A Kernel Search Algorithm for Virtual Machine Consolidation Problem

Virtual machine consolidation describes the process of reallocation of virtual machines (VMs) on a set of target servers. It can be formulated as a mixed integer linear programming problem which is proven to be an NP-hard problem. In this paper, we propose a kernel search (KS) heuristic algorithm based on hard variable fixing to quickly obtain a high-quality solution for large-scale virtual machine consolidation problems (VMCPs). Since variable fixing strategies in existing KS works may make VMCP infeasible, our proposed KS algorithm employs a more efficient strategy to choose a set of fixed variables according to the corresponding reduced cost. Numerical results on VMCP instances demonstrate that our proposed KS algorithm significantly outperforms the state-of-the-art mixed integer linear programming solver in terms of CPU time, and our proposed strategy of variable fixing significantly improves the efficiency of the KS algorithm as well as the degradation of solution quality can be negligible.Comment: 17 pages, 3 figure

Theory for charge and orbital density-wave states in manganite La0.5_{0.5}Sr1.5_{1.5}MnO4_4

We investigate the high temperature phase of layered manganites, and demonstrate that the charge-orbital phase transition without magnetic order in La$_{0.5}$Sr$_{1.5}$MnO$_4$ can be understood in terms of the density wave instability. The orbital ordering is found to be induced by the nesting between segments of Fermi surface with different orbital characters. The simultaneous charge and orbital orderings are elaborated with a mean field theory. The ordered orbitals are shown to be $d_{x^2-y^2} \pm d_{3z^2-r^2}$.Comment: published versio

1-(3-Chloro-2-pyrid­yl)-3-methyl-1H-pyrazole-5-carboxylic acid

In the title mol­ecule, C10H8ClN3O2, the dihedral angle between the pyridine and pyrazole rings is 64.01 (8)°. In the crystal structure, inter­molecular O—H⋯N hydrogen bonds link mol­ecules, forming extended chains along [001]. These chains are, in turn, linked by weak inter­molecular C—H⋯O inter­actions, forming a two-dimensional network perpendicular to the b axis

Ethyl 2-(2-hy­droxy-5-nitro­phen­yl)acetate

In the crystal structure of the title compound, C10H11NO5, inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into chains along the b-axis direction. Weak C—H.·O hydrogen bonds also occur