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101.
In this paper we consider the natural generalizations of two fundamental problems, the Set-Cover problem and the Min-Knapsack problem. We are given a hypergraph, each vertex of which has a nonnegative weight, and each edge of which has a nonnegative length. For a given threshold
, our objective is to find a subset of the vertices with minimum total cost, such that at least a length of
of the edges is covered. This problem is called the partial set cover problem. We present an O(|V|2 + |H|)-time, ΔE-approximation algorithm for this problem, where ΔE ≥ 2 is an upper bound on the edge cardinality of the hypergraph and |H| is the size of the hypergraph (i.e., the sum of all its edges cardinalities). The special case where ΔE = 2 is called the partial vertex cover problem. For this problem a 2-approximation was previously known, however, the time complexity of our solution, i.e., O(|V|2), is a dramatic improvement.We show that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation. Now, using the local-ratio technique, it is sufficient to repeatedly subtract a homogeneous weight function from the given weight function. 相似文献
102.
Mazar R 《The Journal of the Acoustical Society of America》2002,111(2):809-822
When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media. 相似文献
103.
We present two randomized entropy-based algorithms for approximating quite general #P-complete counting problems, like the
number of Hamiltonian cycles in a graph, the permanent, the number of self-avoiding walks and the satisfiability problem.
In our algorithms we first cast the underlying counting problem into an associate rare-event probability estimation, and then
apply dynamic importance sampling (IS) to estimate efficiently the desired counting quantity. We construct the IS distribution
by using two different approaches: one based on the cross-entropy (CE) method and the other one on the stochastic version
of the well known minimum entropy (MinxEnt) method. We also establish convergence of our algorithms and confidence intervals
for some special settings and present supportive numerical results, which strongly suggest that both ones (CE and MinxEnt)
have polynomial running time in the size of the problem. 相似文献
104.
Exact numerical solution of a one-dimensional three-level lasing system (homogeneously broadened) is used to establish the relevance of spatially independent rate equations. It is shown that these equations can be applied not only for unsaturated lasing media but also for highly saturated media. However the loss term and the correlation term have to be modified. 相似文献
105.
We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions. 相似文献
106.
Quasi-invariant domain constants 总被引:3,自引:0,他引:3
Five domain constants are studied in our paper, all related to the hyperbolic geometry in hyperbolic plane regions which are
uniformly perfect (in Pommerenke’s terminology). Relations among these domain constants are obtained, from which bounds are
derived for the variance ratio of each constant under conformal mappings of the regions, and we also show that each constant
may be used to characterize uniformly perfect regions.
The authors wish to thank the University of California, San Diego for its hospitality during the 1988–89 academic year when
this research was begun.
Supported by the Landau Center for Mathematical Research in Analysis.
Research partially supported by NSF Grant No. DMS-8801439. 相似文献
107.
108.
This paper explores an approximate method for solving a routing problem in a four-level distribution which has “double-ended” demand. Routes are represented as columns in a linear program and column generation is used to improve the solution by generating new routes. The generation of new routes is based on an LP sub-problem. Its solution is rounded down to integer values to insure its feasibility as a route for inclusion in the restricted master problem. Finally, an illustrative problem is solved. 相似文献
109.
Reuven Harmelin 《Israel Journal of Mathematics》1982,43(3):244-254
Several properties of a certain series of differential operators which are invariant under the Möbius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established. 相似文献
110.