36,331 research outputs found
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Energy Efficient Ant Colony Algorithms for Data Aggregation in Wireless Sensor Networks
In this paper, a family of ant colony algorithms called DAACA for data
aggregation has been presented which contains three phases: the initialization,
packet transmission and operations on pheromones. After initialization, each
node estimates the remaining energy and the amount of pheromones to compute the
probabilities used for dynamically selecting the next hop. After certain rounds
of transmissions, the pheromones adjustment is performed periodically, which
combines the advantages of both global and local pheromones adjustment for
evaporating or depositing pheromones. Four different pheromones adjustment
strategies are designed to achieve the global optimal network lifetime, namely
Basic-DAACA, ES-DAACA, MM-DAACA and ACS-DAACA. Compared with some other data
aggregation algorithms, DAACA shows higher superiority on average degree of
nodes, energy efficiency, prolonging the network lifetime, computation
complexity and success ratio of one hop transmission. At last we analyze the
characteristic of DAACA in the aspects of robustness, fault tolerance and
scalability.Comment: To appear in Journal of Computer and System Science
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