7,007 research outputs found
Rooted Spiral Trees on Hyper-cubical lattices
We study rooted spiral trees in 2,3 and 4 dimensions on a hyper cubical
lattice using exact enumeration and Monte-Carlo techniques. On the square
lattice, we also obtain exact lower bound of 1.93565 on the growth constant
. Series expansions give and on a square lattice. With Monte-Carlo simulations we get the
estimates as , and . These results
are numerical evidence against earlier proposed dimensional reduction by four
in this problem. In dimensions higher than two, the spiral constraint can be
implemented in two ways. In either case, our series expansion results do not
support the proposed dimensional reduction.Comment: replaced with published versio
Finding long cycles in graphs
We analyze the problem of discovering long cycles inside a graph. We propose
and test two algorithms for this task. The first one is based on recent
advances in statistical mechanics and relies on a message passing procedure.
The second follows a more standard Monte Carlo Markov Chain strategy. Special
attention is devoted to Hamiltonian cycles of (non-regular) random graphs of
minimal connectivity equal to three
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
- …