Visible to Intel only — GUID: GUID-38887CF2-7380-47B5-B160-A382AC6CFC9A
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
cor_dense_batch.cpp
cov_dense_batch.cpp
dbscan_brute_force_batch.cpp
df_cls_hist_batch.cpp
df_cls_hist_batch_random.cpp
df_cls_traverse_model.cpp
df_reg_hist_batch.cpp
df_reg_hist_batch_random.cpp
df_reg_traverse_model.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_reg_brute_force_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
pca_cor_dense_batch.cpp
pca_precomputed_cor_dense_batch.cpp
pca_precomputed_cov_dense_batch.cpp
rbf_kernel_dense_batch.cpp
svm_two_class_thunder_dense_batch.cpp
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
connected_components_batch.cpp
cor_dense_batch.cpp
cov_dense_batch.cpp
csr_accessor.cpp
dbscan_brute_force_batch.cpp
df_cls_dense_batch.cpp
df_reg_dense_batch.cpp
directed_graph.cpp
graph_service_functions.cpp
jaccard_batch.cpp
jaccard_batch_app.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_cls_kd_tree_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
logloss_dense_batch.cpp
louvain_batch.cpp
pca_dense_batch.cpp
pca_precomputed_dense_batch.cpp
polynomial_kernel_dense_batch.cpp
rbf_kernel_dense_batch.cpp
shortest_paths_batch.cpp
sigmoid_kernel_dense_batch.cpp
subgraph_isomorphism_batch.cpp
svm_multi_class_thunder_csr_batch.cpp
svm_multi_class_thunder_dense_batch.cpp
svm_nu_cls_thunder_csr_batch.cpp
svm_nu_cls_thunder_dense_batch.cpp
svm_nu_reg_thunder_csr_batch.cpp
svm_nu_reg_thunder_dense_batch.cpp
svm_reg_thunder_csr_batch.cpp
svm_reg_thunder_dense_batch.cpp
svm_two_class_smo_csr_batch.cpp
svm_two_class_smo_dense_batch.cpp
svm_two_class_thunder_csr_batch.cpp
svm_two_class_thunder_dense_batch.cpp
triangle_counting_batch.cpp
Mathematical Notations
Mathematical Notations
Correlation and Variance-Covariance Matrices
Mathematical Notations
Principal Components Analysis Transform
Singular Value Decomposition
Association Rules
Mathematical Notations
Mathematical Notations
Cholesky Decomposition
QR Decomposition
Outlier Detection
Distance Matrix
Distributions
Engines
Moments of Low Order
Mathematical Notations
Quality Metrics
Sorting
Normalization
Mathematical Notations
Visible to Intel only — GUID: GUID-38887CF2-7380-47B5-B160-A382AC6CFC9A
Connected Components
Connected components algorithm receives an undirected graph G as an input and searches for connected components in G. For each vertex in G, the algorithm returns the label of the component this vertex belongs to. The result of the algorithm is a set of labels for all vertices in G.
Operation |
Computational methods |
Programming Interface |
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Mathematical formulation
Computing
Given an undirected graph<Undirected graph>G, the problem is to find connected components<Component> in G, determine their quantity, and label vertices so that vertices from the same component have the same label.
Example
Сomponents are labeled from 0 to k-1, where k is the number of components. For the example above, the labels for vertices are [0, 1, 1, 1, 2, 0, 1, 3, 4, 4, 4, 4, 4].
This notation means that:
vertices with ids 0 and 5 belong to the connected component with id 0
vertices with ids 1, 2, 3, and 6 belong to the connected component with id 1
vertex with id 4 belongs to the connected component with id 2
vertex with id 7 belongs to the connected component with id 3
vertices with ids 8, 9, 10, 11, and 12 belong to the connected component with id 4
Computation method: afforest
The method defines Afforest algorithm and solves the problem of сonnected components identification in an undirected graph.
This algorithm expands the Shiloach-Vishkin connected components algorithm and uses component approximation to decrease redundant edge processing. The method consists of the following steps:
Process a fixed number of edges for each vertex (Vertex Neighbor Sampling optimization).
Identify the largest intermediate component using probabilistic method.
Process the rest of the neighborhoods only for the vertices that do not belong to the largest component (Large Component Skipping optimization).
For more details, see [Sutton2018].
Programming Interface
Refer to API Reference: Connected Components.