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E. Alper Yildirim Xiaofei Fan-Orzechowski 《Computational Optimization and Applications》2006,33(2-3):229-247
We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions
of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph
to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable
set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite
formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex
that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure
is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly
rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start
strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently
extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality.
This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author
was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA. 相似文献
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用Chapman-Enskog方法计算了相对论性重离子碰撞快度中心区产生的π介子物质的输运系数,并建立了相应的粘滞流体力学方程,进而讨论了粘滞对π介子物质演化过程的影响.结果表明,粘滞将减缓快度中心区π介子物质的冷却速度. 相似文献
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The hydrothermal reaction of CuBr2 and CuBr with phen·H2O (phen= 1,10-phenanthroline) in a molar ratio of 1:1:1.5 gave birth to the first copper-halo cationic cluster [Cu2^Ⅱ Cu2^Br4 (phen)4 ] ^2+(1) with tetranuclear anionic cluster [Cu4Br6]^2-. Changing the precursors or their molar ratios, two mononuclear complexes [Cu(phen)2Br]Br·H2O (2) and [Ni(phen)3][CuCl2]2 (3) as well as two unusual copper-halo chains found in polymers [Cu2Br2(phen)]∞ (4) and [Cu^ⅡCu3^ⅠBr2Ⅰ3 (phen)2 ]∞ (5) were obtained. The (Cu2Br2)∞ chain of 4 looks like a linearar ray of hexagons based on fused Cu3Br3 units, and the linear (Cu3Ⅰ3Br^-)∞ chain of 5 is an alternate combination of the rhombic Cu2I2 cores and the Cu4I4Br2^2- units. In addition, the hydrothermal reaction of CuBr2 with NA(NA=nicotinic acid) or INA (INA =isonicotinic acid) resulted in the syntheses of two compounds [CuBr(NA)] (6) and [CuBr(INA)]∞(7) containing staircase chain. Among them the third-order non-linear optical properties of 2, 5, 6 and 7 were investigated and all exhibit the reverse saturable absorption (α2〉0) and self-defocusing performance (n2〈0). 相似文献
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