Matroid and Knapsack Center Problems
Danny Z. Chen, Jian Li, Hongyu Liang, Haitao Wang

TL;DR
This paper explores generalized $k$-center problems involving matroid and knapsack constraints, providing approximation algorithms and hardness results relevant to content distribution networks.
Contribution
It introduces approximation algorithms for matroid and knapsack center problems, including outlier versions, and establishes hardness results for multi-constraint cases.
Findings
3-approximation for matroid center problem on general metrics
7-approximation for matroid outlier problem
Polynomial-time 3-approximate algorithm for multi-knapsack center with constraint violation
Abstract
In the classic -center problem, we are given a metric graph, and the objective is to open nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of -center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version.…
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Taxonomy
TopicsFacility Location and Emergency Management · Optimization and Search Problems · Complexity and Algorithms in Graphs
