Abstract
Computing shortest-path distances is a fundamental primitive in the context of graph data mining, since this kind of information is essential in a broad range of prominent applications, which include social network analysis, data routing, web search optimization, database design and route planning. Standard algorithms for shortest paths (e.g., Dijkstra’s) do not scale well with the graph size, as they take more than a second or huge memory overheads to answer a single query on the distance for large-scale graph datasets. Hence, they are not suited to mine distances from big graphs, which are becoming the norm in most modern application contexts. Therefore, to achieve faster query answering, smarter and more scalable methods have been designed, the most effective of them based on precomputing and querying a compact representation of the transitive closure of the input graph, called the 2-hop-cover labeling. To use such approaches in realistic time-evolving scenarios, when the managed graph undergoes topological modifications over time, specific dynamic algorithms, carefully updating the labeling as the graph evolves, have been introduced. In fact, recomputing from scratch the 2-hop-cover structure every time the graph changes is not an option, as it induces unsustainable time overheads. While the state-of-the-art dynamic algorithm to update a 2-hop-cover labeling against incremental modifications (insertions of arcs/vertices, arc weights decreases) offers very fast update times, the only known solution for decremental modifications (deletions of arcs/vertices, arc weights increases) is still far from being considered practical, as it requires up to tens of seconds of processing per update in several prominent classes of real-world inputs, as experimentation shows. In this paper, we introduce a new dynamic algorithm to update 2-hop-cover labelings against decremental changes. We prove its correctness, formally analyze its worst-case performance, and assess its effectiveness through an experimental evaluation employing both real-world and synthetic inputs. Our results show that it improves, by up to several orders of magnitude, upon average update times of the only existing decremental algorithm, thus representing a step forward towards real-time distance mining in general, massive time-evolving graphs.
Highlights
Mining shortest-path distances is universally considered one of the most fundamental operation to be performed on graph data, due to the wide range of applications it finds
For 2- HOP - COVER labelings, two dynamic algorithms that do not compromise on query performance are known, both employing the common strategy of identifying and updating only the part of the labeling that is compromised by a graph change
Both have been combined and tested as a single fully dynamic algorithm in [26]. While the former exhibits extremely low update times that are compatible with real-time applications, the latter is slower, and sometimes only slightly better, on average, than the recomputation from scratch in some categories of input instances that are highly relevant to application domains, e.g., sparse weighted graphs. We focus on this latter issue and try to overcome the above limiting factor of BIDIR –2 HC by introducing a new dynamic algorithm, called QUEUE –2 HC, to update 2- HOP - COVER
Summary
Mining shortest-path distances is universally considered one of the most fundamental operation to be performed on graph data, due to the wide range of applications it finds. In the last few years, researchers have worked to adapt known methods, for mining (generic) properties from static graphs, to function in such time-evolving scenarios through the design of specific dynamic algorithms, i.e., algorithms that are able to update the preprocessed data to reflect graph changes without performing any full recomputation from scratch [8,14,17,24,25,26,27,30,31] Such algorithms are typically divided in two broad categories, namely incremental and decremental algorithms, depending on whether they able to handle incremental updates only (i.e., insertion of vertices/arcs and arc weight decreases) or decremental updates only (deletion of vertices/arcs and arc weight increases). Please note that the investigation on dynamic algorithms can have a general graph theoretical interest since, often, studying how decremental changes affect shortest paths can have applications to static graphs problems or other contexts (see, e.g., works on multi-commodity flows or cut problems [34])
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