107,379 research outputs found
Capturing Topology in Graph Pattern Matching
Graph pattern matching is often defined in terms of subgraph isomorphism, an
NP-complete problem. To lower its complexity, various extensions of graph
simulation have been considered instead. These extensions allow pattern
matching to be conducted in cubic-time. However, they fall short of capturing
the topology of data graphs, i.e., graphs may have a structure drastically
different from pattern graphs they match, and the matches found are often too
large to understand and analyze. To rectify these problems, this paper proposes
a notion of strong simulation, a revision of graph simulation, for graph
pattern matching. (1) We identify a set of criteria for preserving the topology
of graphs matched. We show that strong simulation preserves the topology of
data graphs and finds a bounded number of matches. (2) We show that strong
simulation retains the same complexity as earlier extensions of simulation, by
providing a cubic-time algorithm for computing strong simulation. (3) We
present the locality property of strong simulation, which allows us to
effectively conduct pattern matching on distributed graphs. (4) We
experimentally verify the effectiveness and efficiency of these algorithms,
using real-life data and synthetic data.Comment: VLDB201
New Classes of Distributed Time Complexity
A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al.
(FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang &
Pettie (FOCS 2017) -- have advanced our understanding of one of the most
fundamental questions in theory of distributed computing: what are the possible
time complexity classes of LCL problems in the LOCAL model? In essence, we have
a graph problem in which a solution can be verified by checking all
radius- neighbourhoods, and the question is what is the smallest such
that a solution can be computed so that each node chooses its own output based
on its radius- neighbourhood. Here is the distributed time complexity of
.
The time complexity classes for deterministic algorithms in bounded-degree
graphs that are known to exist by prior work are , , , , and . It is also known
that there are two gaps: one between and , and
another between and . It has been conjectured
that many more gaps exist, and that the overall time hierarchy is relatively
simple -- indeed, this is known to be the case in restricted graph families
such as cycles and grids.
We show that the picture is much more diverse than previously expected. We
present a general technique for engineering LCL problems with numerous
different deterministic time complexities, including
for any , for any , and
for any in the high end of the complexity
spectrum, and for any ,
for any , and
for any in the low end; here
is a positive rational number
- ā¦