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Cited by 41 publications
(45 citation statements)
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“…To resolve this difficulty, we generate a chordal extension G(N, E ) of the csp graph G(N, E) and use the extended csp graph G(N, E ) instead of G(N, E). See [1,7] for chordal graphs and finding all maximal cliques.…”
Section: Correlative Sparsity Pattern Graphsmentioning
confidence: 99%
See 1 more Smart Citation
“…To resolve this difficulty, we generate a chordal extension G(N, E ) of the csp graph G(N, E) and use the extended csp graph G(N, E ) instead of G(N, E). See [1,7] for chordal graphs and finding all maximal cliques.…”
Section: Correlative Sparsity Pattern Graphsmentioning
confidence: 99%
“…, n} and the edge set E = {{i, j} : R ij = , i < j} corresponding to the nonzero offdiagonal elements of R. We call G(N, E) the correlative sparsity pattern graph (csp graph) of the POP. We employ some results of graph theory regarding maximal cliques of chordal graphs [1]. A key idea in this paper is to use the maximal cliques of a chordal extension of the csp graph G(N, E) to construct sets of supports for a sparse SOS relaxation.…”
Section: Introductionmentioning
confidence: 99%
“…The second approach emphasizes the role of chordal graphs in sparse matrix factorizations and is discussed in §4. Surveys of the theory of chordal graphs can be found in the articles [193,38] and the book [101].…”
Section: Chordal Graphmentioning
confidence: 99%
“…The induced subtree property is also referred to as the running intersection property [38] because it can be rephrased as follows. If two cliques W and W intersect, then W ∩ W is included in all the cliques on the path in the clique tree between W and W .…”
Section: Casementioning
confidence: 99%
“…If the maximum number of vertices in a minimal vertex separator is p, then the chordal graph is said to be p-chordal. For more on chordal graphs see [19].…”
mentioning
confidence: 99%