281 research outputs found
Arboricity, h-Index, and Dynamic Algorithms
In this paper we present a modification of a technique by Chiba and Nishizeki
[Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J.
Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure
suitable for dynamic graph algorithms. We employ the data structure to
formulate new algorithms for several problems, including counting subgraphs of
four vertices, recognition of diamond-free graphs, cop-win graphs and strongly
chordal graphs, among others. We improve the time complexity for graphs with
low arboricity or h-index.Comment: 19 pages, no figure
DDSL: Efficient Subgraph Listing on Distributed and Dynamic Graphs
Subgraph listing is a fundamental problem in graph theory and has wide
applications in areas like sociology, chemistry, and social networks. Modern
graphs can usually be large-scale as well as highly dynamic, which challenges
the efficiency of existing subgraph listing algorithms. Recent works have shown
the benefits of partitioning and processing big graphs in a distributed system,
however, there is only few work targets subgraph listing on dynamic graphs in a
distributed environment. In this paper, we propose an efficient approach,
called Distributed and Dynamic Subgraph Listing (DDSL), which can incrementally
update the results instead of running from scratch. DDSL follows a general
distributed join framework. In this framework, we use a Neighbor-Preserved
storage for data graphs, which takes bounded extra space and supports dynamic
updating. After that, we propose a comprehensive cost model to estimate the I/O
cost of listing subgraphs. Then based on this cost model, we develop an
algorithm to find the optimal join tree for a given pattern. To handle dynamic
graphs, we propose an efficient left-deep join algorithm to incrementally
update the join results. Extensive experiments are conducted on real-world
datasets. The results show that DDSL outperforms existing methods in dealing
with both static dynamic graphs in terms of the responding time
Document Retrieval on Repetitive Collections
Document retrieval aims at finding the most important documents where a
pattern appears in a collection of strings. Traditional pattern-matching
techniques yield brute-force document retrieval solutions, which has motivated
the research on tailored indexes that offer near-optimal performance. However,
an experimental study establishing which alternatives are actually better than
brute force, and which perform best depending on the collection
characteristics, has not been carried out. In this paper we address this
shortcoming by exploring the relationship between the nature of the underlying
collection and the performance of current methods. Via extensive experiments we
show that established solutions are often beaten in practice by brute-force
alternatives. We also design new methods that offer superior time/space
trade-offs, particularly on repetitive collections.Comment: Accepted to ESA 2014. Implementation and experiments at
http://www.cs.helsinki.fi/group/suds/rlcsa
Fast Quasi-Threshold Editing
We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the
quasi-threshold (also called trivially perfect) graph editing problem with edge
insertion and deletion. Given a graph it computes a quasi-threshold graph which
is close in terms of edit count. This edit problem is NP-hard. We present an
extensive experimental study, in which we show that QTM is the first algorithm
that is able to scale to large real-world graphs in practice. As a side result
we further present a simple linear-time algorithm for the quasi-threshold
recognition problem.Comment: 26 pages, 4 figures, submitted to ESA 201
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