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Abstract. A subset A of the vertices of a graph G is an asteroidal set if for each vertex a ∈ A a connected component of G-N[a] exists containing A\backslash{a} . An asteroidal set of cardinality three is called asteriodal triple and graphs without an asteriodal triple are called AT-free . The maximum cardinality of an asteroidal set of G , denoted by \an(G) , is said to be the asteriodal number of G . We present a scheme for designing algorithms for triangulation problems on graphs. As a consequence, we obtain algorithms
to compute graph parameters such as treewidth, minimum fill-in and vertex ranking number. The running time of these algorithms
is a polynomial (of degree asteriodal number plus a small constant) in the number of vertices and the number of minimal separators
of the input graph. 相似文献
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Fixed Parameter Algorithms for DOMINATING SET and Related Problems on Planar Graphs 总被引:12,自引:0,他引:12
Abstract. We present an algorithm that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) , where c=4^ 6\sqrt 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ (G) is O(\sqrt \rule 0pt 4pt \smash γ (G) ) , and that such a tree decomposition can be found in O(\sqrt \rule 0pt 4pt \smash γ (G) n) time. The same technique can be used to show that the k -FACE COVER problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c
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^ \sqrt k n) time, where c
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=3^ 36\sqrt 34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of k -DOMINATING SET, e.g., k -INDEPENDENT DOMINATING SET and k -WEIGHTED DOMINATING SET. 相似文献
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MX Li SM Gagné L Spyracopoulos CP Kloks G Audette M Chandra RJ Solaro LB Smillie BD Sykes 《Canadian Metallurgical Quarterly》1997,36(41):12519-12525
Ca2+ binding to the N-domain of skeletal muscle troponin C (sNTnC) induces an "opening" of the structure [Gagné, S. M., et al. (1995) Nat. Struct. Biol. 2, 784-789], which is typical of Ca2+-regulatory proteins. However, the recent structures of the E41A mutant of skeletal troponin C (E41A sNTnC) [Gagné, S. M., et al. (1997) Biochemistry 36, 4386-4392] and of cardiac muscle troponin C (cNTnC) [Sia, S. K., et al. (1997) J. Biol. Chem. 272, 18216-18221] reveal that both of these proteins remain essentially in the "closed" conformation in their Ca2+-saturated states. Both of these proteins are modified in Ca2+-binding site I, albeit differently, suggesting a critical role for this region in the coupling of Ca2+ binding to the induced structural change. To understand the mechanism and the energetics involved in the Ca2+-induced structural transition, Ca2+ binding to E41A sNTnC and to cNTnC have been investigated by using one-dimensional 1H and two-dimensional {1H,15N}-HSQC NMR spectroscopy. Monitoring the chemical shift changes during Ca2+ titration of E41A sNTnC permits us to assign the order of stepwise binding as site II followed by site I and reveals that the mutation reduced the Ca2+ binding affinity of the site I by approximately 100-fold [from KD2 = 16 microM [sNTnC; Li, M. X., et al. (1995) Biochemistry 34, 8330-8340] to 1.3 mM (E41A sNTnC)] and of the site II by approximately 10-fold [from KD1 = 1.7 microM (sNTnC) to 15 microM (E41A sNTnC)]. Ca2+ titration of cNTnC confirms that cNTnC binds only one Ca2+ with a determined dissociation constant KD of 2.6 microM. The Ca2+-induced chemical shift changes occur over the entire sequence in cNTnC, suggesting that the defunct site I is perturbed when site II binds Ca2+. These measurements allow us to dissect the mechanism and energetics of the Ca2+-induced structural changes. 相似文献
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A subset A of the vertices of a graph G is an asteroidal set if for each vertex a ∈ A a connected component of G-N[a] exists containing A\backslash{a} . An asteroidal set of cardinality three is called asteriodal triple and graphs without an asteriodal triple are called AT-free . The maximum cardinality of an asteroidal set of G , denoted by \an(G) , is said to be the asteriodal number of G . We present a scheme for designing algorithms for triangulation problems on graphs. As a consequence, we obtain algorithms to compute graph parameters such as treewidth, minimum fill-in and vertex ranking number. The running time of these algorithms is a polynomial (of degree asteriodal number plus a small constant) in the number of vertices and the number of minimal separators of the input graph. 相似文献
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