural index based on k-path-bisimulation, tightly coupled to the expressive power of CPQ, and develop algorithms for efficient query processing with our index. Furthermore, we study workload-aware structural indexes to reduce both the construction and space costs according to a given workload. We demonstrate through extensive experiments using real and synthetic graphs that our methods accelerate query processing by up to multiple orders of magnitude over the state-of-the-art methods, without increasing index size.
Marx (STOC~2010, J.~ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class $Phi$ of Boolean CQs of bounded submodular width, the model-checking problem for $Phi$ on the class of all finite structures is fixed-parameter tractable (FPT). Note that for non-Boolean queries, the size of the query result may be far too large to be computed entirely within FPT time. We investigate the free-connex variant of submodular width and generalise Marxs result to non-Boolean queries as follows: For every class $Phi$ of CQs of bounded free-connex submodular width, within FPT-preprocessing time we can build a data structure that allows to enumerate, without repetition and with constant delay, all tuples of the query result. Our proof builds upon Marxs splitting routine to decompose the query result into a union of results; but we have to tackle the additional technical difficulty to ensure that these can be enumerated efficiently.
Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be divided into two categories: spatial-coherence-based methods and vertex-importance-based approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a state-of-the-art technique was examined based on a faulty implementation that led to incorrect query results. To address the above issues, this paper presents a comprehensive comparison of the most advanced spatial-coherence-based and vertex-importance-based approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios.
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