Structural Iterative Rounding for Generalized k-Median Problems

by   Anupam Gupta, et al.

This paper considers approximation algorithms for generalized k-median problems. This class of problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution, with a constant number of fractional variables. The algorithm builds on the iterative rounding framework introduced by Krishnaswamy, Li, and Sandeep for k-median with outliers. The main technical innovation is allowing richer constraint sets in the iterative rounding and taking advantage of the structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios 6.994 + ϵ and 6.387 + ϵ for k-median with outliers and knapsack median, respectively. These improve on the best-known approximation ratio 7.081 + ϵ for both problems <cit.>.



There are no comments yet.


page 1

page 2

page 3

page 4


Constant Approximation for k-Median and k-Means with Outliers via Iterative Rounding

In this paper, we present a novel iterative rounding framework for many ...

Deterministic metric 1-median selection with very few queries

Given an n-point metric space (M,d), metric 1-median asks for a point p∈...

Approximation Algorithms for Probabilistic Graphs

We study the k-median and k-center problems in probabilistic graphs. We ...

Outliers Detection Is Not So Hard: Approximation Algorithms for Robust Clustering Problems Using Local Search Techniques

In this paper, we consider two types of robust models of the k-median/k-...

Distributed k-Clustering for Data with Heavy Noise

In this paper, we consider the k-center/median/means clustering with out...

The Flag Median and FlagIRLS

Finding prototypes (e.g., mean and median) for a dataset is central to a...

On the Relation Between the Common Labelling and the Median Graph

In structural pattern recognition, given a set of graphs, the computatio...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.