On a reduction of the weighted induced bipartite subgraph problem to the weighted independent set problem

TL;DR

This paper demonstrates a reduction from the weighted induced bipartite subgraph problem to the weighted independent set problem, enabling the application of existing algorithms for WISP to solve WIBSP more effectively.

Contribution

The paper introduces a reduction from WIBSP to WISP, increasing the number of nodes and degree by a small factor, facilitating the use of known algorithms for WISP to address WIBSP.

Findings

Reduction increases node count by a factor of two

Degree increases by one due to reduction

Enables application of WISP algorithms to WIBSP

Abstract

We study the weighted induced bipartite subgraph problem (WIBSP). The goal of WIBSP is, given a graph and nonnegative weights for the nodes, to find a set W of nodes with the maximum total weight such that a subgraph induced by W is bipartite. WIBSP is also referred as to the graph bipartization problem or the odd cycle transversal problem. In this paper, we show that WIBSP can be reduced to the weighted independent set problem (WISP) where the number of nodes becomes twice and the maximum degree increase by 1. WISP is a well-studied combinatorial optimization problem. Thus, by using the reduction and results about WISP, we can obtain nontrivial approximation and exact algorithms for WIBSP.