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Approximating k-Center with Outliers in the Sliding Window Model

Mostafavi, Ali | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51102 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Zarrabi Zadeh, Hamid
  7. Abstract:
  8. With the emergence of massive datasets, storing all of the data in memory is not feasible for many problems. This fact motivated the introduction of new data processing models such as the streaming model. In this model, data points arrive one by one and the available memory is too small to store all of the data points. For many problems, more recent data points are more important than the old ones. The sliding window model captures this fact by trying to find the solution for the n most recent data points using only o(n) memory. The k-center problem is an important optimization problem in which given a graph, we are interested in labeling k vertices of the graph as centers such that the maximum distance of all vertices to closest center is minimized. One of the major deterrents of more widespread use of the k-center problem in practice is its sensitivity to outliers to the point that even a small number of outlier points can increase the optimal radius unboundedly. This lead to the introduction of k center problem with outliers where we are able to ignore some of the points by labeling them as outliers. In this thesis, we try to develop approximation algorithms for the k-center problem with outliers in the sliding window model. First, we study the case where k=1 and we develop a 2-approximation algorithm for the Euclidean space and a (3+\epsilon)-approximation algortihm for general metric spaces. We also show that if the doubling dimension of the metric space is a known constant, the approximation ratio can be reduced to 2+ε. Next, we present an (8+ε)-approximation algorithm for all k and we show that it is possible to reduce the approximation factor to 3+ε in metric spaces with constant doubling dimension. We also prove a lower bound showing that our algorithm is almost space-optimal. Finally, we show that if we are allowed to approximate the number of outliers in addition to radius, it is possible to beat our lower bound, by developing a bi-criterial approximation algorithm with approximation factor 1+ on the number of outliers and 14+ε on the radius
  9. Keywords:
  10. Approximate Algorithm ; Outliers ; Sliding Window ; Computational Geometry ; Metric Space ; K-Center Problem

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