3,888 research outputs found
Approximate Set Union Via Approximate Randomization
We develop an randomized approximation algorithm for the size of set union
problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list
of sets with approximate set size for with , and biased random generators
with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over
|A_i|}\right] for each input set and element where . The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup
A_m\arrowvert is in the range for any , where
. The complexity of the algorithm
is measured by both time complexity, and round complexity. The algorithm is
allowed to make multiple membership queries and get random elements from the
input sets in one round. Our algorithm makes adaptive accesses to input sets
with multiple rounds. Our algorithm gives an approximation scheme with
O(\setCount\cdot(\log \setCount)^{O(1)}) running time and rounds,
where is the number of sets. Our algorithm can handle input sets that can
generate random elements with bias, and its approximation ratio depends on the
bias. Our algorithm gives a flexible tradeoff with time complexity
O\left(\setCount^{1+\xi}\right) and round complexity for any
The Impact of Online Service Recovery on Customer Satisfaction: Empirical Evidences from Service Operations
Online service recovery tools such as managerial responses are increasingly used by service providers to address customer concerns in online WOM platforms. In this paper, we analyze the effectiveness of such online service recovery effort on customer satisfaction using data retrieved from a major online travel agency in China. We find that online service recovery is highly effective among the least satisfied customers but has limited influence on other customers. Moreover, we show that the public nature of online service recovery introduces a new dynamic among customers. While online service recovery increases future satisfaction of the complaining customers who receive the recovery effort, it significantly decreases future satisfaction of those complaining customers who observe but do not receive the recovery effort. We show the result is consistent with the peer-induced fairness theory. In addition, this study reveals that a customer’s satisfaction with a service provider demonstrates mean reversion over multiple interactions. It is important to control for such dependence in assessing the true impact of online service recovery
Evaluating Feynman integrals by the hypergeometry
The hypergeometric function method naturally provides the analytic
expressions of scalar integrals from concerned Feynman diagrams in some
connected regions of independent kinematic variables, also presents the systems
of homogeneous linear partial differential equations satisfied by the
corresponding scalar integrals. Taking examples of the one-loop and
massless functions, as well as the scalar integrals of two-loop vacuum
and sunset diagrams, we verify our expressions coinciding with the well-known
results of literatures. Based on the multiple hypergeometric functions of
independent kinematic variables, the systems of homogeneous linear partial
differential equations satisfied by the mentioned scalar integrals are
established. Using the calculus of variations, one recognizes the system of
linear partial differential equations as stationary conditions of a functional
under some given restrictions, which is the cornerstone to perform the
continuation of the scalar integrals to whole kinematic domains numerically
with the finite element methods. In principle this method can be used to
evaluate the scalar integrals of any Feynman diagrams.Comment: 39 pages, including 2 ps figure
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