27,323 research outputs found
New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification
We discover new P-time computable six-vertex models on planar graphs beyond
Kasteleyn's algorithm for counting planar perfect matchings. We further prove
that there are no more: Together, they exhaust all P-time computable six-vertex
models on planar graphs, assuming #P is not P. This leads to the following
exact complexity classification: For every parameter setting in
for the six-vertex model, the partition function is either (1) computable in
P-time for every graph, or (2) #P-hard for general graphs but computable in
P-time for planar graphs, or (3) #P-hard even for planar graphs. The
classification has an explicit criterion. The new P-time cases in (2) provably
cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local
connection to #CSP, defined in terms of a "loop space".
This is the first substantive advance toward a planar Holant classification
with not necessarily symmetric constraints. We introduce M\"obius
transformation on as a powerful new tool in hardness proofs for
counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202
Approximability of the Eight-Vertex Model
We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs. The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively studied models in statistical physics, and can be stated as a problem of counting weighted orientations in graph theory. Our result concerns the approximability of the partition function on all 4-regular graphs, classified according to the parameters of the model. Our complexity results conform to the phase transition phenomenon from physics.
We introduce a quantum decomposition of the eight-vertex model and prove a set of closure properties in various regions of the parameter space. Furthermore, we show that there are extra closure properties on 4-regular planar graphs. These regions of the parameter space are concordant with the phase transition threshold. Using these closure properties, we derive polynomial time approximation algorithms via Markov chain Monte Carlo. We also show that the eight-vertex model is NP-hard to approximate on the other side of the phase transition threshold
DHLP 1&2: Giraph based distributed label propagation algorithms on heterogeneous drug-related networks
Background and Objective: Heterogeneous complex networks are large graphs
consisting of different types of nodes and edges. The knowledge extraction from
these networks is complicated. Moreover, the scale of these networks is
steadily increasing. Thus, scalable methods are required. Methods: In this
paper, two distributed label propagation algorithms for heterogeneous networks,
namely DHLP-1 and DHLP-2 have been introduced. Biological networks are one type
of the heterogeneous complex networks. As a case study, we have measured the
efficiency of our proposed DHLP-1 and DHLP-2 algorithms on a biological network
consisting of drugs, diseases, and targets. The subject we have studied in this
network is drug repositioning but our algorithms can be used as general methods
for heterogeneous networks other than the biological network. Results: We
compared the proposed algorithms with similar non-distributed versions of them
namely MINProp and Heter-LP. The experiments revealed the good performance of
the algorithms in terms of running time and accuracy.Comment: Source code available for Apache Giraph on Hadoo
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