Improved Bounds for Metric Capacitated Covering Problems

by   Sayan Bandyapadhyay, et al.

In the Metric Capacitated Covering (MCC) problem, given a set of balls ℬ in a metric space P with metric d and a capacity parameter U, the goal is to find a minimum sized subset ℬ'⊆ℬ and an assignment of the points in P to the balls in ℬ' such that each point is assigned to a ball that contains it and each ball is assigned with at most U points. MCC achieves an O(log |P|)-approximation using a greedy algorithm. On the other hand, it is hard to approximate within a factor of o(log |P|) even with β < 3 factor expansion of the balls. Bandyapadhyay et al. [SoCG 2018, DCG 2019] showed that one can obtain an O(1)-approximation for the problem with 6.47 factor expansion of the balls. An open question left by their work is to reduce the gap between the lower bound 3 and the upper bound 6.47. In this current work, we show that it is possible to obtain an O(1)-approximation with only 4.24 factor expansion of the balls. We also show a similar upper bound of 5 for a more generalized version of MCC for which the best previously known bound was 9.


page 1

page 2

page 3

page 4


Approximate Covering with Lower and Upper Bounds via LP Rounding

In this paper, we study the lower- and upper-bounded covering (LUC) prob...

A better lower bound for Lower-Left Anchored Rectangle Packing

Given any set of points S in the unit square that contains the origin, d...

Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

Monotone submodular maximization with a knapsack constraint is NP-hard. ...

A Nearly Tight Analysis of Greedy k-means++

The famous k-means++ algorithm of Arthur and Vassilvitskii [SODA 2007] i...

On the Approximation Ratio of the k-Opt and Lin-Kernighan Algorithm for Metric TSP

The k-Opt and Lin-Kernighan algorithm are two of the most important loca...

Agnostic Learnability of Halfspaces via Logistic Loss

We investigate approximation guarantees provided by logistic regression ...

Ordinary differential equations (ODE): metric entropy and nonasymptotic theory for noisy function fitting

This paper establishes novel results on the metric entropy of ODE soluti...

Please sign up or login with your details

Forgot password? Click here to reset