Approximation by Lexicographically Maximal Solutions in Matching and Matroid Intersection Problems

07/21/2021
by   Kristóf Bérczi, et al.
0

We study how good a lexicographically maximal solution is in the weighted matching and matroid intersection problems. A solution is lexicographically maximal if it takes as many heaviest elements as possible, and subject to this, it takes as many second heaviest elements as possible, and so on. If the distinct weight values are sufficiently dispersed, e.g., the minimum ratio of two distinct weight values is at least the ground set size, then the lexicographical maximality and the usual weighted optimality are equivalent. We show that the threshold of the ratio for this equivalence to hold is exactly 2. Furthermore, we prove that if the ratio is less than 2, say α, then a lexicographically maximal solution achieves (α/2)-approximation, and this bound is tight.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/26/2021

RLWE/PLWE equivalence for the maximal totally real subextension of the 2^rpq-th cyclotomic field

We prove the RLWE/PLWE equivalence for the maximal totally real subexten...
research
04/21/2022

The average size of maximal matchings in graphs

We investigate the ratio I(G) of the average size of a maximal matching ...
research
11/20/2018

Tight Approximation Ratio for Minimum Maximal Matching

We study a combinatorial problem called Minimum Maximal Matching, where ...
research
07/26/2019

On maximal isolation sets in the uniform intersection matrix

Let A_k,t be the matrix that represents the adjacency matrix of the inte...
research
04/05/2023

Improved Analysis of two Algorithms for Min-Weighted Sum Bin Packing

We study the Min-Weighted Sum Bin Packing problem, a variant of the clas...
research
02/12/2015

An Efficient Metric of Automatic Weight Generation for Properties in Instance Matching Technique

The proliferation of heterogeneous data sources of semantic knowledge ba...
research
12/28/2021

Sharp Elements and Apartness in Domains

Working constructively, we study continuous directed complete posets (dc...

Please sign up or login with your details

Forgot password? Click here to reset