On Competitive Permutations for Set Cover by Intervals

10/27/2021
by   Sariel Har-Peled, et al.
0

We revisit the problem of computing an optimal partial cover of points by intervals. We show that the greedy algorithm computes a permutation Π = π_1, π_2,… of the intervals that is 3/4-competitive for any prefix of k intervals. That is, for any k, the intervals π_1 ∪⋯∪π_k covers at least 3/4-fraction of the points covered by the optimal solution using k intervals. We also provide an approximation algorithm that, in O(n + m/ε) time, computes a cover by (1+ε)k intervals that is as good as the optimal solution using k intervals, where n is the number of input points, and m is the number of intervals (we assume here the input is presorted). Finally, we show a counter example illustrating that the optimal solutions for set cover do not have the diminishing return property – that is, the marginal benefit from using more sets is not monotonically decreasing. Fortunately, the diminishing returns does hold for intervals.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/18/2020

Combinatorics of intervals in the plane I: trapezoids

We study arrangements of intervals in ℝ^2 for which many pairs form trap...
research
11/20/2018

Approximation Algorithm for the Partial Set Multi-Cover Problem

Partial set cover problem and set multi-cover problem are two generaliza...
research
04/09/2018

Fully Dynamic Set Cover -- Improved and Simple

In this paper, we revisit the unweighted set cover problem in the fully ...
research
09/01/2021

Moving intervals for packing and covering

We study several problems on geometric packing and covering with movemen...
research
09/22/2021

Estimating the number of serial killers that were never caught

Many serial killers commit tens of murders. At the same time inter-murde...
research
06/17/2018

Cover Song Synthesis by Analogy

In this work, we pose and address the following "cover song analogies" p...
research
11/24/2021

Characterization of canonical systems with six types of coins for the change-making problem

This paper analyzes a necessary and sufficient condition for the change-...

Please sign up or login with your details

Forgot password? Click here to reset