In this paper, we study a family of clustering problems that require error-resilient solutions which are also robust against the presence of outlier connections . We consider several variants of the robust fault-tolerant k-center, matroid center and knapsack center problems , and develop pure or multi-criteria approximation algorithms for them. Unfairness is common for some clients and they may always be regarded as outliers, so we also consider the fairness problem, and give randomized algorithms that embody lottery models, so that for each client j with its submitted parameter e_j%DIFDELCMD < \geq0%%% , the expected number of connections for it is at least e_j. Our techniques include the design of various linear programs for rounding LP solutions, as well as a primal-dual schema using the ellipsoid algorithm .
We study a family of clustering problems that require fault-tolerant solutions that are also robust with the presence of outliers . We consider robust fault-tolerant k-center, matroid center and knapsack center , and develop pure or multi-criteria approximation algorithms for them. In order to address the fairness concern, we also consider variants of the aforementioned problems, namely fair robust fault-tolerant center problems. In these problems, each client j %DIFDELCMD < \geq0%%% has a value e_j, and we need to stochastically open a set of facilities such that the expected number of facilities that are assigned to j is at least e_j. We develop a pure approximation for fair robust fault-tolerant k-center and multi-criteria approximation algorithms for the knapsack and matroid variations .
R
In this paper, we
We
R
error-resilient solutions which
fault-tolerant solutions that
R
against
with
R
outlier connections
outliers
D
several variants of the
D
problems
R
Unfairness is common for some clients and they may always be regarded as outliers, so
In order to address the fairness concern,
R
the fairness problem, and give randomized algorithms that embody lottery models, so that for
variants of the aforementioned problems, namely fair robust fault-tolerant center problems. In these problems,
D
with its submitted parameter e_j
R
,
has a value e_j, and we need to stochastically open a set of facilities such that
R
connections for it
facilities that are assigned to j
R
Our techniques include the design of various linear programs for rounding LP solutions, as well as a primal-dual schema using the ellipsoid algorithm
We develop a pure approximation for fair robust fault-tolerant k-center and multi-criteria approximation algorithms for the knapsack and matroid variations