1,470 research outputs found
Faster Algorithms for the Maximum Common Subtree Isomorphism Problem
The maximum common subtree isomorphism problem asks for the largest possible
isomorphism between subtrees of two given input trees. This problem is a
natural restriction of the maximum common subgraph problem, which is -hard in general graphs. Confining to trees renders polynomial time
algorithms possible and is of fundamental importance for approaches on more
general graph classes. Various variants of this problem in trees have been
intensively studied. We consider the general case, where trees are neither
rooted nor ordered and the isomorphism is maximum w.r.t. a weight function on
the mapped vertices and edges. For trees of order and maximum degree
our algorithm achieves a running time of by
exploiting the structure of the matching instances arising as subproblems. Thus
our algorithm outperforms the best previously known approaches. No faster
algorithm is possible for trees of bounded degree and for trees of unbounded
degree we show that a further reduction of the running time would directly
improve the best known approach to the assignment problem. Combining a
polynomial-delay algorithm for the enumeration of all maximum common subtree
isomorphisms with central ideas of our new algorithm leads to an improvement of
its running time from to ,
where is the order of the larger tree, is the number of different
solutions, and is the minimum of the maximum degrees of the input
trees. Our theoretical results are supplemented by an experimental evaluation
on synthetic and real-world instances
The Vadalog System: Datalog-based Reasoning for Knowledge Graphs
Over the past years, there has been a resurgence of Datalog-based systems in
the database community as well as in industry. In this context, it has been
recognized that to handle the complex knowl\-edge-based scenarios encountered
today, such as reasoning over large knowledge graphs, Datalog has to be
extended with features such as existential quantification. Yet, Datalog-based
reasoning in the presence of existential quantification is in general
undecidable. Many efforts have been made to define decidable fragments. Warded
Datalog+/- is a very promising one, as it captures PTIME complexity while
allowing ontological reasoning. Yet so far, no implementation of Warded
Datalog+/- was available. In this paper we present the Vadalog system, a
Datalog-based system for performing complex logic reasoning tasks, such as
those required in advanced knowledge graphs. The Vadalog system is Oxford's
contribution to the VADA research programme, a joint effort of the universities
of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the
main contribution of this paper, we illustrate the first implementation of
Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive
termination control strategy. We also provide a comprehensive experimental
evaluation.Comment: Extended version of VLDB paper
<https://doi.org/10.14778/3213880.3213888
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
Graph Symmetry Detection and Canonical Labeling: Differences and Synergies
Symmetries of combinatorial objects are known to complicate search
algorithms, but such obstacles can often be removed by detecting symmetries
early and discarding symmetric subproblems. Canonical labeling of combinatorial
objects facilitates easy equivalence checking through quick matching. All
existing canonical labeling software also finds symmetries, but the fastest
symmetry-finding software does not perform canonical labeling. In this work, we
contrast the two problems and dissect typical algorithms to identify their
similarities and differences. We then develop a novel approach to canonical
labeling where symmetries are found first and then used to speed up the
canonical labeling algorithms. Empirical results show that this approach
outperforms state-of-the-art canonical labelers.Comment: 15 pages, 10 figures, 1 table, Turing-10
An Algebraic View of the Relation between Largest Common Subtrees and Smallest Common Supertrees
The relationship between two important problems in tree pattern matching, the
largest common subtree and the smallest common supertree problems, is
established by means of simple constructions, which allow one to obtain a
largest common subtree of two trees from a smallest common supertree of them,
and vice versa. These constructions are the same for isomorphic, homeomorphic,
topological, and minor embeddings, they take only time linear in the size of
the trees, and they turn out to have a clear algebraic meaning.Comment: 32 page
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