An Improved Approximation Algorithm for the Maximum Weight Independent Set Problem in d-Claw Free Graphs

06/07/2021
by   Meike Neuwohner, et al.
0

In this paper, we consider the task of computing an independent set of maximum weight in a given d-claw free graph G=(V,E) equipped with a positive weight function w:V→ℝ^+. In doing so, d≥ 2 is considered a constant. The previously best known approximation algorithm for this problem is the local improvement algorithm SquareImp proposed by Berman. It achieves a performance ratio of d/2+ϵ in time 𝒪(|V(G)|^d+1·(|V(G)|+|E(G)|)· (d-1)^2·(d/2ϵ+1)^2) for any ϵ>0, which has remained unimproved for the last twenty years. By considering a broader class of local improvements, we obtain an approximation ratio of d/2-1/63,700,992+ϵ for any ϵ>0 at the cost of an additional factor of 𝒪(|V(G)|^(d-1)^2) in the running time. In particular, our result implies a polynomial time d/2-approximation algorithm. Furthermore, the well-known reduction from the weighted k-Set Packing Problem to the Maximum Weight Independent Set Problem in k+1-claw free graphs provides a k+1/2-1/63,700,992+ϵ-approximation algorithm for the weighted k-Set Packing Problem for any ϵ>0. This improves on the previously best known approximation guarantee of k+1/2+ϵ originating from the result of Berman.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 3

06/07/2021

The Limits of Local Search for the Maximum Weight Independent Set Problem in d-Claw Free Graphs

We consider the Maximum Weight Independent Set Problem (MWIS) in d-claw ...
05/21/2020

New Approximation Algorithms for Maximum Asymmetric Traveling Salesman and Shortest Superstring

In the maximum asymmetric traveling salesman problem (Max ATSP) we are g...
12/28/2020

A 3/4 Differential Approximation Algorithm for Traveling Salesman Problem

In this paper, we consider differential approximability of the traveling...
12/17/2019

Approximating MIS over equilateral B_1-VPG graphs

We present an approximation algorithm for the maximum independent set (M...
12/06/2021

Faster Cut Sparsification of Weighted Graphs

A cut sparsifier is a reweighted subgraph that maintains the weights of ...
12/14/2020

Concerning Iterative Graph Normalization and Maximum Weight Independent Sets

We consider a very simple dynamical system on weighted graphs which we c...
10/06/2021

An Improved Approximation for Maximum k-Dependent Set on Bipartite Graphs

We present a (1+k/k+2)-approximation algorithm for the Maximum k-depende...
This week in AI

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