Finding path motifs in large temporal graphs using algebraic fingerprints

Thejaswi, Suhas; Gionis, Aristides; Lauri, Juho

doi:10.48550/arxiv.2001.07158

Cited by 1 publication

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More recently, Thejaswi et al [32] extended the sieving technique to solve a family of pattern-detection problems in temporal graphs. They also presented a vertex-localized variant of the sieve and a memory-efficient implementation that can scale to graphs with one billion edges [33].…”

Section: Related Workmentioning

confidence: 99%

“…This re-design of the polynomial evaluation scheme improves the runtime for solving the temporal-path problems described in previous work [32,33], where they search for a temporal path that contains colors specified in the query. Our approach reduces log 𝜏 queries by replacing the decision oracle of Thejaswi et al [33] with our fine-grained oracle, there by reducing the asymptotic complexity of running time to detect an optimal solution for problems in earlier work [32,33] from 𝒪 (2 ℓ ℓ (𝑛𝜏 +𝑚) log 𝜏) to 𝒪 (2 ℓ ℓ (𝑛𝜏 +𝑚)). Using a decision oracle instead of a fine-grained oracle, we require at least 𝜏 queries to obtain the list of reachable timestamps r 𝑢 for each vertex 𝑢 ∈ 𝑉 .…”

Section: A Fine-grained Decision Oraclementioning

confidence: 99%

“…However, enabling such computation requires 𝒪 (𝑛𝜏𝑘) space. The fine-grained oracle reports the existence of a restless path with a YES/NO answer, in many cases we also need to extract a solution, for which we can make use of the approaches described in previous work [9,33] using the fine-grained oracle as a subroutine. Note that our algorithm can handle a general case where each vertex is associated with a set of colors and the vertex can match to one of the associated colors enabling wild-card entries.…”

Section: Extending the Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

Restless reachability problems in temporal graphs

Thejaswi¹,

Lauri²,

Gionis³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We study a family of temporal reachability problems under waiting-time restrictions. In particular, given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via a time-respecting path, and such that the difference in timestamps between consecutive edges is at most a resting time. This kind of problems have several interesting applications in understanding the spread of a disease in a network, tracing contacts in epidemic outbreaks, and finding signaling pathways in the brain network.We present an algebraic algorithm based on constrained multilinear sieving for solving the restless reachability problems we propose. With an open-source implementation we demonstrate that the algorithm can scale to large temporal graphs with tens of millions of edges, despite the problem being NP-hard. The implementation is efficiently engineered and highly optimized. For instance, we can solve the restless reachability problem by restricting the path length to 9 in a real-world graph dataset with over 36 million directed edges in less than one hour on a 4-core Haswell desktop.

show abstract

Section: Related Workmentioning

confidence: 99%