918 research outputs found
Mining Patterns in Networks using Homomorphism
In recent years many algorithms have been developed for finding patterns in
graphs and networks. A disadvantage of these algorithms is that they use
subgraph isomorphism to determine the support of a graph pattern; subgraph
isomorphism is a well-known NP complete problem. In this paper, we propose an
alternative approach which mines tree patterns in networks by using subgraph
homomorphism. The advantage of homomorphism is that it can be computed in
polynomial time, which allows us to develop an algorithm that mines tree
patterns in arbitrary graphs in incremental polynomial time. Homomorphism
however entails two problems not found when using isomorphism: (1) two patterns
of different size can be equivalent; (2) patterns of unbounded size can be
frequent. In this paper we formalize these problems and study solutions that
easily fit within our algorithm
Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs
Many problems in areas as diverse as recommendation systems, social network
analysis, semantic search, and distributed root cause analysis can be modeled
as pattern search on labeled graphs (also called "heterogeneous information
networks" or HINs). Given a large graph and a query pattern with node and edge
label constraints, a fundamental challenge is to nd the top-k matches ac-
cording to a ranking function over edge and node weights. For users, it is di
cult to select value k . We therefore propose the novel notion of an any-k
ranking algorithm: for a given time budget, re- turn as many of the top-ranked
results as possible. Then, given additional time, produce the next lower-ranked
results quickly as well. It can be stopped anytime, but may have to continues
until all results are returned. This paper focuses on acyclic patterns over
arbitrary labeled graphs. We are interested in practical algorithms that
effectively exploit (1) properties of heterogeneous networks, in particular
selective constraints on labels, and (2) that the users often explore only a
fraction of the top-ranked results. Our solution, KARPET, carefully integrates
aggressive pruning that leverages the acyclic nature of the query, and
incremental guided search. It enables us to prove strong non-trivial time and
space guarantees, which is generally considered very hard for this type of
graph search problem. Through experimental studies we show that KARPET achieves
running times in the order of milliseconds for tree patterns on large networks
with millions of nodes and edges.Comment: To appear in WWW 201
Challenges in Bridging Social Semantics and Formal Semantics on the Web
This paper describes several results of Wimmics, a research lab which names
stands for: web-instrumented man-machine interactions, communities, and
semantics. The approaches introduced here rely on graph-oriented knowledge
representation, reasoning and operationalization to model and support actors,
actions and interactions in web-based epistemic communities. The re-search
results are applied to support and foster interactions in online communities
and manage their resources
Expectation-Complete Graph Representations with Homomorphisms
We investigate novel random graph embeddings that can be computed in expected
polynomial time and that are able to distinguish all non-isomorphic graphs in
expectation. Previous graph embeddings have limited expressiveness and either
cannot distinguish all graphs or cannot be computed efficiently for every
graph. To be able to approximate arbitrary functions on graphs, we are
interested in efficient alternatives that become arbitrarily expressive with
increasing resources. Our approach is based on Lov\'asz' characterisation of
graph isomorphism through an infinite dimensional vector of homomorphism
counts. Our empirical evaluation shows competitive results on several benchmark
graph learning tasks.Comment: accepted for publication at ICML 202
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